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One Round DKG (#589)

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* Upstream GBP, divisor, circuit abstraction, and EC gadgets from FCMP++

* Initial eVRF implementation

Not quite done yet. It needs to communicate the resulting points and proofs to
extract them from the Pedersen Commitments in order to return those, and then
be tested.

* Add the openings of the PCs to the eVRF as necessary

* Add implementation of secq256k1

* Make DKG Encryption a bit more flexible

No longer requires the use of an EncryptionKeyMessage, and allows pre-defined
keys for encryption.

* Make NUM_BITS an argument for the field macro

* Have the eVRF take a Zeroizing private key

* Initial eVRF-based DKG

* Add embedwards25519 curve

* Inline the eVRF into the DKG library

Due to how we're handling share encryption, we'd either need two circuits or to
dedicate this circuit to the DKG. The latter makes sense at this time.

* Add documentation to the eVRF-based DKG

* Add paragraph claiming robustness

* Update to the new eVRF proof

* Finish routing the eVRF functionality

Still needs errors and serialization, along with a few other TODOs.

* Add initial eVRF DKG test

* Improve eVRF DKG

Updates how we calculcate verification shares, improves performance when
extracting multiple sets of keys, and adds more to the test for it.

* Start using a proper error for the eVRF DKG

* Resolve various TODOs

Supports recovering multiple key shares from the eVRF DKG.

Inlines two loops to save 2**16 iterations.

Adds support for creating a constant time representation of scalars < NUM_BITS.

* Ban zero ECDH keys, document non-zero requirements

* Implement eVRF traits, all the way up to the DKG, for secp256k1/ed25519

* Add Ristretto eVRF trait impls

* Support participating multiple times in the eVRF DKG

* Only participate once per key, not once per key share

* Rewrite processor key-gen around the eVRF DKG

Still a WIP.

* Finish routing the new key gen in the processor

Doesn't touch the tests, coordinator, nor Substrate yet.
`cargo +nightly fmt && cargo +nightly-2024-07-01 clippy --all-features -p serai-processor`
does pass.

* Deduplicate and better document in processor key_gen

* Update serai-processor tests to the new key gen

* Correct amount of yx coefficients, get processor key gen test to pass

* Add embedded elliptic curve keys to Substrate

* Update processor key gen tests to the eVRF DKG

* Have set_keys take signature_participants, not removed_participants

Now no one is removed from the DKG. Only `t` people publish the key however.

Uses a BitVec for an efficient encoding of the participants.

* Update the coordinator binary for the new DKG

This does not yet update any tests.

* Add sensible Debug to key_gen::[Processor, Coordinator]Message

* Have the DKG explicitly declare how to interpolate its shares

Removes the hack for MuSig where we multiply keys by the inverse of their
lagrange interpolation factor.

* Replace Interpolation::None with Interpolation::Constant

Allows the MuSig DKG to keep the secret share as the original private key,
enabling deriving FROST nonces consistently regardless of the MuSig context.

* Get coordinator tests to pass

* Update spec to the new DKG

* Get clippy to pass across the repo

* cargo machete

* Add an extra sleep to ensure expected ordering of `Participation`s

* Update orchestration

* Remove bad panic in coordinator

It expected ConfirmationShare to be n-of-n, not t-of-n.

* Improve documentation on  functions

* Update TX size limit

We now no longer have to support the ridiculous case of having 49 DKG
participations within a 101-of-150 DKG. It does remain quite high due to
needing to _sign_ so many times. It'd may be optimal for parties with multiple
key shares to independently send their preprocesses/shares (despite the
overhead that'll cause with signatures and the transaction structure).

* Correct error in the Processor spec document

* Update a few comments in the validator-sets pallet

* Send/Recv Participation one at a time

Sending all, then attempting to receive all in an expected order, wasn't working
even with notable delays between sending messages. This points to the mempool
not working as expected...

* Correct ThresholdKeys serialization in modular-frost test

* Updating existing TX size limit test for the new DKG parameters

* Increase time allowed for the DKG on the GH CI

* Correct construction of signature_participants in serai-client tests

Fault identified by akil.

* Further contextualize DkgConfirmer by ValidatorSet

Caught by a safety check we wouldn't reuse preprocesses across messages. That
raises the question of we were prior reusing preprocesses (reusing keys)?
Except that'd have caused a variety of signing failures (suggesting we had some
staggered timing avoiding it in practice but yes, this was possible in theory).

* Add necessary calls to set_embedded_elliptic_curve_key in coordinator set rotation tests

* Correct shimmed setting of a secq256k1 key

* cargo fmt

* Don't use `[0; 32]` for the embedded keys in the coordinator rotation test

The key_gen function expects the random values already decided.

* Big-endian secq256k1 scalars

Also restores the prior, safer, Encryption::register function.
This commit is contained in:
Luke Parker
2024-08-16 11:26:07 -07:00
parent 669b2fef72
commit e4e4245ee3
121 changed files with 10388 additions and 2480 deletions
Download Patch File Download Diff File Expand all files Collapse all files

34
crypto/dkg/Cargo.toml
View File

@@ -36,9 +36,26 @@ multiexp = { path = "../multiexp", version = "0.4", default-features = false }
schnorr = { package = "schnorr-signatures", path = "../schnorr", version = "^0.5.1", default-features = false }
dleq = { path = "../dleq", version = "^0.4.1", default-features = false }
# eVRF DKG dependencies
subtle = { version = "2", default-features = false, features = ["std"], optional = true }
generic-array = { version = "1", default-features = false, features = ["alloc"], optional = true }
blake2 = { version = "0.10", default-features = false, features = ["std"], optional = true }
rand_chacha = { version = "0.3", default-features = false, features = ["std"], optional = true }
generalized-bulletproofs = { path = "../evrf/generalized-bulletproofs", default-features = false, optional = true }
ec-divisors = { path = "../evrf/divisors", default-features = false, optional = true }
generalized-bulletproofs-circuit-abstraction = { path = "../evrf/circuit-abstraction", optional = true }
generalized-bulletproofs-ec-gadgets = { path = "../evrf/ec-gadgets", optional = true }
secq256k1 = { path = "../evrf/secq256k1", optional = true }
embedwards25519 = { path = "../evrf/embedwards25519", optional = true }
[dev-dependencies]
rand_core = { version = "0.6", default-features = false, features = ["getrandom"] }
rand = { version = "0.8", default-features = false, features = ["std"] }
ciphersuite = { path = "../ciphersuite", default-features = false, features = ["ristretto"] }
generalized-bulletproofs = { path = "../evrf/generalized-bulletproofs", features = ["tests"] }
ec-divisors = { path = "../evrf/divisors", features = ["pasta"] }
pasta_curves = "0.5"
[features]
std = [
@@ -62,5 +79,22 @@ std = [
"dleq/serialize"
]
borsh = ["dep:borsh"]
evrf = [
"std",
"dep:subtle",
"dep:generic-array",
"dep:blake2",
"dep:rand_chacha",
"dep:generalized-bulletproofs",
"dep:ec-divisors",
"dep:generalized-bulletproofs-circuit-abstraction",
"dep:generalized-bulletproofs-ec-gadgets",
]
evrf-secp256k1 = ["evrf", "ciphersuite/secp256k1", "secq256k1"]
evrf-ed25519 = ["evrf", "ciphersuite/ed25519", "embedwards25519"]
evrf-ristretto = ["evrf", "ciphersuite/ristretto", "embedwards25519"]
tests = ["rand_core/getrandom"]
default = ["std"]

214
crypto/dkg/src/encryption.rs
View File

@@ -98,11 +98,11 @@ fn ecdh<C: Ciphersuite>(private: &Zeroizing<C::F>, public: C::G) -> Zeroizing<C:
// Each ecdh must be distinct. Reuse of an ecdh for multiple ciphers will cause the messages to be
// leaked.
fn cipher<C: Ciphersuite>(context: &str, ecdh: &Zeroizing<C::G>) -> ChaCha20 {
fn cipher<C: Ciphersuite>(context: [u8; 32], ecdh: &Zeroizing<C::G>) -> ChaCha20 {
// Ideally, we'd box this transcript with ZAlloc, yet that's only possible on nightly
// TODO: https://github.com/serai-dex/serai/issues/151
let mut transcript = RecommendedTranscript::new(b"DKG Encryption v0.2");
transcript.append_message(b"context", context.as_bytes());
transcript.append_message(b"context", context);
transcript.domain_separate(b"encryption_key");
@@ -134,7 +134,7 @@ fn cipher<C: Ciphersuite>(context: &str, ecdh: &Zeroizing<C::G>) -> ChaCha20 {
fn encrypt<R: RngCore + CryptoRng, C: Ciphersuite, E: Encryptable>(
rng: &mut R,
context: &str,
context: [u8; 32],
from: Participant,
to: C::G,
mut msg: Zeroizing<E>,
@@ -197,7 +197,7 @@ impl<C: Ciphersuite, E: Encryptable> EncryptedMessage<C, E> {
pub(crate) fn invalidate_msg<R: RngCore + CryptoRng>(
&mut self,
rng: &mut R,
context: &str,
context: [u8; 32],
from: Participant,
) {
// Invalidate the message by specifying a new key/Schnorr PoP
@@ -219,7 +219,7 @@ impl<C: Ciphersuite, E: Encryptable> EncryptedMessage<C, E> {
pub(crate) fn invalidate_share_serialization<R: RngCore + CryptoRng>(
&mut self,
rng: &mut R,
context: &str,
context: [u8; 32],
from: Participant,
to: C::G,
) {
@@ -243,7 +243,7 @@ impl<C: Ciphersuite, E: Encryptable> EncryptedMessage<C, E> {
pub(crate) fn invalidate_share_value<R: RngCore + CryptoRng>(
&mut self,
rng: &mut R,
context: &str,
context: [u8; 32],
from: Participant,
to: C::G,
) {
@@ -300,14 +300,14 @@ impl<C: Ciphersuite> EncryptionKeyProof<C> {
// This still doesn't mean the DKG offers an authenticated channel. The per-message keys have no
// root of trust other than their existence in the assumed-to-exist external authenticated channel.
fn pop_challenge<C: Ciphersuite>(
context: &str,
context: [u8; 32],
nonce: C::G,
key: C::G,
sender: Participant,
msg: &[u8],
) -> C::F {
let mut transcript = RecommendedTranscript::new(b"DKG Encryption Key Proof of Possession v0.2");
transcript.append_message(b"context", context.as_bytes());
transcript.append_message(b"context", context);
transcript.domain_separate(b"proof_of_possession");
@@ -323,9 +323,9 @@ fn pop_challenge<C: Ciphersuite>(
C::hash_to_F(b"DKG-encryption-proof_of_possession", &transcript.challenge(b"schnorr"))
}
fn encryption_key_transcript(context: &str) -> RecommendedTranscript {
fn encryption_key_transcript(context: [u8; 32]) -> RecommendedTranscript {
let mut transcript = RecommendedTranscript::new(b"DKG Encryption Key Correctness Proof v0.2");
transcript.append_message(b"context", context.as_bytes());
transcript.append_message(b"context", context);
transcript
}
@@ -337,58 +337,17 @@ pub(crate) enum DecryptionError {
InvalidProof,
}
// A simple box for managing encryption.
#[derive(Clone)]
pub(crate) struct Encryption<C: Ciphersuite> {
context: String,
i: Option<Participant>,
enc_key: Zeroizing<C::F>,
enc_pub_key: C::G,
// A simple box for managing decryption.
#[derive(Clone, Debug)]
pub(crate) struct Decryption<C: Ciphersuite> {
context: [u8; 32],
enc_keys: HashMap<Participant, C::G>,
}
impl<C: Ciphersuite> fmt::Debug for Encryption<C> {
fn fmt(&self, fmt: &mut fmt::Formatter<'_>) -> fmt::Result {
fmt
.debug_struct("Encryption")
.field("context", &self.context)
.field("i", &self.i)
.field("enc_pub_key", &self.enc_pub_key)
.field("enc_keys", &self.enc_keys)
.finish_non_exhaustive()
impl<C: Ciphersuite> Decryption<C> {
pub(crate) fn new(context: [u8; 32]) -> Self {
Self { context, enc_keys: HashMap::new() }
}
}
impl<C: Ciphersuite> Zeroize for Encryption<C> {
fn zeroize(&mut self) {
self.enc_key.zeroize();
self.enc_pub_key.zeroize();
for (_, mut value) in self.enc_keys.drain() {
value.zeroize();
}
}
}
impl<C: Ciphersuite> Encryption<C> {
pub(crate) fn new<R: RngCore + CryptoRng>(
context: String,
i: Option<Participant>,
rng: &mut R,
) -> Self {
let enc_key = Zeroizing::new(C::random_nonzero_F(rng));
Self {
context,
i,
enc_pub_key: C::generator() * enc_key.deref(),
enc_key,
enc_keys: HashMap::new(),
}
}
pub(crate) fn registration<M: Message>(&self, msg: M) -> EncryptionKeyMessage<C, M> {
EncryptionKeyMessage { msg, enc_key: self.enc_pub_key }
}
pub(crate) fn register<M: Message>(
&mut self,
participant: Participant,
@@ -402,13 +361,109 @@ impl<C: Ciphersuite> Encryption<C> {
msg.msg
}
// Given a message, and the intended decryptor, and a proof for its key, decrypt the message.
// Returns None if the key was wrong.
pub(crate) fn decrypt_with_proof<E: Encryptable>(
&self,
from: Participant,
decryptor: Participant,
mut msg: EncryptedMessage<C, E>,
// There's no encryption key proof if the accusation is of an invalid signature
proof: Option<EncryptionKeyProof<C>>,
) -> Result<Zeroizing<E>, DecryptionError> {
if !msg.pop.verify(
msg.key,
pop_challenge::<C>(self.context, msg.pop.R, msg.key, from, msg.msg.deref().as_ref()),
) {
Err(DecryptionError::InvalidSignature)?;
}
if let Some(proof) = proof {
// Verify this is the decryption key for this message
proof
.dleq
.verify(
&mut encryption_key_transcript(self.context),
&[C::generator(), msg.key],
&[self.enc_keys[&decryptor], *proof.key],
)
.map_err(|_| DecryptionError::InvalidProof)?;
cipher::<C>(self.context, &proof.key).apply_keystream(msg.msg.as_mut().as_mut());
Ok(msg.msg)
} else {
Err(DecryptionError::InvalidProof)
}
}
}
// A simple box for managing encryption.
#[derive(Clone)]
pub(crate) struct Encryption<C: Ciphersuite> {
context: [u8; 32],
i: Participant,
enc_key: Zeroizing<C::F>,
enc_pub_key: C::G,
decryption: Decryption<C>,
}
impl<C: Ciphersuite> fmt::Debug for Encryption<C> {
fn fmt(&self, fmt: &mut fmt::Formatter<'_>) -> fmt::Result {
fmt
.debug_struct("Encryption")
.field("context", &self.context)
.field("i", &self.i)
.field("enc_pub_key", &self.enc_pub_key)
.field("decryption", &self.decryption)
.finish_non_exhaustive()
}
}
impl<C: Ciphersuite> Zeroize for Encryption<C> {
fn zeroize(&mut self) {
self.enc_key.zeroize();
self.enc_pub_key.zeroize();
for (_, mut value) in self.decryption.enc_keys.drain() {
value.zeroize();
}
}
}
impl<C: Ciphersuite> Encryption<C> {
pub(crate) fn new<R: RngCore + CryptoRng>(
context: [u8; 32],
i: Participant,
rng: &mut R,
) -> Self {
let enc_key = Zeroizing::new(C::random_nonzero_F(rng));
Self {
context,
i,
enc_pub_key: C::generator() * enc_key.deref(),
enc_key,
decryption: Decryption::new(context),
}
}
pub(crate) fn registration<M: Message>(&self, msg: M) -> EncryptionKeyMessage<C, M> {
EncryptionKeyMessage { msg, enc_key: self.enc_pub_key }
}
pub(crate) fn register<M: Message>(
&mut self,
participant: Participant,
msg: EncryptionKeyMessage<C, M>,
) -> M {
self.decryption.register(participant, msg)
}
pub(crate) fn encrypt<R: RngCore + CryptoRng, E: Encryptable>(
&self,
rng: &mut R,
participant: Participant,
msg: Zeroizing<E>,
) -> EncryptedMessage<C, E> {
encrypt(rng, &self.context, self.i.unwrap(), self.enc_keys[&participant], msg)
encrypt(rng, self.context, self.i, self.decryption.enc_keys[&participant], msg)
}
pub(crate) fn decrypt<R: RngCore + CryptoRng, I: Copy + Zeroize, E: Encryptable>(
@@ -426,18 +481,18 @@ impl<C: Ciphersuite> Encryption<C> {
batch,
batch_id,
msg.key,
pop_challenge::<C>(&self.context, msg.pop.R, msg.key, from, msg.msg.deref().as_ref()),
pop_challenge::<C>(self.context, msg.pop.R, msg.key, from, msg.msg.deref().as_ref()),
);
let key = ecdh::<C>(&self.enc_key, msg.key);
cipher::<C>(&self.context, &key).apply_keystream(msg.msg.as_mut().as_mut());
cipher::<C>(self.context, &key).apply_keystream(msg.msg.as_mut().as_mut());
(
msg.msg,
EncryptionKeyProof {
key,
dleq: DLEqProof::prove(
rng,
&mut encryption_key_transcript(&self.context),
&mut encryption_key_transcript(self.context),
&[C::generator(), msg.key],
&self.enc_key,
),
@@ -445,38 +500,7 @@ impl<C: Ciphersuite> Encryption<C> {
)
}
// Given a message, and the intended decryptor, and a proof for its key, decrypt the message.
// Returns None if the key was wrong.
pub(crate) fn decrypt_with_proof<E: Encryptable>(
&self,
from: Participant,
decryptor: Participant,
mut msg: EncryptedMessage<C, E>,
// There's no encryption key proof if the accusation is of an invalid signature
proof: Option<EncryptionKeyProof<C>>,
) -> Result<Zeroizing<E>, DecryptionError> {
if !msg.pop.verify(
msg.key,
pop_challenge::<C>(&self.context, msg.pop.R, msg.key, from, msg.msg.deref().as_ref()),
) {
Err(DecryptionError::InvalidSignature)?;
}
if let Some(proof) = proof {
// Verify this is the decryption key for this message
proof
.dleq
.verify(
&mut encryption_key_transcript(&self.context),
&[C::generator(), msg.key],
&[self.enc_keys[&decryptor], *proof.key],
)
.map_err(|_| DecryptionError::InvalidProof)?;
cipher::<C>(&self.context, &proof.key).apply_keystream(msg.msg.as_mut().as_mut());
Ok(msg.msg)
} else {
Err(DecryptionError::InvalidProof)
}
pub(crate) fn into_decryption(self) -> Decryption<C> {
self.decryption
}
}

584
crypto/dkg/src/evrf/mod.rs Normal file
View File

@@ -0,0 +1,584 @@
/*
We implement a DKG using an eVRF, as detailed in the eVRF paper. For the eVRF itself, we do not
use a Paillier-based construction, nor the detailed construction premised on a Bulletproof.
For reference, the detailed construction premised on a Bulletproof involves two curves, notated
here as `C` and `E`, where the scalar field of `C` is the field of `E`. Accordingly, Bulletproofs
over `C` can efficiently perform group operations of points of curve `E`. Each participant has a
private point (`P_i`) on curve `E` committed to over curve `C`. The eVRF selects a pair of
scalars `a, b`, where the participant proves in-Bulletproof the points `A_i, B_i` are
`a * P_i, b * P_i`. The eVRF proceeds to commit to `A_i.x + B_i.x` in a Pedersen Commitment.
Our eVRF uses
[Generalized Bulletproofs](
https://repo.getmonero.org/monero-project/ccs-proposals
/uploads/a9baa50c38c6312efc0fea5c6a188bb9/gbp.pdf
).
This allows us much larger witnesses without growing the reference string, and enables us to
efficiently sample challenges off in-circuit variables (via placing the variables in a vector
commitment, then challenging from a transcript of the commitments). We proceed to use
[elliptic curve divisors](
https://repo.getmonero.org/-/project/54/
uploads/eb1bf5b4d4855a3480c38abf895bd8e8/Veridise_Divisor_Proofs.pdf
)
(which require the ability to sample a challenge off in-circuit variables) to prove discrete
logarithms efficiently.
This is done via having a private scalar (`p_i`) on curve `E`, not a private point, and
publishing the public key for it (`P_i = p_i * G`, where `G` is a generator of `E`). The eVRF
samples two points with unknown discrete logarithms `A, B`, and the circuit proves a Pedersen
Commitment commits to `(p_i * A).x + (p_i * B).x`.
With the eVRF established, we now detail our other novel aspect. The eVRF paper expects secret
shares to be sent to the other parties yet does not detail a precise way to do so. If we
encrypted the secret shares with some stream cipher, each recipient would have to attest validity
or accuse the sender of impropriety. We want an encryption scheme where anyone can verify the
secret shares were encrypted properly, without additional info, efficiently.
Please note from the published commitments, it's possible to calculcate a commitment to the
secret share each party should receive (`V_i`).
We have the sender sample two scalars per recipient, denoted `x_i, y_i` (where `i` is the
recipient index). They perform the eVRF to prove a Pedersen Commitment commits to
`z_i = (x_i * P_i).x + (y_i * P_i).x` and `x_i, y_i` are the discrete logarithms of `X_i, Y_i`
over `G`. They then publish the encrypted share `s_i + z_i` and `X_i, Y_i`.
The recipient is able to decrypt the share via calculating
`s_i - ((p_i * X_i).x + (p_i * Y_i).x)`.
To verify the secret share, we have the `F` terms of the Pedersen Commitments revealed (where
`F, H` are generators of `C`, `F` is used for binding and `H` for blinding). This already needs
to be done for the eVRF outputs used within the DKG, in order to obtain thecommitments to the
coefficients. When we have the commitment `Z_i = ((p_i * A).x + (p_i * B).x) * F`, we simply
check `s_i * F = Z_i + V_i`.
In order to open the Pedersen Commitments to their `F` terms, we transcript the commitments and
the claimed openings, then assign random weights to each pair of `(commitment, opening). The
prover proves knowledge of the discrete logarithm of the sum weighted commitments, minus the sum
sum weighted openings, over `H`.
The benefit to this construction is that given an broadcast channel which is reliable and
ordered, only `t` messages must be broadcast from honest parties in order to create a `t`-of-`n`
multisig. If the encrypted secret shares were not verifiable, one would need at least `t + n`
messages to ensure every participant has a correct dealing and can participate in future
reconstructions of the secret. This would also require all `n` parties be online, whereas this is
robust to threshold `t`.
*/
use core::ops::Deref;
use std::{
io::{self, Read, Write},
collections::{HashSet, HashMap},
};
use rand_core::{RngCore, CryptoRng};
use zeroize::{Zeroize, Zeroizing};
use blake2::{Digest, Blake2s256};
use ciphersuite::{
group::{
ff::{Field, PrimeField},
Group, GroupEncoding,
},
Ciphersuite,
};
use multiexp::multiexp_vartime;
use generalized_bulletproofs::arithmetic_circuit_proof::*;
use ec_divisors::DivisorCurve;
use crate::{Participant, ThresholdParams, Interpolation, ThresholdCore, ThresholdKeys};
pub(crate) mod proof;
use proof::*;
pub use proof::{EvrfCurve, EvrfGenerators};
/// Participation in the DKG.
///
/// `Participation` is meant to be broadcast to all other participants over an authenticated,
/// reliable broadcast channel.
#[derive(Clone, PartialEq, Eq, Debug)]
pub struct Participation<C: Ciphersuite> {
proof: Vec<u8>,
encrypted_secret_shares: HashMap<Participant, C::F>,
}
impl<C: Ciphersuite> Participation<C> {
pub fn read<R: Read>(reader: &mut R, n: u16) -> io::Result<Self> {
// TODO: Replace `len` with some calculcation deterministic to the params
let mut len = [0; 4];
reader.read_exact(&mut len)?;
let len = usize::try_from(u32::from_le_bytes(len)).expect("<32-bit platform?");
// Don't allocate a buffer for the claimed length
// Read chunks until we reach the claimed length
// This means if we were told to read GB, we must actually be sent GB before allocating as such
const CHUNK_SIZE: usize = 1024;
let mut proof = Vec::with_capacity(len.min(CHUNK_SIZE));
while proof.len() < len {
let next_chunk = (len - proof.len()).min(CHUNK_SIZE);
let old_proof_len = proof.len();
proof.resize(old_proof_len + next_chunk, 0);
reader.read_exact(&mut proof[old_proof_len ..])?;
}
let mut encrypted_secret_shares = HashMap::with_capacity(usize::from(n));
for i in (1 ..= n).map(Participant) {
encrypted_secret_shares.insert(i, C::read_F(reader)?);
}
Ok(Self { proof, encrypted_secret_shares })
}
pub fn write<W: Write>(&self, writer: &mut W) -> io::Result<()> {
writer.write_all(&u32::try_from(self.proof.len()).unwrap().to_le_bytes())?;
writer.write_all(&self.proof)?;
for i in (1 ..= u16::try_from(self.encrypted_secret_shares.len())
.expect("writing a Participation which has a n > u16::MAX"))
.map(Participant)
{
writer.write_all(self.encrypted_secret_shares[&i].to_repr().as_ref())?;
}
Ok(())
}
}
fn polynomial<F: PrimeField + Zeroize>(
coefficients: &[Zeroizing<F>],
l: Participant,
) -> Zeroizing<F> {
let l = F::from(u64::from(u16::from(l)));
// This should never be reached since Participant is explicitly non-zero
assert!(l != F::ZERO, "zero participant passed to polynomial");
let mut share = Zeroizing::new(F::ZERO);
for (idx, coefficient) in coefficients.iter().rev().enumerate() {
*share += coefficient.deref();
if idx != (coefficients.len() - 1) {
*share *= l;
}
}
share
}
#[allow(clippy::type_complexity)]
fn share_verification_statements<C: Ciphersuite>(
rng: &mut (impl RngCore + CryptoRng),
commitments: &[C::G],
n: u16,
encryption_commitments: &[C::G],
encrypted_secret_shares: &HashMap<Participant, C::F>,
) -> (C::F, Vec<(C::F, C::G)>) {
debug_assert_eq!(usize::from(n), encryption_commitments.len());
debug_assert_eq!(usize::from(n), encrypted_secret_shares.len());
let mut g_scalar = C::F::ZERO;
let mut pairs = Vec::with_capacity(commitments.len() + encryption_commitments.len());
for commitment in commitments {
pairs.push((C::F::ZERO, *commitment));
}
let mut weight;
for (i, enc_share) in encrypted_secret_shares {
let enc_commitment = encryption_commitments[usize::from(u16::from(*i)) - 1];
weight = C::F::random(&mut *rng);
// s_i F
g_scalar += weight * enc_share;
// - Z_i
let weight = -weight;
pairs.push((weight, enc_commitment));
// - V_i
{
let i = C::F::from(u64::from(u16::from(*i)));
// The first `commitments.len()` pairs are for the commitments
(0 .. commitments.len()).fold(weight, |exp, j| {
pairs[j].0 += exp;
exp * i
});
}
}
(g_scalar, pairs)
}
/// Errors from the eVRF DKG.
#[derive(Clone, PartialEq, Eq, Debug, thiserror::Error)]
pub enum EvrfError {
#[error("n, the amount of participants, exceeded a u16")]
TooManyParticipants,
#[error("the threshold t wasn't in range 1 <= t <= n")]
InvalidThreshold,
#[error("a public key was the identity point")]
PublicKeyWasIdentity,
#[error("participating in a DKG we aren't a participant in")]
NotAParticipant,
#[error("a participant with an unrecognized ID participated")]
NonExistentParticipant,
#[error("the passed in generators did not have enough generators for this DKG")]
NotEnoughGenerators,
}
/// The result of calling EvrfDkg::verify.
pub enum VerifyResult<C: EvrfCurve> {
Valid(EvrfDkg<C>),
Invalid(Vec<Participant>),
NotEnoughParticipants,
}
/// Struct to perform/verify the DKG with.
#[derive(Debug)]
pub struct EvrfDkg<C: EvrfCurve> {
t: u16,
n: u16,
evrf_public_keys: Vec<<C::EmbeddedCurve as Ciphersuite>::G>,
group_key: C::G,
verification_shares: HashMap<Participant, C::G>,
#[allow(clippy::type_complexity)]
encrypted_secret_shares:
HashMap<Participant, HashMap<Participant, ([<C::EmbeddedCurve as Ciphersuite>::G; 2], C::F)>>,
}
impl<C: EvrfCurve> EvrfDkg<C> {
// Form the initial transcript for the proofs.
fn initial_transcript(
invocation: [u8; 32],
evrf_public_keys: &[<C::EmbeddedCurve as Ciphersuite>::G],
t: u16,
) -> [u8; 32] {
let mut transcript = Blake2s256::new();
transcript.update(invocation);
for key in evrf_public_keys {
transcript.update(key.to_bytes().as_ref());
}
transcript.update(t.to_le_bytes());
transcript.finalize().into()
}
/// Participate in performing the DKG for the specified parameters.
///
/// The context MUST be unique across invocations. Reuse of context will lead to sharing
/// prior-shared secrets.
///
/// Public keys are not allowed to be the identity point. This will error if any are.
pub fn participate(
rng: &mut (impl RngCore + CryptoRng),
generators: &EvrfGenerators<C>,
context: [u8; 32],
t: u16,
evrf_public_keys: &[<C::EmbeddedCurve as Ciphersuite>::G],
evrf_private_key: &Zeroizing<<C::EmbeddedCurve as Ciphersuite>::F>,
) -> Result<Participation<C>, EvrfError> {
let Ok(n) = u16::try_from(evrf_public_keys.len()) else { Err(EvrfError::TooManyParticipants)? };
if (t == 0) || (t > n) {
Err(EvrfError::InvalidThreshold)?;
}
if evrf_public_keys.iter().any(|key| bool::from(key.is_identity())) {
Err(EvrfError::PublicKeyWasIdentity)?;
};
let evrf_public_key = <C::EmbeddedCurve as Ciphersuite>::generator() * evrf_private_key.deref();
if !evrf_public_keys.iter().any(|key| *key == evrf_public_key) {
Err(EvrfError::NotAParticipant)?;
};
let transcript = Self::initial_transcript(context, evrf_public_keys, t);
// Further bind to the participant index so each index gets unique generators
// This allows reusing eVRF public keys as the prover
let mut per_proof_transcript = Blake2s256::new();
per_proof_transcript.update(transcript);
per_proof_transcript.update(evrf_public_key.to_bytes());
// The above transcript is expected to be binding to all arguments here
// The generators are constant to this ciphersuite's generator, and the parameters are
// transcripted
let EvrfProveResult { coefficients, encryption_masks, proof } = match Evrf::prove(
rng,
&generators.0,
per_proof_transcript.finalize().into(),
usize::from(t),
evrf_public_keys,
evrf_private_key,
) {
Ok(res) => res,
Err(AcError::NotEnoughGenerators) => Err(EvrfError::NotEnoughGenerators)?,
Err(
AcError::DifferingLrLengths |
AcError::InconsistentAmountOfConstraints |
AcError::ConstrainedNonExistentTerm |
AcError::ConstrainedNonExistentCommitment |
AcError::InconsistentWitness |
AcError::Ip(_) |
AcError::IncompleteProof,
) => {
panic!("failed to prove for the eVRF proof")
}
};
let mut encrypted_secret_shares = HashMap::with_capacity(usize::from(n));
for (l, encryption_mask) in (1 ..= n).map(Participant).zip(encryption_masks) {
let share = polynomial::<C::F>(&coefficients, l);
encrypted_secret_shares.insert(l, *share + *encryption_mask);
}
Ok(Participation { proof, encrypted_secret_shares })
}
/// Check if a batch of `Participation`s are valid.
///
/// If any `Participation` is invalid, the list of all invalid participants will be returned.
/// If all `Participation`s are valid and there's at least `t`, an instance of this struct
/// (usable to obtain a threshold share of generated key) is returned. If all are valid and
/// there's not at least `t`, `VerifyResult::NotEnoughParticipants` is returned.
///
/// This DKG is unbiased if all `n` people participate. This DKG is biased if only a threshold
/// participate.
pub fn verify(
rng: &mut (impl RngCore + CryptoRng),
generators: &EvrfGenerators<C>,
context: [u8; 32],
t: u16,
evrf_public_keys: &[<C::EmbeddedCurve as Ciphersuite>::G],
participations: &HashMap<Participant, Participation<C>>,
) -> Result<VerifyResult<C>, EvrfError> {
let Ok(n) = u16::try_from(evrf_public_keys.len()) else { Err(EvrfError::TooManyParticipants)? };
if (t == 0) || (t > n) {
Err(EvrfError::InvalidThreshold)?;
}
if evrf_public_keys.iter().any(|key| bool::from(key.is_identity())) {
Err(EvrfError::PublicKeyWasIdentity)?;
};
for i in participations.keys() {
if u16::from(*i) > n {
Err(EvrfError::NonExistentParticipant)?;
}
}
let mut valid = HashMap::with_capacity(participations.len());
let mut faulty = HashSet::new();
let transcript = Self::initial_transcript(context, evrf_public_keys, t);
let mut evrf_verifier = generators.0.batch_verifier();
for (i, participation) in participations {
let evrf_public_key = evrf_public_keys[usize::from(u16::from(*i)) - 1];
let mut per_proof_transcript = Blake2s256::new();
per_proof_transcript.update(transcript);
per_proof_transcript.update(evrf_public_key.to_bytes());
// Clone the verifier so if this proof is faulty, it doesn't corrupt the verifier
let mut verifier_clone = evrf_verifier.clone();
let Ok(data) = Evrf::<C>::verify(
rng,
&generators.0,
&mut verifier_clone,
per_proof_transcript.finalize().into(),
usize::from(t),
evrf_public_keys,
evrf_public_key,
&participation.proof,
) else {
faulty.insert(*i);
continue;
};
evrf_verifier = verifier_clone;
valid.insert(*i, (participation.encrypted_secret_shares.clone(), data));
}
debug_assert_eq!(valid.len() + faulty.len(), participations.len());
// Perform the batch verification of the eVRFs
if !generators.0.verify(evrf_verifier) {
// If the batch failed, verify them each individually
for (i, participation) in participations {
if faulty.contains(i) {
continue;
}
let mut evrf_verifier = generators.0.batch_verifier();
Evrf::<C>::verify(
rng,
&generators.0,
&mut evrf_verifier,
context,
usize::from(t),
evrf_public_keys,
evrf_public_keys[usize::from(u16::from(*i)) - 1],
&participation.proof,
)
.expect("evrf failed basic checks yet prover wasn't prior marked faulty");
if !generators.0.verify(evrf_verifier) {
valid.remove(i);
faulty.insert(*i);
}
}
}
debug_assert_eq!(valid.len() + faulty.len(), participations.len());
// Perform the batch verification of the shares
let mut sum_encrypted_secret_shares = HashMap::with_capacity(usize::from(n));
let mut sum_masks = HashMap::with_capacity(usize::from(n));
let mut all_encrypted_secret_shares = HashMap::with_capacity(usize::from(t));
{
let mut share_verification_statements_actual = HashMap::with_capacity(valid.len());
if !{
let mut g_scalar = C::F::ZERO;
let mut pairs = Vec::with_capacity(valid.len() * (usize::from(t) + evrf_public_keys.len()));
for (i, (encrypted_secret_shares, data)) in &valid {
let (this_g_scalar, mut these_pairs) = share_verification_statements::<C>(
&mut *rng,
&data.coefficients,
evrf_public_keys
.len()
.try_into()
.expect("n prior checked to be <= u16::MAX couldn't be converted to a u16"),
&data.encryption_commitments,
encrypted_secret_shares,
);
// Queue this into our batch
g_scalar += this_g_scalar;
pairs.extend(&these_pairs);
// Also push this g_scalar onto these_pairs so these_pairs can be verified individually
// upon error
these_pairs.push((this_g_scalar, generators.0.g()));
share_verification_statements_actual.insert(*i, these_pairs);
// Also format this data as we'd need it upon success
let mut formatted_encrypted_secret_shares = HashMap::with_capacity(usize::from(n));
for (j, enc_share) in encrypted_secret_shares {
/*
We calculcate verification shares as the sum of the encrypted scalars, minus their
masks. This only does one scalar multiplication, and `1+t` point additions (with
one negation), and is accordingly much cheaper than interpolating the commitments.
This is only possible because already interpolated the commitments to verify the
encrypted secret share.
*/
let sum_encrypted_secret_share =
sum_encrypted_secret_shares.get(j).copied().unwrap_or(C::F::ZERO);
let sum_mask = sum_masks.get(j).copied().unwrap_or(C::G::identity());
sum_encrypted_secret_shares.insert(*j, sum_encrypted_secret_share + enc_share);
let j_index = usize::from(u16::from(*j)) - 1;
sum_masks.insert(*j, sum_mask + data.encryption_commitments[j_index]);
formatted_encrypted_secret_shares.insert(*j, (data.ecdh_keys[j_index], *enc_share));
}
all_encrypted_secret_shares.insert(*i, formatted_encrypted_secret_shares);
}
pairs.push((g_scalar, generators.0.g()));
bool::from(multiexp_vartime(&pairs).is_identity())
} {
// If the batch failed, verify them each individually
for (i, pairs) in share_verification_statements_actual {
if !bool::from(multiexp_vartime(&pairs).is_identity()) {
valid.remove(&i);
faulty.insert(i);
}
}
}
}
debug_assert_eq!(valid.len() + faulty.len(), participations.len());
let mut faulty = faulty.into_iter().collect::<Vec<_>>();
if !faulty.is_empty() {
faulty.sort_unstable();
return Ok(VerifyResult::Invalid(faulty));
}
// We check at least t key shares of people have participated in contributing entropy
// Since the key shares of the participants exceed t, meaning if they're malicious they can
// reconstruct the key regardless, this is safe to the threshold
{
let mut participating_weight = 0;
let mut evrf_public_keys_mut = evrf_public_keys.to_vec();
for i in valid.keys() {
let evrf_public_key = evrf_public_keys[usize::from(u16::from(*i)) - 1];
// Remove this key from the Vec to prevent double-counting
/*
Double-counting would be a risk if multiple participants shared an eVRF public key and
participated. This code does still allow such participants (in order to let participants
be weighted), and any one of them participating will count as all participating. This is
fine as any one such participant will be able to decrypt the shares for themselves and
all other participants, so this is still a key generated by an amount of participants who
could simply reconstruct the key.
*/
let start_len = evrf_public_keys_mut.len();
evrf_public_keys_mut.retain(|key| *key != evrf_public_key);
let end_len = evrf_public_keys_mut.len();
let count = start_len - end_len;
participating_weight += count;
}
if participating_weight < usize::from(t) {
return Ok(VerifyResult::NotEnoughParticipants);
}
}
// If we now have >= t participations, calculate the group key and verification shares
// The group key is the sum of the zero coefficients
let group_key = valid.values().map(|(_, evrf_data)| evrf_data.coefficients[0]).sum::<C::G>();
// Calculate each user's verification share
let mut verification_shares = HashMap::with_capacity(usize::from(n));
for i in (1 ..= n).map(Participant) {
verification_shares
.insert(i, (C::generator() * sum_encrypted_secret_shares[&i]) - sum_masks[&i]);
}
Ok(VerifyResult::Valid(EvrfDkg {
t,
n,
evrf_public_keys: evrf_public_keys.to_vec(),
group_key,
verification_shares,
encrypted_secret_shares: all_encrypted_secret_shares,
}))
}
pub fn keys(
&self,
evrf_private_key: &Zeroizing<<C::EmbeddedCurve as Ciphersuite>::F>,
) -> Vec<ThresholdKeys<C>> {
let evrf_public_key = <C::EmbeddedCurve as Ciphersuite>::generator() * evrf_private_key.deref();
let mut is = Vec::with_capacity(1);
for (i, evrf_key) in self.evrf_public_keys.iter().enumerate() {
if *evrf_key == evrf_public_key {
let i = u16::try_from(i).expect("n <= u16::MAX yet i > u16::MAX?");
let i = Participant(1 + i);
is.push(i);
}
}
let mut res = Vec::with_capacity(is.len());
for i in is {
let mut secret_share = Zeroizing::new(C::F::ZERO);
for shares in self.encrypted_secret_shares.values() {
let (ecdh_keys, enc_share) = shares[&i];
let mut ecdh = Zeroizing::new(C::F::ZERO);
for point in ecdh_keys {
let (mut x, mut y) =
<C::EmbeddedCurve as Ciphersuite>::G::to_xy(point * evrf_private_key.deref()).unwrap();
*ecdh += x;
x.zeroize();
y.zeroize();
}
*secret_share += enc_share - ecdh.deref();
}
debug_assert_eq!(self.verification_shares[&i], C::generator() * secret_share.deref());
res.push(ThresholdKeys::from(ThresholdCore {
params: ThresholdParams::new(self.t, self.n, i).unwrap(),
interpolation: Interpolation::Lagrange,
secret_share,
group_key: self.group_key,
verification_shares: self.verification_shares.clone(),
}));
}
res
}
}

861
crypto/dkg/src/evrf/proof.rs Normal file
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@@ -0,0 +1,861 @@
use core::{marker::PhantomData, ops::Deref, fmt};
use subtle::*;
use zeroize::{Zeroize, Zeroizing};
use rand_core::{RngCore, CryptoRng, SeedableRng};
use rand_chacha::ChaCha20Rng;
use generic_array::{typenum::Unsigned, ArrayLength, GenericArray};
use blake2::{Digest, Blake2s256};
use ciphersuite::{
group::{
ff::{Field, PrimeField, PrimeFieldBits},
Group, GroupEncoding,
},
Ciphersuite,
};
use generalized_bulletproofs::{
*,
transcript::{Transcript as ProverTranscript, VerifierTranscript},
arithmetic_circuit_proof::*,
};
use generalized_bulletproofs_circuit_abstraction::*;
use ec_divisors::{DivisorCurve, new_divisor};
use generalized_bulletproofs_ec_gadgets::*;
/// A pair of curves to perform the eVRF with.
pub trait EvrfCurve: Ciphersuite {
type EmbeddedCurve: Ciphersuite<G: DivisorCurve<FieldElement = <Self as Ciphersuite>::F>>;
type EmbeddedCurveParameters: DiscreteLogParameters;
}
#[cfg(feature = "evrf-secp256k1")]
impl EvrfCurve for ciphersuite::Secp256k1 {
type EmbeddedCurve = secq256k1::Secq256k1;
type EmbeddedCurveParameters = secq256k1::Secq256k1;
}
#[cfg(feature = "evrf-ed25519")]
impl EvrfCurve for ciphersuite::Ed25519 {
type EmbeddedCurve = embedwards25519::Embedwards25519;
type EmbeddedCurveParameters = embedwards25519::Embedwards25519;
}
#[cfg(feature = "evrf-ristretto")]
impl EvrfCurve for ciphersuite::Ristretto {
type EmbeddedCurve = embedwards25519::Embedwards25519;
type EmbeddedCurveParameters = embedwards25519::Embedwards25519;
}
fn sample_point<C: Ciphersuite>(rng: &mut (impl RngCore + CryptoRng)) -> C::G {
let mut repr = <C::G as GroupEncoding>::Repr::default();
loop {
rng.fill_bytes(repr.as_mut());
if let Ok(point) = C::read_G(&mut repr.as_ref()) {
if bool::from(!point.is_identity()) {
return point;
}
}
}
}
/// Generators for eVRF proof.
#[derive(Clone, Debug)]
pub struct EvrfGenerators<C: EvrfCurve>(pub(crate) Generators<C>);
impl<C: EvrfCurve> EvrfGenerators<C> {
/// Create a new set of generators.
pub fn new(max_threshold: u16, max_participants: u16) -> EvrfGenerators<C> {
let g = C::generator();
let mut rng = ChaCha20Rng::from_seed(Blake2s256::digest(g.to_bytes()).into());
let h = sample_point::<C>(&mut rng);
let (_, generators) =
Evrf::<C>::muls_and_generators_to_use(max_threshold.into(), max_participants.into());
let mut g_bold = vec![];
let mut h_bold = vec![];
for _ in 0 .. generators {
g_bold.push(sample_point::<C>(&mut rng));
h_bold.push(sample_point::<C>(&mut rng));
}
Self(Generators::new(g, h, g_bold, h_bold).unwrap())
}
}
/// The result of proving for an eVRF.
pub(crate) struct EvrfProveResult<C: Ciphersuite> {
/// The coefficients for use in the DKG.
pub(crate) coefficients: Vec<Zeroizing<C::F>>,
/// The masks to encrypt secret shares with.
pub(crate) encryption_masks: Vec<Zeroizing<C::F>>,
/// The proof itself.
pub(crate) proof: Vec<u8>,
}
/// The result of verifying an eVRF.
pub(crate) struct EvrfVerifyResult<C: EvrfCurve> {
/// The commitments to the coefficients for use in the DKG.
pub(crate) coefficients: Vec<C::G>,
/// The ephemeral public keys to perform ECDHs with
pub(crate) ecdh_keys: Vec<[<C::EmbeddedCurve as Ciphersuite>::G; 2]>,
/// The commitments to the masks used to encrypt secret shares with.
pub(crate) encryption_commitments: Vec<C::G>,
}
impl<C: EvrfCurve> fmt::Debug for EvrfVerifyResult<C> {
fn fmt(&self, fmt: &mut fmt::Formatter<'_>) -> fmt::Result {
fmt.debug_struct("EvrfVerifyResult").finish_non_exhaustive()
}
}
/// A struct to prove/verify eVRFs with.
pub(crate) struct Evrf<C: EvrfCurve>(PhantomData<C>);
impl<C: EvrfCurve> Evrf<C> {
// Sample uniform points (via rejection-sampling) on the embedded elliptic curve
fn transcript_to_points(
seed: [u8; 32],
coefficients: usize,
) -> Vec<<C::EmbeddedCurve as Ciphersuite>::G> {
// We need to do two Diffie-Hellman's per coefficient in order to achieve an unbiased result
let quantity = 2 * coefficients;
let mut rng = ChaCha20Rng::from_seed(seed);
let mut res = Vec::with_capacity(quantity);
for _ in 0 .. quantity {
res.push(sample_point::<C::EmbeddedCurve>(&mut rng));
}
res
}
/// Read a Variable from a theoretical vector commitment tape
fn read_one_from_tape(generators_to_use: usize, start: &mut usize) -> Variable {
// Each commitment has twice as many variables as generators in use
let commitment = *start / (2 * generators_to_use);
// The index will be less than the amount of generators in use, as half are left and half are
// right
let index = *start % generators_to_use;
let res = if (*start / generators_to_use) % 2 == 0 {
Variable::CG { commitment, index }
} else {
Variable::CH { commitment, index }
};
*start += 1;
res
}
/// Read a set of variables from a theoretical vector commitment tape
fn read_from_tape<N: ArrayLength>(
generators_to_use: usize,
start: &mut usize,
) -> GenericArray<Variable, N> {
let mut buf = Vec::with_capacity(N::USIZE);
for _ in 0 .. N::USIZE {
buf.push(Self::read_one_from_tape(generators_to_use, start));
}
GenericArray::from_slice(&buf).clone()
}
/// Read `PointWithDlog`s, which share a discrete logarithm, from the theoretical vector
/// commitment tape.
fn point_with_dlogs(
start: &mut usize,
quantity: usize,
generators_to_use: usize,
) -> Vec<PointWithDlog<C::EmbeddedCurveParameters>> {
// We define a serialized tape of the discrete logarithm, then for each divisor/point, we push:
// zero, x**i, y x**i, y, x_coord, y_coord
// We then chunk that into vector commitments
// Here, we take the assumed layout and generate the expected `Variable`s for this layout
let dlog = Self::read_from_tape(generators_to_use, start);
let mut res = Vec::with_capacity(quantity);
let mut read_point_with_dlog = || {
let zero = Self::read_one_from_tape(generators_to_use, start);
let x_from_power_of_2 = Self::read_from_tape(generators_to_use, start);
let yx = Self::read_from_tape(generators_to_use, start);
let y = Self::read_one_from_tape(generators_to_use, start);
let divisor = Divisor { zero, x_from_power_of_2, yx, y };
let point = (
Self::read_one_from_tape(generators_to_use, start),
Self::read_one_from_tape(generators_to_use, start),
);
res.push(PointWithDlog { dlog: dlog.clone(), divisor, point });
};
for _ in 0 .. quantity {
read_point_with_dlog();
}
res
}
fn muls_and_generators_to_use(coefficients: usize, ecdhs: usize) -> (usize, usize) {
const MULS_PER_DH: usize = 7;
// 1 DH to prove the discrete logarithm corresponds to the eVRF public key
// 2 DHs per generated coefficient
// 2 DHs per generated ECDH
let expected_muls = MULS_PER_DH * (1 + (2 * coefficients) + (2 * 2 * ecdhs));
let generators_to_use = {
let mut padded_pow_of_2 = 1;
while padded_pow_of_2 < expected_muls {
padded_pow_of_2 <<= 1;
}
// This may as small as 16, which would create an excessive amount of vector commitments
// We set a floor of 1024 rows for bandwidth reasons
padded_pow_of_2.max(1024)
};
(expected_muls, generators_to_use)
}
fn circuit(
curve_spec: &CurveSpec<C::F>,
evrf_public_key: (C::F, C::F),
coefficients: usize,
ecdh_commitments: &[[(C::F, C::F); 2]],
generator_tables: &[GeneratorTable<C::F, C::EmbeddedCurveParameters>],
circuit: &mut Circuit<C>,
transcript: &mut impl Transcript,
) {
let (expected_muls, generators_to_use) =
Self::muls_and_generators_to_use(coefficients, ecdh_commitments.len());
let (challenge, challenged_generators) =
circuit.discrete_log_challenge(transcript, curve_spec, generator_tables);
debug_assert_eq!(challenged_generators.len(), 1 + (2 * coefficients) + ecdh_commitments.len());
// The generators tables/challenged generators are expected to have the following layouts
// G, coefficients * [A, B], ecdhs * [P]
#[allow(non_snake_case)]
let challenged_G = &challenged_generators[0];
// Execute the circuit for the coefficients
let mut tape_pos = 0;
{
let mut point_with_dlogs =
Self::point_with_dlogs(&mut tape_pos, 1 + (2 * coefficients), generators_to_use)
.into_iter();
// Verify the discrete logarithm is in the fact the discrete logarithm of the eVRF public key
let point = circuit.discrete_log(
curve_spec,
point_with_dlogs.next().unwrap(),
&challenge,
challenged_G,
);
circuit.equality(LinComb::from(point.x()), &LinComb::empty().constant(evrf_public_key.0));
circuit.equality(LinComb::from(point.y()), &LinComb::empty().constant(evrf_public_key.1));
// Verify the DLog claims against the sampled points
for (i, pair) in challenged_generators[1 ..].chunks(2).take(coefficients).enumerate() {
let mut lincomb = LinComb::empty();
debug_assert_eq!(pair.len(), 2);
for challenged_generator in pair {
let point = circuit.discrete_log(
curve_spec,
point_with_dlogs.next().unwrap(),
&challenge,
challenged_generator,
);
// For each point in this pair, add its x coordinate to a lincomb
lincomb = lincomb.term(C::F::ONE, point.x());
}
// Constrain the sum of the two x coordinates to be equal to the value in the Pedersen
// commitment
circuit.equality(lincomb, &LinComb::from(Variable::V(i)));
}
debug_assert!(point_with_dlogs.next().is_none());
}
// Now execute the circuit for the ECDHs
let mut challenged_generators = challenged_generators.iter().skip(1 + (2 * coefficients));
for (i, ecdh) in ecdh_commitments.iter().enumerate() {
let challenged_generator = challenged_generators.next().unwrap();
let mut lincomb = LinComb::empty();
for ecdh in ecdh {
let mut point_with_dlogs =
Self::point_with_dlogs(&mut tape_pos, 2, generators_to_use).into_iter();
// One proof of the ECDH secret * G for the commitment published
let point = circuit.discrete_log(
curve_spec,
point_with_dlogs.next().unwrap(),
&challenge,
challenged_G,
);
circuit.equality(LinComb::from(point.x()), &LinComb::empty().constant(ecdh.0));
circuit.equality(LinComb::from(point.y()), &LinComb::empty().constant(ecdh.1));
// One proof of the ECDH secret * P for the ECDH
let point = circuit.discrete_log(
curve_spec,
point_with_dlogs.next().unwrap(),
&challenge,
challenged_generator,
);
// For each point in this pair, add its x coordinate to a lincomb
lincomb = lincomb.term(C::F::ONE, point.x());
}
// Constrain the sum of the two x coordinates to be equal to the value in the Pedersen
// commitment
circuit.equality(lincomb, &LinComb::from(Variable::V(coefficients + i)));
}
debug_assert_eq!(expected_muls, circuit.muls());
debug_assert!(challenged_generators.next().is_none());
}
/// Convert a scalar to a sequence of coefficients for the polynomial 2**i, where the sum of the
/// coefficients is F::NUM_BITS.
///
/// Despite the name, the returned coefficients are not guaranteed to be bits (0 or 1).
///
/// This scalar will presumably be used in a discrete log proof. That requires calculating a
/// divisor which is variable time to the amount of points interpolated. Since the amount of
/// points interpolated is equal to the sum of the coefficients in the polynomial, we need all
/// scalars to have a constant sum of their coefficients (instead of one variable to its bits).
///
/// We achieve this by finding the highest non-0 coefficient, decrementing it, and increasing the
/// immediately less significant coefficient by 2. This increases the sum of the coefficients by
/// 1 (-1+2=1).
fn scalar_to_bits(scalar: &<C::EmbeddedCurve as Ciphersuite>::F) -> Vec<u64> {
let num_bits = u64::from(<<C as EvrfCurve>::EmbeddedCurve as Ciphersuite>::F::NUM_BITS);
// Obtain the bits of the private key
let num_bits_usize = usize::try_from(num_bits).unwrap();
let mut decomposition = vec![0; num_bits_usize];
for (i, bit) in scalar.to_le_bits().into_iter().take(num_bits_usize).enumerate() {
let bit = u64::from(u8::from(bit));
decomposition[i] = bit;
}
// The following algorithm only works if the value of the scalar exceeds num_bits
// If it isn't, we increase it by the modulus such that it does exceed num_bits
{
let mut less_than_num_bits = Choice::from(0);
for i in 0 .. num_bits {
less_than_num_bits |= scalar.ct_eq(&<C::EmbeddedCurve as Ciphersuite>::F::from(i));
}
let mut decomposition_of_modulus = vec![0; num_bits_usize];
// Decompose negative one
for (i, bit) in (-<C::EmbeddedCurve as Ciphersuite>::F::ONE)
.to_le_bits()
.into_iter()
.take(num_bits_usize)
.enumerate()
{
let bit = u64::from(u8::from(bit));
decomposition_of_modulus[i] = bit;
}
// Increment it by one
decomposition_of_modulus[0] += 1;
// Add the decomposition onto the decomposition of the modulus
for i in 0 .. num_bits_usize {
let new_decomposition = <_>::conditional_select(
&decomposition[i],
&(decomposition[i] + decomposition_of_modulus[i]),
less_than_num_bits,
);
decomposition[i] = new_decomposition;
}
}
// Calculcate the sum of the coefficients
let mut sum_of_coefficients: u64 = 0;
for decomposition in &decomposition {
sum_of_coefficients += *decomposition;
}
/*
Now, because we added a log2(k)-bit number to a k-bit number, we may have our sum of
coefficients be *too high*. We attempt to reduce the sum of the coefficients accordingly.
This algorithm is guaranteed to complete as expected. Take the sequence `222`. `222` becomes
`032` becomes `013`. Even if the next coefficient in the sequence is `2`, the third
coefficient will be reduced once and the next coefficient (`2`, increased to `3`) will only
be eligible for reduction once. This demonstrates, even for a worst case of log2(k) `2`s
followed by `1`s (as possible if the modulus is a Mersenne prime), the log2(k) `2`s can be
reduced as necessary so long as there is a single coefficient after (requiring the entire
sequence be at least of length log2(k) + 1). For a 2-bit number, log2(k) + 1 == 2, so this
holds for any odd prime field.
To fully type out the demonstration for the Mersenne prime 3, with scalar to encode 1 (the
highest value less than the number of bits):
10 - Little-endian bits of 1
21 - Little-endian bits of 1, plus the modulus
02 - After one reduction, where the sum of the coefficients does in fact equal 2 (the target)
*/
{
let mut log2_num_bits = 0;
while (1 << log2_num_bits) < num_bits {
log2_num_bits += 1;
}
for _ in 0 .. log2_num_bits {
// If the sum of coefficients is the amount of bits, we're done
let mut done = sum_of_coefficients.ct_eq(&num_bits);
for i in 0 .. (num_bits_usize - 1) {
let should_act = (!done) & decomposition[i].ct_gt(&1);
// Subtract 2 from this coefficient
let amount_to_sub = <_>::conditional_select(&0, &2, should_act);
decomposition[i] -= amount_to_sub;
// Add 1 to the next coefficient
let amount_to_add = <_>::conditional_select(&0, &1, should_act);
decomposition[i + 1] += amount_to_add;
// Also update the sum of coefficients
sum_of_coefficients -= <_>::conditional_select(&0, &1, should_act);
// If we updated the coefficients this loop iter, we're done for this loop iter
done |= should_act;
}
}
}
for _ in 0 .. num_bits {
// If the sum of coefficients is the amount of bits, we're done
let mut done = sum_of_coefficients.ct_eq(&num_bits);
// Find the highest coefficient currently non-zero
for i in (1 .. decomposition.len()).rev() {
// If this is non-zero, we should decrement this coefficient if we haven't already
// decremented a coefficient this round
let is_non_zero = !(0.ct_eq(&decomposition[i]));
let should_act = (!done) & is_non_zero;
// Update this coefficient and the prior coefficient
let amount_to_sub = <_>::conditional_select(&0, &1, should_act);
decomposition[i] -= amount_to_sub;
let amount_to_add = <_>::conditional_select(&0, &2, should_act);
// i must be at least 1, so i - 1 will be at least 0 (meaning it's safe to index with)
decomposition[i - 1] += amount_to_add;
// Also update the sum of coefficients
sum_of_coefficients += <_>::conditional_select(&0, &1, should_act);
// If we updated the coefficients this loop iter, we're done for this loop iter
done |= should_act;
}
}
debug_assert!(bool::from(decomposition.iter().sum::<u64>().ct_eq(&num_bits)));
decomposition
}
/// Prove a point on an elliptic curve had its discrete logarithm generated via an eVRF.
pub(crate) fn prove(
rng: &mut (impl RngCore + CryptoRng),
generators: &Generators<C>,
transcript: [u8; 32],
coefficients: usize,
ecdh_public_keys: &[<<C as EvrfCurve>::EmbeddedCurve as Ciphersuite>::G],
evrf_private_key: &Zeroizing<<<C as EvrfCurve>::EmbeddedCurve as Ciphersuite>::F>,
) -> Result<EvrfProveResult<C>, AcError> {
let curve_spec = CurveSpec {
a: <<C as EvrfCurve>::EmbeddedCurve as Ciphersuite>::G::a(),
b: <<C as EvrfCurve>::EmbeddedCurve as Ciphersuite>::G::b(),
};
// A tape of the discrete logarithm, then [zero, x**i, y x**i, y, x_coord, y_coord]
let mut vector_commitment_tape = vec![];
let mut generator_tables = Vec::with_capacity(1 + (2 * coefficients) + ecdh_public_keys.len());
// A function to calculate a divisor and push it onto the tape
// This defines a vec, divisor_points, outside of the fn to reuse its allocation
let mut divisor_points =
Vec::with_capacity((<C::EmbeddedCurve as Ciphersuite>::F::NUM_BITS as usize) + 1);
let mut divisor =
|vector_commitment_tape: &mut Vec<_>,
dlog: &[u64],
push_generator: bool,
generator: <<C as EvrfCurve>::EmbeddedCurve as Ciphersuite>::G,
dh: <<C as EvrfCurve>::EmbeddedCurve as Ciphersuite>::G| {
if push_generator {
let (x, y) = <C::EmbeddedCurve as Ciphersuite>::G::to_xy(generator).unwrap();
generator_tables.push(GeneratorTable::new(&curve_spec, x, y));
}
{
let mut generator = generator;
for coefficient in dlog {
let mut coefficient = *coefficient;
while coefficient != 0 {
coefficient -= 1;
divisor_points.push(generator);
}
generator = generator.double();
}
debug_assert_eq!(
dlog.iter().sum::<u64>(),
u64::from(<C::EmbeddedCurve as Ciphersuite>::F::NUM_BITS)
);
}
divisor_points.push(-dh);
let mut divisor = new_divisor(&divisor_points).unwrap().normalize_x_coefficient();
divisor_points.zeroize();
vector_commitment_tape.push(divisor.zero_coefficient);
for coefficient in divisor.x_coefficients.iter().skip(1) {
vector_commitment_tape.push(*coefficient);
}
for _ in divisor.x_coefficients.len() ..
<C::EmbeddedCurveParameters as DiscreteLogParameters>::XCoefficientsMinusOne::USIZE
{
vector_commitment_tape.push(<C as Ciphersuite>::F::ZERO);
}
for coefficient in divisor.yx_coefficients.first().unwrap_or(&vec![]) {
vector_commitment_tape.push(*coefficient);
}
for _ in divisor.yx_coefficients.first().unwrap_or(&vec![]).len() ..
<C::EmbeddedCurveParameters as DiscreteLogParameters>::YxCoefficients::USIZE
{
vector_commitment_tape.push(<C as Ciphersuite>::F::ZERO);
}
vector_commitment_tape
.push(divisor.y_coefficients.first().copied().unwrap_or(<C as Ciphersuite>::F::ZERO));
divisor.zeroize();
drop(divisor);
let (x, y) = <C::EmbeddedCurve as Ciphersuite>::G::to_xy(dh).unwrap();
vector_commitment_tape.push(x);
vector_commitment_tape.push(y);
(x, y)
};
// Start with the coefficients
let evrf_public_key;
let mut actual_coefficients = Vec::with_capacity(coefficients);
{
let mut dlog = Self::scalar_to_bits(evrf_private_key);
let points = Self::transcript_to_points(transcript, coefficients);
// Start by pushing the discrete logarithm onto the tape
for coefficient in &dlog {
vector_commitment_tape.push(<_>::from(*coefficient));
}
// Push a divisor for proving that we're using the correct scalar
evrf_public_key = divisor(
&mut vector_commitment_tape,
&dlog,
true,
<<C as EvrfCurve>::EmbeddedCurve as Ciphersuite>::generator(),
<<C as EvrfCurve>::EmbeddedCurve as Ciphersuite>::generator() * evrf_private_key.deref(),
);
// Push a divisor for each point we use in the eVRF
for pair in points.chunks(2) {
let mut res = Zeroizing::new(C::F::ZERO);
for point in pair {
let (dh_x, _) = divisor(
&mut vector_commitment_tape,
&dlog,
true,
*point,
*point * evrf_private_key.deref(),
);
*res += dh_x;
}
actual_coefficients.push(res);
}
debug_assert_eq!(actual_coefficients.len(), coefficients);
dlog.zeroize();
}
// Now do the ECDHs for the encryption
let mut encryption_masks = Vec::with_capacity(ecdh_public_keys.len());
let mut ecdh_commitments = Vec::with_capacity(2 * ecdh_public_keys.len());
let mut ecdh_commitments_xy = Vec::with_capacity(ecdh_public_keys.len());
for ecdh_public_key in ecdh_public_keys {
ecdh_commitments_xy.push([(C::F::ZERO, C::F::ZERO); 2]);
let mut res = Zeroizing::new(C::F::ZERO);
for j in 0 .. 2 {
let mut ecdh_private_key;
loop {
ecdh_private_key = <C::EmbeddedCurve as Ciphersuite>::F::random(&mut *rng);
// Generate a non-0 ECDH private key, as necessary to not produce an identity output
// Identity isn't representable with the divisors, hence the explicit effort
if bool::from(!ecdh_private_key.is_zero()) {
break;
}
}
let mut dlog = Self::scalar_to_bits(&ecdh_private_key);
let ecdh_commitment = <C::EmbeddedCurve as Ciphersuite>::generator() * ecdh_private_key;
ecdh_commitments.push(ecdh_commitment);
ecdh_commitments_xy.last_mut().unwrap()[j] =
<<C::EmbeddedCurve as Ciphersuite>::G as DivisorCurve>::to_xy(ecdh_commitment).unwrap();
// Start by pushing the discrete logarithm onto the tape
for coefficient in &dlog {
vector_commitment_tape.push(<_>::from(*coefficient));
}
// Push a divisor for proving that we're using the correct scalar for the commitment
divisor(
&mut vector_commitment_tape,
&dlog,
false,
<<C as EvrfCurve>::EmbeddedCurve as Ciphersuite>::generator(),
<<C as EvrfCurve>::EmbeddedCurve as Ciphersuite>::generator() * ecdh_private_key,
);
// Push a divisor for the key we're performing the ECDH with
let (dh_x, _) = divisor(
&mut vector_commitment_tape,
&dlog,
j == 0,
*ecdh_public_key,
*ecdh_public_key * ecdh_private_key,
);
*res += dh_x;
ecdh_private_key.zeroize();
dlog.zeroize();
}
encryption_masks.push(res);
}
debug_assert_eq!(encryption_masks.len(), ecdh_public_keys.len());
// Now that we have the vector commitment tape, chunk it
let (_, generators_to_use) =
Self::muls_and_generators_to_use(coefficients, ecdh_public_keys.len());
let mut vector_commitments =
Vec::with_capacity(vector_commitment_tape.len().div_ceil(2 * generators_to_use));
for chunk in vector_commitment_tape.chunks(2 * generators_to_use) {
let g_values = chunk[.. generators_to_use.min(chunk.len())].to_vec().into();
let h_values = chunk[generators_to_use.min(chunk.len()) ..].to_vec().into();
vector_commitments.push(PedersenVectorCommitment {
g_values,
h_values,
mask: C::F::random(&mut *rng),
});
}
vector_commitment_tape.zeroize();
drop(vector_commitment_tape);
let mut commitments = Vec::with_capacity(coefficients + ecdh_public_keys.len());
for coefficient in &actual_coefficients {
commitments.push(PedersenCommitment { value: **coefficient, mask: C::F::random(&mut *rng) });
}
for enc_mask in &encryption_masks {
commitments.push(PedersenCommitment { value: **enc_mask, mask: C::F::random(&mut *rng) });
}
let mut transcript = ProverTranscript::new(transcript);
let commited_commitments = transcript.write_commitments(
vector_commitments
.iter()
.map(|commitment| {
commitment
.commit(generators.g_bold_slice(), generators.h_bold_slice(), generators.h())
.ok_or(AcError::NotEnoughGenerators)
})
.collect::<Result<_, _>>()?,
commitments
.iter()
.map(|commitment| commitment.commit(generators.g(), generators.h()))
.collect(),
);
for ecdh_commitment in ecdh_commitments {
transcript.push_point(ecdh_commitment);
}
let mut circuit = Circuit::prove(vector_commitments, commitments.clone());
Self::circuit(
&curve_spec,
evrf_public_key,
coefficients,
&ecdh_commitments_xy,
&generator_tables,
&mut circuit,
&mut transcript,
);
let (statement, Some(witness)) = circuit
.statement(
generators.reduce(generators_to_use).ok_or(AcError::NotEnoughGenerators)?,
commited_commitments,
)
.unwrap()
else {
panic!("proving yet wasn't yielded the witness");
};
statement.prove(&mut *rng, &mut transcript, witness).unwrap();
// Push the reveal onto the transcript
for commitment in &commitments {
transcript.push_point(generators.g() * commitment.value);
}
// Define a weight to aggregate the commitments with
let mut agg_weights = Vec::with_capacity(commitments.len());
agg_weights.push(C::F::ONE);
while agg_weights.len() < commitments.len() {
agg_weights.push(transcript.challenge::<C::F>());
}
let mut x = commitments
.iter()
.zip(&agg_weights)
.map(|(commitment, weight)| commitment.mask * *weight)
.sum::<C::F>();
// Do a Schnorr PoK for the randomness of the aggregated Pedersen commitment
let mut r = C::F::random(&mut *rng);
transcript.push_point(generators.h() * r);
let c = transcript.challenge::<C::F>();
transcript.push_scalar(r + (c * x));
r.zeroize();
x.zeroize();
Ok(EvrfProveResult {
coefficients: actual_coefficients,
encryption_masks,
proof: transcript.complete(),
})
}
/// Verify an eVRF proof, returning the commitments output.
#[allow(clippy::too_many_arguments)]
pub(crate) fn verify(
rng: &mut (impl RngCore + CryptoRng),
generators: &Generators<C>,
verifier: &mut BatchVerifier<C>,
transcript: [u8; 32],
coefficients: usize,
ecdh_public_keys: &[<<C as EvrfCurve>::EmbeddedCurve as Ciphersuite>::G],
evrf_public_key: <<C as EvrfCurve>::EmbeddedCurve as Ciphersuite>::G,
proof: &[u8],
) -> Result<EvrfVerifyResult<C>, ()> {
let curve_spec = CurveSpec {
a: <<C as EvrfCurve>::EmbeddedCurve as Ciphersuite>::G::a(),
b: <<C as EvrfCurve>::EmbeddedCurve as Ciphersuite>::G::b(),
};
let mut generator_tables = Vec::with_capacity(1 + (2 * coefficients) + ecdh_public_keys.len());
{
let (x, y) =
<C::EmbeddedCurve as Ciphersuite>::G::to_xy(<C::EmbeddedCurve as Ciphersuite>::generator())
.unwrap();
generator_tables.push(GeneratorTable::new(&curve_spec, x, y));
}
let points = Self::transcript_to_points(transcript, coefficients);
for generator in points {
let (x, y) = <C::EmbeddedCurve as Ciphersuite>::G::to_xy(generator).unwrap();
generator_tables.push(GeneratorTable::new(&curve_spec, x, y));
}
for generator in ecdh_public_keys {
let (x, y) = <C::EmbeddedCurve as Ciphersuite>::G::to_xy(*generator).unwrap();
generator_tables.push(GeneratorTable::new(&curve_spec, x, y));
}
let (_, generators_to_use) =
Self::muls_and_generators_to_use(coefficients, ecdh_public_keys.len());
let mut transcript = VerifierTranscript::new(transcript, proof);
let dlog_len = <C::EmbeddedCurveParameters as DiscreteLogParameters>::ScalarBits::USIZE;
let divisor_len = 1 +
<C::EmbeddedCurveParameters as DiscreteLogParameters>::XCoefficientsMinusOne::USIZE +
<C::EmbeddedCurveParameters as DiscreteLogParameters>::YxCoefficients::USIZE +
1;
let dlog_proof_len = divisor_len + 2;
let coeffs_vc_variables = dlog_len + ((1 + (2 * coefficients)) * dlog_proof_len);
let ecdhs_vc_variables = ((2 * ecdh_public_keys.len()) * dlog_len) +
((2 * 2 * ecdh_public_keys.len()) * dlog_proof_len);
let vcs = (coeffs_vc_variables + ecdhs_vc_variables).div_ceil(2 * generators_to_use);
let all_commitments =
transcript.read_commitments(vcs, coefficients + ecdh_public_keys.len()).map_err(|_| ())?;
let commitments = all_commitments.V().to_vec();
let mut ecdh_keys = Vec::with_capacity(ecdh_public_keys.len());
let mut ecdh_keys_xy = Vec::with_capacity(ecdh_public_keys.len());
for _ in 0 .. ecdh_public_keys.len() {
let ecdh_keys_i = [
transcript.read_point::<C::EmbeddedCurve>().map_err(|_| ())?,
transcript.read_point::<C::EmbeddedCurve>().map_err(|_| ())?,
];
ecdh_keys.push(ecdh_keys_i);
// This bans zero ECDH keys
ecdh_keys_xy.push([
<<C::EmbeddedCurve as Ciphersuite>::G as DivisorCurve>::to_xy(ecdh_keys_i[0]).ok_or(())?,
<<C::EmbeddedCurve as Ciphersuite>::G as DivisorCurve>::to_xy(ecdh_keys_i[1]).ok_or(())?,
]);
}
let mut circuit = Circuit::verify();
Self::circuit(
&curve_spec,
<C::EmbeddedCurve as Ciphersuite>::G::to_xy(evrf_public_key).ok_or(())?,
coefficients,
&ecdh_keys_xy,
&generator_tables,
&mut circuit,
&mut transcript,
);
let (statement, None) =
circuit.statement(generators.reduce(generators_to_use).ok_or(())?, all_commitments).unwrap()
else {
panic!("verifying yet was yielded a witness");
};
statement.verify(rng, verifier, &mut transcript).map_err(|_| ())?;
// Read the openings for the commitments
let mut openings = Vec::with_capacity(commitments.len());
for _ in 0 .. commitments.len() {
openings.push(transcript.read_point::<C>().map_err(|_| ())?);
}
// Verify the openings of the commitments
let mut agg_weights = Vec::with_capacity(commitments.len());
agg_weights.push(C::F::ONE);
while agg_weights.len() < commitments.len() {
agg_weights.push(transcript.challenge::<C::F>());
}
let sum_points =
openings.iter().zip(&agg_weights).map(|(point, weight)| *point * *weight).sum::<C::G>();
let sum_commitments =
commitments.into_iter().zip(agg_weights).map(|(point, weight)| point * weight).sum::<C::G>();
#[allow(non_snake_case)]
let A = sum_commitments - sum_points;
#[allow(non_snake_case)]
let R = transcript.read_point::<C>().map_err(|_| ())?;
let c = transcript.challenge::<C::F>();
let s = transcript.read_scalar::<C>().map_err(|_| ())?;
// Doesn't batch verify this as we can't access the internals of the GBP batch verifier
if (R + (A * c)) != (generators.h() * s) {
Err(())?;
}
if !transcript.complete().is_empty() {
Err(())?
};
let encryption_commitments = openings[coefficients ..].to_vec();
let coefficients = openings[.. coefficients].to_vec();
Ok(EvrfVerifyResult { coefficients, ecdh_keys, encryption_commitments })
}
}

102
crypto/dkg/src/lib.rs
View File

@@ -21,6 +21,10 @@ pub mod encryption;
#[cfg(feature = "std")]
pub mod pedpop;
/// The one-round DKG described in the [eVRF paper](https://eprint.iacr.org/2024/397).
#[cfg(all(feature = "std", feature = "evrf"))]
pub mod evrf;
/// Promote keys between ciphersuites.
#[cfg(feature = "std")]
pub mod promote;
@@ -205,25 +209,37 @@ mod lib {
}
}
/// Calculate the lagrange coefficient for a signing set.
pub fn lagrange<F: PrimeField>(i: Participant, included: &[Participant]) -> F {
let i_f = F::from(u64::from(u16::from(i)));
#[derive(Clone, PartialEq, Eq, Debug, Zeroize)]
pub(crate) enum Interpolation<F: Zeroize + PrimeField> {
Constant(Vec<F>),
Lagrange,
}
let mut num = F::ONE;
let mut denom = F::ONE;
for l in included {
if i == *l {
continue;
impl<F: Zeroize + PrimeField> Interpolation<F> {
pub(crate) fn interpolation_factor(&self, i: Participant, included: &[Participant]) -> F {
match self {
Interpolation::Constant(c) => c[usize::from(u16::from(i) - 1)],
Interpolation::Lagrange => {
let i_f = F::from(u64::from(u16::from(i)));
let mut num = F::ONE;
let mut denom = F::ONE;
for l in included {
if i == *l {
continue;
}
let share = F::from(u64::from(u16::from(*l)));
num *= share;
denom *= share - i_f;
}
// Safe as this will only be 0 if we're part of the above loop
// (which we have an if case to avoid)
num * denom.invert().unwrap()
}
}
let share = F::from(u64::from(u16::from(*l)));
num *= share;
denom *= share - i_f;
}
// Safe as this will only be 0 if we're part of the above loop
// (which we have an if case to avoid)
num * denom.invert().unwrap()
}
/// Keys and verification shares generated by a DKG.
@@ -232,6 +248,8 @@ mod lib {
pub struct ThresholdCore<C: Ciphersuite> {
/// Threshold Parameters.
pub(crate) params: ThresholdParams,
/// The interpolation method used.
pub(crate) interpolation: Interpolation<C::F>,
/// Secret share key.
pub(crate) secret_share: Zeroizing<C::F>,
@@ -246,6 +264,7 @@ mod lib {
fmt
.debug_struct("ThresholdCore")
.field("params", &self.params)
.field("interpolation", &self.interpolation)
.field("group_key", &self.group_key)
.field("verification_shares", &self.verification_shares)
.finish_non_exhaustive()
@@ -255,6 +274,7 @@ mod lib {
impl<C: Ciphersuite> Zeroize for ThresholdCore<C> {
fn zeroize(&mut self) {
self.params.zeroize();
self.interpolation.zeroize();
self.secret_share.zeroize();
self.group_key.zeroize();
for share in self.verification_shares.values_mut() {
@@ -266,16 +286,14 @@ mod lib {
impl<C: Ciphersuite> ThresholdCore<C> {
pub(crate) fn new(
params: ThresholdParams,
interpolation: Interpolation<C::F>,
secret_share: Zeroizing<C::F>,
verification_shares: HashMap<Participant, C::G>,
) -> ThresholdCore<C> {
let t = (1 ..= params.t()).map(Participant).collect::<Vec<_>>();
ThresholdCore {
params,
secret_share,
group_key: t.iter().map(|i| verification_shares[i] * lagrange::<C::F>(*i, &t)).sum(),
verification_shares,
}
let group_key =
t.iter().map(|i| verification_shares[i] * interpolation.interpolation_factor(*i, &t)).sum();
ThresholdCore { params, interpolation, secret_share, group_key, verification_shares }
}
/// Parameters for these keys.
@@ -304,6 +322,15 @@ mod lib {
writer.write_all(&self.params.t.to_le_bytes())?;
writer.write_all(&self.params.n.to_le_bytes())?;
writer.write_all(&self.params.i.to_bytes())?;
match &self.interpolation {
Interpolation::Constant(c) => {
writer.write_all(&[0])?;
for c in c {
writer.write_all(c.to_repr().as_ref())?;
}
}
Interpolation::Lagrange => writer.write_all(&[1])?,
};
let mut share_bytes = self.secret_share.to_repr();
writer.write_all(share_bytes.as_ref())?;
share_bytes.as_mut().zeroize();
@@ -352,6 +379,20 @@ mod lib {
)
};
let mut interpolation = [0];
reader.read_exact(&mut interpolation)?;
let interpolation = match interpolation[0] {
0 => Interpolation::Constant({
let mut res = Vec::with_capacity(usize::from(n));
for _ in 0 .. n {
res.push(C::read_F(reader)?);
}
res
}),
1 => Interpolation::Lagrange,
_ => Err(io::Error::other("invalid interpolation method"))?,
};
let secret_share = Zeroizing::new(C::read_F(reader)?);
let mut verification_shares = HashMap::new();
@@ -361,6 +402,7 @@ mod lib {
Ok(ThresholdCore::new(
ThresholdParams::new(t, n, i).map_err(|_| io::Error::other("invalid parameters"))?,
interpolation,
secret_share,
verification_shares,
))
@@ -383,6 +425,7 @@ mod lib {
/// View of keys, interpolated and offset for usage.
#[derive(Clone)]
pub struct ThresholdView<C: Ciphersuite> {
interpolation: Interpolation<C::F>,
offset: C::F,
group_key: C::G,
included: Vec<Participant>,
@@ -395,6 +438,7 @@ mod lib {
fn fmt(&self, fmt: &mut fmt::Formatter<'_>) -> fmt::Result {
fmt
.debug_struct("ThresholdView")
.field("interpolation", &self.interpolation)
.field("offset", &self.offset)
.field("group_key", &self.group_key)
.field("included", &self.included)
@@ -480,12 +524,13 @@ mod lib {
included.sort();
let mut secret_share = Zeroizing::new(
lagrange::<C::F>(self.params().i(), &included) * self.secret_share().deref(),
self.core.interpolation.interpolation_factor(self.params().i(), &included) *
self.secret_share().deref(),
);
let mut verification_shares = self.verification_shares();
for (i, share) in &mut verification_shares {
*share *= lagrange::<C::F>(*i, &included);
*share *= self.core.interpolation.interpolation_factor(*i, &included);
}
// The offset is included by adding it to the participant with the lowest ID
@@ -496,6 +541,7 @@ mod lib {
*verification_shares.get_mut(&included[0]).unwrap() += C::generator() * offset;
Ok(ThresholdView {
interpolation: self.core.interpolation.clone(),
offset,
group_key: self.group_key(),
secret_share,
@@ -528,6 +574,14 @@ mod lib {
&self.included
}
/// Return the interpolation factor for a signer.
pub fn interpolation_factor(&self, participant: Participant) -> Option<C::F> {
if !self.included.contains(&participant) {
None?
}
Some(self.interpolation.interpolation_factor(participant, &self.included))
}
/// Return the interpolated, offset secret share.
pub fn secret_share(&self) -> &Zeroizing<C::F> {
&self.secret_share

43
crypto/dkg/src/musig.rs
View File

@@ -7,8 +7,6 @@ use std_shims::collections::HashMap;
#[cfg(feature = "std")]
use zeroize::Zeroizing;
#[cfg(feature = "std")]
use ciphersuite::group::ff::Field;
use ciphersuite::{
group::{Group, GroupEncoding},
Ciphersuite,
@@ -16,7 +14,7 @@ use ciphersuite::{
use crate::DkgError;
#[cfg(feature = "std")]
use crate::{Participant, ThresholdParams, ThresholdCore, lagrange};
use crate::{Participant, ThresholdParams, Interpolation, ThresholdCore};
fn check_keys<C: Ciphersuite>(keys: &[C::G]) -> Result<u16, DkgError<()>> {
if keys.is_empty() {
@@ -67,6 +65,7 @@ pub fn musig_key<C: Ciphersuite>(context: &[u8], keys: &[C::G]) -> Result<C::G,
let transcript = binding_factor_transcript::<C>(context, keys)?;
let mut res = C::G::identity();
for i in 1 ..= keys_len {
// TODO: Calculate this with a multiexp
res += keys[usize::from(i - 1)] * binding_factor::<C>(transcript.clone(), i);
}
Ok(res)
@@ -104,38 +103,26 @@ pub fn musig<C: Ciphersuite>(
binding.push(binding_factor::<C>(transcript.clone(), i));
}
// Multiply our private key by our binding factor
let mut secret_share = private_key.clone();
*secret_share *= binding[pos];
// Our secret share is our private key
let secret_share = private_key.clone();
// Calculate verification shares
let mut verification_shares = HashMap::new();
// When this library offers a ThresholdView for a specific signing set, it applies the lagrange
// factor
// Since this is a n-of-n scheme, there's only one possible signing set, and one possible
// lagrange factor
// In the name of simplicity, we define the group key as the sum of all bound keys
// Accordingly, the secret share must be multiplied by the inverse of the lagrange factor, along
// with all verification shares
// This is less performant than simply defining the group key as the sum of all post-lagrange
// bound keys, yet the simplicity is preferred
let included = (1 ..= keys_len)
// This error also shouldn't be possible, for the same reasons as documented above
.map(|l| Participant::new(l).ok_or(DkgError::InvalidSigningSet))
.collect::<Result<Vec<_>, _>>()?;
let mut group_key = C::G::identity();
for (l, p) in included.iter().enumerate() {
let bound = keys[l] * binding[l];
group_key += bound;
for l in 1 ..= keys_len {
let key = keys[usize::from(l) - 1];
group_key += key * binding[usize::from(l - 1)];
let lagrange_inv = lagrange::<C::F>(*p, &included).invert().unwrap();
if params.i() == *p {
*secret_share *= lagrange_inv;
}
verification_shares.insert(*p, bound * lagrange_inv);
// These errors also shouldn't be possible, for the same reasons as documented above
verification_shares.insert(Participant::new(l).ok_or(DkgError::InvalidSigningSet)?, key);
}
debug_assert_eq!(C::generator() * secret_share.deref(), verification_shares[&params.i()]);
debug_assert_eq!(musig_key::<C>(context, keys).unwrap(), group_key);
Ok(ThresholdCore { params, secret_share, group_key, verification_shares })
Ok(ThresholdCore::new(
params,
Interpolation::Constant(binding),
secret_share,
verification_shares,
))
}

35
crypto/dkg/src/pedpop.rs
View File

@@ -22,9 +22,9 @@ use multiexp::{multiexp_vartime, BatchVerifier};
use schnorr::SchnorrSignature;
use crate::{
Participant, DkgError, ThresholdParams, ThresholdCore, validate_map,
Participant, DkgError, ThresholdParams, Interpolation, ThresholdCore, validate_map,
encryption::{
ReadWrite, EncryptionKeyMessage, EncryptedMessage, Encryption, EncryptionKeyProof,
ReadWrite, EncryptionKeyMessage, EncryptedMessage, Encryption, Decryption, EncryptionKeyProof,
DecryptionError,
},
};
@@ -32,10 +32,10 @@ use crate::{
type FrostError<C> = DkgError<EncryptionKeyProof<C>>;
#[allow(non_snake_case)]
fn challenge<C: Ciphersuite>(context: &str, l: Participant, R: &[u8], Am: &[u8]) -> C::F {
fn challenge<C: Ciphersuite>(context: [u8; 32], l: Participant, R: &[u8], Am: &[u8]) -> C::F {
let mut transcript = RecommendedTranscript::new(b"DKG FROST v0.2");
transcript.domain_separate(b"schnorr_proof_of_knowledge");
transcript.append_message(b"context", context.as_bytes());
transcript.append_message(b"context", context);
transcript.append_message(b"participant", l.to_bytes());
transcript.append_message(b"nonce", R);
transcript.append_message(b"commitments", Am);
@@ -86,15 +86,15 @@ impl<C: Ciphersuite> ReadWrite for Commitments<C> {
#[derive(Debug, Zeroize)]
pub struct KeyGenMachine<C: Ciphersuite> {
params: ThresholdParams,
context: String,
context: [u8; 32],
_curve: PhantomData<C>,
}
impl<C: Ciphersuite> KeyGenMachine<C> {
/// Create a new machine to generate a key.
///
/// The context string should be unique among multisigs.
pub fn new(params: ThresholdParams, context: String) -> KeyGenMachine<C> {
/// The context should be unique among multisigs.
pub fn new(params: ThresholdParams, context: [u8; 32]) -> KeyGenMachine<C> {
KeyGenMachine { params, context, _curve: PhantomData }
}
@@ -129,11 +129,11 @@ impl<C: Ciphersuite> KeyGenMachine<C> {
// There's no reason to spend the time and effort to make this deterministic besides a
// general obsession with canonicity and determinism though
r,
challenge::<C>(&self.context, self.params.i(), nonce.to_bytes().as_ref(), &cached_msg),
challenge::<C>(self.context, self.params.i(), nonce.to_bytes().as_ref(), &cached_msg),
);
// Additionally create an encryption mechanism to protect the secret shares
let encryption = Encryption::new(self.context.clone(), Some(self.params.i), rng);
let encryption = Encryption::new(self.context, self.params.i, rng);
// Step 4: Broadcast
let msg =
@@ -225,7 +225,7 @@ impl<F: PrimeField> ReadWrite for SecretShare<F> {
#[derive(Zeroize)]
pub struct SecretShareMachine<C: Ciphersuite> {
params: ThresholdParams,
context: String,
context: [u8; 32],
coefficients: Vec<Zeroizing<C::F>>,
our_commitments: Vec<C::G>,
encryption: Encryption<C>,
@@ -274,7 +274,7 @@ impl<C: Ciphersuite> SecretShareMachine<C> {
&mut batch,
l,
msg.commitments[0],
challenge::<C>(&self.context, l, msg.sig.R.to_bytes().as_ref(), &msg.cached_msg),
challenge::<C>(self.context, l, msg.sig.R.to_bytes().as_ref(), &msg.cached_msg),
);
commitments.insert(l, msg.commitments.drain(..).collect::<Vec<_>>());
@@ -472,9 +472,10 @@ impl<C: Ciphersuite> KeyMachine<C> {
let KeyMachine { commitments, encryption, params, secret } = self;
Ok(BlameMachine {
commitments,
encryption,
encryption: encryption.into_decryption(),
result: Some(ThresholdCore {
params,
interpolation: Interpolation::Lagrange,
secret_share: secret,
group_key: stripes[0],
verification_shares,
@@ -486,7 +487,7 @@ impl<C: Ciphersuite> KeyMachine<C> {
/// A machine capable of handling blame proofs.
pub struct BlameMachine<C: Ciphersuite> {
commitments: HashMap<Participant, Vec<C::G>>,
encryption: Encryption<C>,
encryption: Decryption<C>,
result: Option<ThresholdCore<C>>,
}
@@ -505,7 +506,6 @@ impl<C: Ciphersuite> Zeroize for BlameMachine<C> {
for commitments in self.commitments.values_mut() {
commitments.zeroize();
}
self.encryption.zeroize();
self.result.zeroize();
}
}
@@ -598,14 +598,13 @@ impl<C: Ciphersuite> AdditionalBlameMachine<C> {
/// authenticated as having come from the supposed party and verified as valid. Usage of invalid
/// commitments is considered undefined behavior, and may cause everything from inaccurate blame
/// to panics.
pub fn new<R: RngCore + CryptoRng>(
rng: &mut R,
context: String,
pub fn new(
context: [u8; 32],
n: u16,
mut commitment_msgs: HashMap<Participant, EncryptionKeyMessage<C, Commitments<C>>>,
) -> Result<Self, FrostError<C>> {
let mut commitments = HashMap::new();
let mut encryption = Encryption::new(context, None, rng);
let mut encryption = Decryption::new(context);
for i in 1 ..= n {
let i = Participant::new(i).unwrap();
let Some(msg) = commitment_msgs.remove(&i) else { Err(DkgError::MissingParticipant(i))? };

1
crypto/dkg/src/promote.rs
View File

@@ -113,6 +113,7 @@ impl<C1: Ciphersuite, C2: Ciphersuite<F = C1::F, G = C1::G>> GeneratorPromotion<
Ok(ThresholdKeys {
core: Arc::new(ThresholdCore::new(
params,
self.base.core.interpolation.clone(),
self.base.secret_share().clone(),
verification_shares,
)),

79
crypto/dkg/src/tests/evrf/mod.rs Normal file
View File

@@ -0,0 +1,79 @@
use std::collections::HashMap;
use zeroize::Zeroizing;
use rand_core::OsRng;
use rand::seq::SliceRandom;
use ciphersuite::{group::ff::Field, Ciphersuite};
use crate::{
Participant,
evrf::*,
tests::{THRESHOLD, PARTICIPANTS, recover_key},
};
mod proof;
use proof::{Pallas, Vesta};
#[test]
fn evrf_dkg() {
let generators = EvrfGenerators::<Pallas>::new(THRESHOLD, PARTICIPANTS);
let context = [0; 32];
let mut priv_keys = vec![];
let mut pub_keys = vec![];
for i in 0 .. PARTICIPANTS {
let priv_key = <Vesta as Ciphersuite>::F::random(&mut OsRng);
pub_keys.push(<Vesta as Ciphersuite>::generator() * priv_key);
priv_keys.push((Participant::new(1 + i).unwrap(), Zeroizing::new(priv_key)));
}
let mut participations = HashMap::new();
// Shuffle the private keys so we iterate over a random subset of them
priv_keys.shuffle(&mut OsRng);
for (i, priv_key) in priv_keys.iter().take(usize::from(THRESHOLD)) {
participations.insert(
*i,
EvrfDkg::<Pallas>::participate(
&mut OsRng,
&generators,
context,
THRESHOLD,
&pub_keys,
priv_key,
)
.unwrap(),
);
}
let VerifyResult::Valid(dkg) = EvrfDkg::<Pallas>::verify(
&mut OsRng,
&generators,
context,
THRESHOLD,
&pub_keys,
&participations,
)
.unwrap() else {
panic!("verify didn't return VerifyResult::Valid")
};
let mut group_key = None;
let mut verification_shares = None;
let mut all_keys = HashMap::new();
for (i, priv_key) in priv_keys {
let keys = dkg.keys(&priv_key).into_iter().next().unwrap();
assert_eq!(keys.params().i(), i);
assert_eq!(keys.params().t(), THRESHOLD);
assert_eq!(keys.params().n(), PARTICIPANTS);
group_key = group_key.or(Some(keys.group_key()));
verification_shares = verification_shares.or(Some(keys.verification_shares()));
assert_eq!(Some(keys.group_key()), group_key);
assert_eq!(Some(keys.verification_shares()), verification_shares);
all_keys.insert(i, keys);
}
// TODO: Test for all possible combinations of keys
assert_eq!(Pallas::generator() * recover_key(&all_keys), group_key.unwrap());
}

118
crypto/dkg/src/tests/evrf/proof.rs Normal file
View File

@@ -0,0 +1,118 @@
use std::time::Instant;
use rand_core::OsRng;
use zeroize::{Zeroize, Zeroizing};
use generic_array::typenum::{Sum, Diff, Quot, U, U1, U2};
use blake2::{Digest, Blake2b512};
use ciphersuite::{
group::{
ff::{FromUniformBytes, Field, PrimeField},
Group,
},
Ciphersuite, Secp256k1, Ed25519, Ristretto,
};
use pasta_curves::{Ep, Eq, Fp, Fq};
use generalized_bulletproofs::tests::generators;
use generalized_bulletproofs_ec_gadgets::DiscreteLogParameters;
use crate::evrf::proof::*;
#[derive(Clone, Copy, PartialEq, Eq, Debug, Zeroize)]
pub(crate) struct Pallas;
impl Ciphersuite for Pallas {
type F = Fq;
type G = Ep;
type H = Blake2b512;
const ID: &'static [u8] = b"Pallas";
fn generator() -> Ep {
Ep::generator()
}
fn hash_to_F(dst: &[u8], msg: &[u8]) -> Self::F {
// This naive concat may be insecure in a real world deployment
// This is solely test code so it's fine
Self::F::from_uniform_bytes(&Self::H::digest([dst, msg].concat()).into())
}
}
#[derive(Clone, Copy, PartialEq, Eq, Debug, Zeroize)]
pub(crate) struct Vesta;
impl Ciphersuite for Vesta {
type F = Fp;
type G = Eq;
type H = Blake2b512;
const ID: &'static [u8] = b"Vesta";
fn generator() -> Eq {
Eq::generator()
}
fn hash_to_F(dst: &[u8], msg: &[u8]) -> Self::F {
// This naive concat may be insecure in a real world deployment
// This is solely test code so it's fine
Self::F::from_uniform_bytes(&Self::H::digest([dst, msg].concat()).into())
}
}
pub struct VestaParams;
impl DiscreteLogParameters for VestaParams {
type ScalarBits = U<{ <<Vesta as Ciphersuite>::F as PrimeField>::NUM_BITS as usize }>;
type XCoefficients = Quot<Sum<Self::ScalarBits, U1>, U2>;
type XCoefficientsMinusOne = Diff<Self::XCoefficients, U1>;
type YxCoefficients = Diff<Quot<Sum<Sum<Self::ScalarBits, U1>, U1>, U2>, U2>;
}
impl EvrfCurve for Pallas {
type EmbeddedCurve = Vesta;
type EmbeddedCurveParameters = VestaParams;
}
fn evrf_proof_test<C: EvrfCurve>() {
let generators = generators(1024);
let vesta_private_key = Zeroizing::new(<C::EmbeddedCurve as Ciphersuite>::F::random(&mut OsRng));
let ecdh_public_keys = [
<C::EmbeddedCurve as Ciphersuite>::G::random(&mut OsRng),
<C::EmbeddedCurve as Ciphersuite>::G::random(&mut OsRng),
];
let time = Instant::now();
let res =
Evrf::<C>::prove(&mut OsRng, &generators, [0; 32], 1, &ecdh_public_keys, &vesta_private_key)
.unwrap();
println!("Proving time: {:?}", time.elapsed());
let time = Instant::now();
let mut verifier = generators.batch_verifier();
Evrf::<C>::verify(
&mut OsRng,
&generators,
&mut verifier,
[0; 32],
1,
&ecdh_public_keys,
C::EmbeddedCurve::generator() * *vesta_private_key,
&res.proof,
)
.unwrap();
assert!(generators.verify(verifier));
println!("Verifying time: {:?}", time.elapsed());
}
#[test]
fn pallas_evrf_proof_test() {
evrf_proof_test::<Pallas>();
}
#[test]
fn secp256k1_evrf_proof_test() {
evrf_proof_test::<Secp256k1>();
}
#[test]
fn ed25519_evrf_proof_test() {
evrf_proof_test::<Ed25519>();
}
#[test]
fn ristretto_evrf_proof_test() {
evrf_proof_test::<Ristretto>();
}

8
crypto/dkg/src/tests/mod.rs
View File

@@ -6,7 +6,7 @@ use rand_core::{RngCore, CryptoRng};
use ciphersuite::{group::ff::Field, Ciphersuite};
use crate::{Participant, ThresholdCore, ThresholdKeys, lagrange, musig::musig as musig_fn};
use crate::{Participant, ThresholdCore, ThresholdKeys, musig::musig as musig_fn};
mod musig;
pub use musig::test_musig;
@@ -19,6 +19,9 @@ use pedpop::pedpop_gen;
mod promote;
use promote::test_generator_promotion;
#[cfg(all(test, feature = "evrf"))]
mod evrf;
/// Constant amount of participants to use when testing.
pub const PARTICIPANTS: u16 = 5;
/// Constant threshold of participants to use when testing.
@@ -43,7 +46,8 @@ pub fn recover_key<C: Ciphersuite>(keys: &HashMap<Participant, ThresholdKeys<C>>
let included = keys.keys().copied().collect::<Vec<_>>();
let group_private = keys.iter().fold(C::F::ZERO, |accum, (i, keys)| {
accum + (lagrange::<C::F>(*i, &included) * keys.secret_share().deref())
accum +
(first.core.interpolation.interpolation_factor(*i, &included) * keys.secret_share().deref())
});
assert_eq!(C::generator() * group_private, first.group_key(), "failed to recover keys");
group_private

18
crypto/dkg/src/tests/pedpop.rs
View File

@@ -14,7 +14,7 @@ use crate::{
type PedPoPEncryptedMessage<C> = EncryptedMessage<C, SecretShare<<C as Ciphersuite>::F>>;
type PedPoPSecretShares<C> = HashMap<Participant, PedPoPEncryptedMessage<C>>;
const CONTEXT: &str = "DKG Test Key Generation";
const CONTEXT: [u8; 32] = *b"DKG Test Key Generation ";
// Commit, then return commitment messages, enc keys, and shares
#[allow(clippy::type_complexity)]
@@ -31,7 +31,7 @@ fn commit_enc_keys_and_shares<R: RngCore + CryptoRng, C: Ciphersuite>(
let mut enc_keys = HashMap::new();
for i in (1 ..= PARTICIPANTS).map(Participant) {
let params = ThresholdParams::new(THRESHOLD, PARTICIPANTS, i).unwrap();
let machine = KeyGenMachine::<C>::new(params, CONTEXT.to_string());
let machine = KeyGenMachine::<C>::new(params, CONTEXT);
let (machine, these_commitments) = machine.generate_coefficients(rng);
machines.insert(i, machine);
@@ -147,14 +147,12 @@ mod literal {
// Verify machines constructed with AdditionalBlameMachine::new work
assert_eq!(
AdditionalBlameMachine::new(
&mut OsRng,
CONTEXT.to_string(),
PARTICIPANTS,
commitment_msgs.clone()
)
.unwrap()
.blame(ONE, TWO, msg.clone(), blame.clone()),
AdditionalBlameMachine::new(CONTEXT, PARTICIPANTS, commitment_msgs.clone()).unwrap().blame(
ONE,
TWO,
msg.clone(),
blame.clone()
),
ONE,
);
}

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[package]
name = "generalized-bulletproofs-circuit-abstraction"
version = "0.1.0"
description = "An abstraction for arithmetic circuits over Generalized Bulletproofs"
license = "MIT"
repository = "https://github.com/serai-dex/serai/tree/develop/crypto/evrf/circuit-abstraction"
authors = ["Luke Parker <lukeparker5132@gmail.com>"]
keywords = ["bulletproofs", "circuit"]
edition = "2021"
[package.metadata.docs.rs]
all-features = true
rustdoc-args = ["--cfg", "docsrs"]
[dependencies]
zeroize = { version = "^1.5", default-features = false, features = ["zeroize_derive"] }
ciphersuite = { path = "../../ciphersuite", version = "0.4", default-features = false, features = ["std"] }
generalized-bulletproofs = { path = "../generalized-bulletproofs" }

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MIT License
Copyright (c) 2024 Luke Parker
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.

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# Generalized Bulletproofs Circuit Abstraction
A circuit abstraction around `generalized-bulletproofs`.

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use ciphersuite::{group::ff::Field, Ciphersuite};
use crate::*;
impl<C: Ciphersuite> Circuit<C> {
/// Constrain two linear combinations to be equal.
pub fn equality(&mut self, a: LinComb<C::F>, b: &LinComb<C::F>) {
self.constrain_equal_to_zero(a - b);
}
/// Calculate (and constrain) the inverse of a value.
///
/// A linear combination may optionally be passed as a constraint for the value being inverted.
/// A reference to the inverted value and its inverse is returned.
///
/// May panic if any linear combinations reference non-existent terms, the witness isn't provided
/// when proving/is provided when verifying, or if the witness is 0 (and accordingly doesn't have
/// an inverse).
pub fn inverse(
&mut self,
lincomb: Option<LinComb<C::F>>,
witness: Option<C::F>,
) -> (Variable, Variable) {
let (l, r, o) = self.mul(lincomb, None, witness.map(|f| (f, f.invert().unwrap())));
// The output of a value multiplied by its inverse is 1
// Constrain `1 o - 1 = 0`
self.constrain_equal_to_zero(LinComb::from(o).constant(-C::F::ONE));
(l, r)
}
/// Constrain two linear combinations as inequal.
///
/// May panic if any linear combinations reference non-existent terms.
pub fn inequality(&mut self, a: LinComb<C::F>, b: &LinComb<C::F>, witness: Option<(C::F, C::F)>) {
let l_constraint = a - b;
// The existence of a multiplicative inverse means a-b != 0, which means a != b
self.inverse(Some(l_constraint), witness.map(|(a, b)| a - b));
}
}

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#![cfg_attr(docsrs, feature(doc_auto_cfg))]
#![doc = include_str!("../README.md")]
#![deny(missing_docs)]
#![allow(non_snake_case)]
use zeroize::{Zeroize, ZeroizeOnDrop};
use ciphersuite::{
group::ff::{Field, PrimeField},
Ciphersuite,
};
use generalized_bulletproofs::{
ScalarVector, PedersenCommitment, PedersenVectorCommitment, ProofGenerators,
transcript::{Transcript as ProverTranscript, VerifierTranscript, Commitments},
arithmetic_circuit_proof::{AcError, ArithmeticCircuitStatement, ArithmeticCircuitWitness},
};
pub use generalized_bulletproofs::arithmetic_circuit_proof::{Variable, LinComb};
mod gadgets;
/// A trait for the transcript, whether proving for verifying, as necessary for sampling
/// challenges.
pub trait Transcript {
/// Sample a challenge from the transacript.
///
/// It is the caller's responsibility to have properly transcripted all variables prior to
/// sampling this challenge.
fn challenge<F: PrimeField>(&mut self) -> F;
}
impl Transcript for ProverTranscript {
fn challenge<F: PrimeField>(&mut self) -> F {
self.challenge()
}
}
impl Transcript for VerifierTranscript<'_> {
fn challenge<F: PrimeField>(&mut self) -> F {
self.challenge()
}
}
/// The witness for the satisfaction of this circuit.
#[derive(Clone, PartialEq, Eq, Debug, Zeroize, ZeroizeOnDrop)]
struct ProverData<C: Ciphersuite> {
aL: Vec<C::F>,
aR: Vec<C::F>,
C: Vec<PedersenVectorCommitment<C>>,
V: Vec<PedersenCommitment<C>>,
}
/// A struct representing a circuit.
#[derive(Clone, PartialEq, Eq, Debug)]
pub struct Circuit<C: Ciphersuite> {
muls: usize,
// A series of linear combinations which must evaluate to 0.
constraints: Vec<LinComb<C::F>>,
prover: Option<ProverData<C>>,
}
impl<C: Ciphersuite> Circuit<C> {
/// Returns the amount of multiplications used by this circuit.
pub fn muls(&self) -> usize {
self.muls
}
/// Create an instance to prove satisfaction of a circuit with.
// TODO: Take the transcript here
#[allow(clippy::type_complexity)]
pub fn prove(
vector_commitments: Vec<PedersenVectorCommitment<C>>,
commitments: Vec<PedersenCommitment<C>>,
) -> Self {
Self {
muls: 0,
constraints: vec![],
prover: Some(ProverData { aL: vec![], aR: vec![], C: vector_commitments, V: commitments }),
}
}
/// Create an instance to verify a proof with.
// TODO: Take the transcript here
pub fn verify() -> Self {
Self { muls: 0, constraints: vec![], prover: None }
}
/// Evaluate a linear combination.
///
/// Yields WL aL + WR aR + WO aO + WCG CG + WCH CH + WV V + c.
///
/// May panic if the linear combination references non-existent terms.
///
/// Returns None if not a prover.
pub fn eval(&self, lincomb: &LinComb<C::F>) -> Option<C::F> {
self.prover.as_ref().map(|prover| {
let mut res = lincomb.c();
for (index, weight) in lincomb.WL() {
res += prover.aL[*index] * weight;
}
for (index, weight) in lincomb.WR() {
res += prover.aR[*index] * weight;
}
for (index, weight) in lincomb.WO() {
res += prover.aL[*index] * prover.aR[*index] * weight;
}
for (WCG, C) in lincomb.WCG().iter().zip(&prover.C) {
for (j, weight) in WCG {
res += C.g_values[*j] * weight;
}
}
for (WCH, C) in lincomb.WCH().iter().zip(&prover.C) {
for (j, weight) in WCH {
res += C.h_values[*j] * weight;
}
}
for (index, weight) in lincomb.WV() {
res += prover.V[*index].value * weight;
}
res
})
}
/// Multiply two values, optionally constrained, returning the constrainable left/right/out
/// terms.
///
/// May panic if any linear combinations reference non-existent terms or if the witness isn't
/// provided when proving/is provided when verifying.
pub fn mul(
&mut self,
a: Option<LinComb<C::F>>,
b: Option<LinComb<C::F>>,
witness: Option<(C::F, C::F)>,
) -> (Variable, Variable, Variable) {
let l = Variable::aL(self.muls);
let r = Variable::aR(self.muls);
let o = Variable::aO(self.muls);
self.muls += 1;
debug_assert_eq!(self.prover.is_some(), witness.is_some());
if let Some(witness) = witness {
let prover = self.prover.as_mut().unwrap();
prover.aL.push(witness.0);
prover.aR.push(witness.1);
}
if let Some(a) = a {
self.constrain_equal_to_zero(a.term(-C::F::ONE, l));
}
if let Some(b) = b {
self.constrain_equal_to_zero(b.term(-C::F::ONE, r));
}
(l, r, o)
}
/// Constrain a linear combination to be equal to 0.
///
/// May panic if the linear combination references non-existent terms.
pub fn constrain_equal_to_zero(&mut self, lincomb: LinComb<C::F>) {
self.constraints.push(lincomb);
}
/// Obtain the statement for this circuit.
///
/// If configured as the prover, the witness to use is also returned.
#[allow(clippy::type_complexity)]
pub fn statement(
self,
generators: ProofGenerators<'_, C>,
commitments: Commitments<C>,
) -> Result<(ArithmeticCircuitStatement<'_, C>, Option<ArithmeticCircuitWitness<C>>), AcError> {
let statement = ArithmeticCircuitStatement::new(generators, self.constraints, commitments)?;
let witness = self
.prover
.map(|mut prover| {
// We can't deconstruct the witness as it implements Drop (per ZeroizeOnDrop)
// Accordingly, we take the values within it and move forward with those
let mut aL = vec![];
std::mem::swap(&mut prover.aL, &mut aL);
let mut aR = vec![];
std::mem::swap(&mut prover.aR, &mut aR);
let mut C = vec![];
std::mem::swap(&mut prover.C, &mut C);
let mut V = vec![];
std::mem::swap(&mut prover.V, &mut V);
ArithmeticCircuitWitness::new(ScalarVector::from(aL), ScalarVector::from(aR), C, V)
})
.transpose()?;
Ok((statement, witness))
}
}

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[package]
name = "ec-divisors"
version = "0.1.0"
description = "A library for calculating elliptic curve divisors"
license = "MIT"
repository = "https://github.com/serai-dex/serai/tree/develop/crypto/evrf/divisors"
authors = ["Luke Parker <lukeparker5132@gmail.com>"]
keywords = ["ciphersuite", "ff", "group"]
edition = "2021"
[package.metadata.docs.rs]
all-features = true
rustdoc-args = ["--cfg", "docsrs"]
[dependencies]
rand_core = { version = "0.6", default-features = false }
zeroize = { version = "^1.5", default-features = false, features = ["zeroize_derive"] }
group = "0.13"
hex = { version = "0.4", optional = true }
dalek-ff-group = { path = "../../dalek-ff-group", features = ["std"], optional = true }
pasta_curves = { version = "0.5", default-features = false, features = ["bits", "alloc"], optional = true }
[dev-dependencies]
rand_core = { version = "0.6", features = ["getrandom"] }
hex = "0.4"
dalek-ff-group = { path = "../../dalek-ff-group", features = ["std"] }
pasta_curves = { version = "0.5", default-features = false, features = ["bits", "alloc"] }
[features]
ed25519 = ["hex", "dalek-ff-group"]
pasta = ["pasta_curves"]

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MIT License
Copyright (c) 2023-2024 Luke Parker
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.

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# Elliptic Curve Divisors
An implementation of a representation for and construction of elliptic curve
divisors, intended for Eagen's [EC IP work](https://eprint.iacr.org/2022/596).

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#![cfg_attr(docsrs, feature(doc_auto_cfg))]
#![doc = include_str!("../README.md")]
#![deny(missing_docs)]
#![allow(non_snake_case)]
use group::{
ff::{Field, PrimeField},
Group,
};
mod poly;
pub use poly::*;
#[cfg(test)]
mod tests;
/// A curve usable with this library.
pub trait DivisorCurve: Group {
/// An element of the field this curve is defined over.
type FieldElement: PrimeField;
/// The A in the curve equation y^2 = x^3 + A x + B.
fn a() -> Self::FieldElement;
/// The B in the curve equation y^2 = x^3 + A x + B.
fn b() -> Self::FieldElement;
/// y^2 - x^3 - A x - B
///
/// Section 2 of the security proofs define this modulus.
///
/// This MUST NOT be overriden.
// TODO: Move to an extension trait
fn divisor_modulus() -> Poly<Self::FieldElement> {
Poly {
// 0 y**1, 1 y*2
y_coefficients: vec![Self::FieldElement::ZERO, Self::FieldElement::ONE],
yx_coefficients: vec![],
x_coefficients: vec![
// - A x
-Self::a(),
// 0 x^2
Self::FieldElement::ZERO,
// - x^3
-Self::FieldElement::ONE,
],
// - B
zero_coefficient: -Self::b(),
}
}
/// Convert a point to its x and y coordinates.
///
/// Returns None if passed the point at infinity.
fn to_xy(point: Self) -> Option<(Self::FieldElement, Self::FieldElement)>;
}
/// Calculate the slope and intercept between two points.
///
/// This function panics when `a @ infinity`, `b @ infinity`, `a == b`, or when `a == -b`.
pub(crate) fn slope_intercept<C: DivisorCurve>(a: C, b: C) -> (C::FieldElement, C::FieldElement) {
let (ax, ay) = C::to_xy(a).unwrap();
debug_assert_eq!(C::divisor_modulus().eval(ax, ay), C::FieldElement::ZERO);
let (bx, by) = C::to_xy(b).unwrap();
debug_assert_eq!(C::divisor_modulus().eval(bx, by), C::FieldElement::ZERO);
let slope = (by - ay) *
Option::<C::FieldElement>::from((bx - ax).invert())
.expect("trying to get slope/intercept of points sharing an x coordinate");
let intercept = by - (slope * bx);
debug_assert!(bool::from((ay - (slope * ax) - intercept).is_zero()));
debug_assert!(bool::from((by - (slope * bx) - intercept).is_zero()));
(slope, intercept)
}
// The line interpolating two points.
fn line<C: DivisorCurve>(a: C, mut b: C) -> Poly<C::FieldElement> {
// If they're both the point at infinity, we simply set the line to one
if bool::from(a.is_identity() & b.is_identity()) {
return Poly {
y_coefficients: vec![],
yx_coefficients: vec![],
x_coefficients: vec![],
zero_coefficient: C::FieldElement::ONE,
};
}
// If either point is the point at infinity, or these are additive inverses, the line is
// `1 * x - x`. The first `x` is a term in the polynomial, the `x` is the `x` coordinate of these
// points (of which there is one, as the second point is either at infinity or has a matching `x`
// coordinate).
if bool::from(a.is_identity() | b.is_identity()) || (a == -b) {
let (x, _) = C::to_xy(if !bool::from(a.is_identity()) { a } else { b }).unwrap();
return Poly {
y_coefficients: vec![],
yx_coefficients: vec![],
x_coefficients: vec![C::FieldElement::ONE],
zero_coefficient: -x,
};
}
// If the points are equal, we use the line interpolating the sum of these points with the point
// at infinity
if a == b {
b = -a.double();
}
let (slope, intercept) = slope_intercept::<C>(a, b);
// Section 4 of the proofs explicitly state the line `L = y - lambda * x - mu`
// y - (slope * x) - intercept
Poly {
y_coefficients: vec![C::FieldElement::ONE],
yx_coefficients: vec![],
x_coefficients: vec![-slope],
zero_coefficient: -intercept,
}
}
/// Create a divisor interpolating the following points.
///
/// Returns None if:
/// - No points were passed in
/// - The points don't sum to the point at infinity
/// - A passed in point was the point at infinity
#[allow(clippy::new_ret_no_self)]
pub fn new_divisor<C: DivisorCurve>(points: &[C]) -> Option<Poly<C::FieldElement>> {
// A single point is either the point at infinity, or this doesn't sum to the point at infinity
// Both cause us to return None
if points.len() < 2 {
None?;
}
if points.iter().sum::<C>() != C::identity() {
None?;
}
// Create the initial set of divisors
let mut divs = vec![];
let mut iter = points.iter().copied();
while let Some(a) = iter.next() {
if a == C::identity() {
None?;
}
let b = iter.next();
if b == Some(C::identity()) {
None?;
}
// Draw the line between those points
divs.push((a + b.unwrap_or(C::identity()), line::<C>(a, b.unwrap_or(-a))));
}
let modulus = C::divisor_modulus();
// Pair them off until only one remains
while divs.len() > 1 {
let mut next_divs = vec![];
// If there's an odd amount of divisors, carry the odd one out to the next iteration
if (divs.len() % 2) == 1 {
next_divs.push(divs.pop().unwrap());
}
while let Some((a, a_div)) = divs.pop() {
let (b, b_div) = divs.pop().unwrap();
// Merge the two divisors
let numerator = a_div.mul_mod(b_div, &modulus).mul_mod(line::<C>(a, b), &modulus);
let denominator = line::<C>(a, -a).mul_mod(line::<C>(b, -b), &modulus);
let (q, r) = numerator.div_rem(&denominator);
assert_eq!(r, Poly::zero());
next_divs.push((a + b, q));
}
divs = next_divs;
}
// Return the unified divisor
Some(divs.remove(0).1)
}
#[cfg(any(test, feature = "pasta"))]
mod pasta {
use group::{ff::Field, Curve};
use pasta_curves::{
arithmetic::{Coordinates, CurveAffine},
Ep, Fp, Eq, Fq,
};
use crate::DivisorCurve;
impl DivisorCurve for Ep {
type FieldElement = Fp;
fn a() -> Self::FieldElement {
Self::FieldElement::ZERO
}
fn b() -> Self::FieldElement {
Self::FieldElement::from(5u64)
}
fn to_xy(point: Self) -> Option<(Self::FieldElement, Self::FieldElement)> {
Option::<Coordinates<_>>::from(point.to_affine().coordinates())
.map(|coords| (*coords.x(), *coords.y()))
}
}
impl DivisorCurve for Eq {
type FieldElement = Fq;
fn a() -> Self::FieldElement {
Self::FieldElement::ZERO
}
fn b() -> Self::FieldElement {
Self::FieldElement::from(5u64)
}
fn to_xy(point: Self) -> Option<(Self::FieldElement, Self::FieldElement)> {
Option::<Coordinates<_>>::from(point.to_affine().coordinates())
.map(|coords| (*coords.x(), *coords.y()))
}
}
}
#[cfg(any(test, feature = "ed25519"))]
mod ed25519 {
use group::{
ff::{Field, PrimeField},
Group, GroupEncoding,
};
use dalek_ff_group::{FieldElement, EdwardsPoint};
impl crate::DivisorCurve for EdwardsPoint {
type FieldElement = FieldElement;
// Wei25519 a/b
// https://www.ietf.org/archive/id/draft-ietf-lwig-curve-representations-02.pdf E.3
fn a() -> Self::FieldElement {
let mut be_bytes =
hex::decode("2aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa984914a144").unwrap();
be_bytes.reverse();
let le_bytes = be_bytes;
Self::FieldElement::from_repr(le_bytes.try_into().unwrap()).unwrap()
}
fn b() -> Self::FieldElement {
let mut be_bytes =
hex::decode("7b425ed097b425ed097b425ed097b425ed097b425ed097b4260b5e9c7710c864").unwrap();
be_bytes.reverse();
let le_bytes = be_bytes;
Self::FieldElement::from_repr(le_bytes.try_into().unwrap()).unwrap()
}
// https://www.ietf.org/archive/id/draft-ietf-lwig-curve-representations-02.pdf E.2
fn to_xy(point: Self) -> Option<(Self::FieldElement, Self::FieldElement)> {
if bool::from(point.is_identity()) {
None?;
}
// Extract the y coordinate from the compressed point
let mut edwards_y = point.to_bytes();
let x_is_odd = edwards_y[31] >> 7;
edwards_y[31] &= (1 << 7) - 1;
let edwards_y = Self::FieldElement::from_repr(edwards_y).unwrap();
// Recover the x coordinate
let edwards_y_sq = edwards_y * edwards_y;
let D = -Self::FieldElement::from(121665u64) *
Self::FieldElement::from(121666u64).invert().unwrap();
let mut edwards_x = ((edwards_y_sq - Self::FieldElement::ONE) *
((D * edwards_y_sq) + Self::FieldElement::ONE).invert().unwrap())
.sqrt()
.unwrap();
if u8::from(bool::from(edwards_x.is_odd())) != x_is_odd {
edwards_x = -edwards_x;
}
// Calculate the x and y coordinates for Wei25519
let edwards_y_plus_one = Self::FieldElement::ONE + edwards_y;
let one_minus_edwards_y = Self::FieldElement::ONE - edwards_y;
let wei_x = (edwards_y_plus_one * one_minus_edwards_y.invert().unwrap()) +
(Self::FieldElement::from(486662u64) * Self::FieldElement::from(3u64).invert().unwrap());
let c =
(-(Self::FieldElement::from(486662u64) + Self::FieldElement::from(2u64))).sqrt().unwrap();
let wei_y = c * edwards_y_plus_one * (one_minus_edwards_y * edwards_x).invert().unwrap();
Some((wei_x, wei_y))
}
}
}

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use core::ops::{Add, Neg, Sub, Mul, Rem};
use zeroize::Zeroize;
use group::ff::PrimeField;
/// A structure representing a Polynomial with x**i, y**i, and y**i * x**j terms.
#[derive(Clone, PartialEq, Eq, Debug, Zeroize)]
pub struct Poly<F: PrimeField + From<u64>> {
/// c[i] * y ** (i + 1)
pub y_coefficients: Vec<F>,
/// c[i][j] * y ** (i + 1) x ** (j + 1)
pub yx_coefficients: Vec<Vec<F>>,
/// c[i] * x ** (i + 1)
pub x_coefficients: Vec<F>,
/// Coefficient for x ** 0, y ** 0, and x ** 0 y ** 0 (the coefficient for 1)
pub zero_coefficient: F,
}
impl<F: PrimeField + From<u64>> Poly<F> {
/// A polynomial for zero.
pub fn zero() -> Self {
Poly {
y_coefficients: vec![],
yx_coefficients: vec![],
x_coefficients: vec![],
zero_coefficient: F::ZERO,
}
}
/// The amount of terms in the polynomial.
#[allow(clippy::len_without_is_empty)]
#[must_use]
pub fn len(&self) -> usize {
self.y_coefficients.len() +
self.yx_coefficients.iter().map(Vec::len).sum::<usize>() +
self.x_coefficients.len() +
usize::from(u8::from(self.zero_coefficient != F::ZERO))
}
// Remove high-order zero terms, allowing the length of the vectors to equal the amount of terms.
pub(crate) fn tidy(&mut self) {
let tidy = |vec: &mut Vec<F>| {
while vec.last() == Some(&F::ZERO) {
vec.pop();
}
};
tidy(&mut self.y_coefficients);
for vec in self.yx_coefficients.iter_mut() {
tidy(vec);
}
while self.yx_coefficients.last() == Some(&vec![]) {
self.yx_coefficients.pop();
}
tidy(&mut self.x_coefficients);
}
}
impl<F: PrimeField + From<u64>> Add<&Self> for Poly<F> {
type Output = Self;
fn add(mut self, other: &Self) -> Self {
// Expand to be the neeeded size
while self.y_coefficients.len() < other.y_coefficients.len() {
self.y_coefficients.push(F::ZERO);
}
while self.yx_coefficients.len() < other.yx_coefficients.len() {
self.yx_coefficients.push(vec![]);
}
for i in 0 .. other.yx_coefficients.len() {
while self.yx_coefficients[i].len() < other.yx_coefficients[i].len() {
self.yx_coefficients[i].push(F::ZERO);
}
}
while self.x_coefficients.len() < other.x_coefficients.len() {
self.x_coefficients.push(F::ZERO);
}
// Perform the addition
for (i, coeff) in other.y_coefficients.iter().enumerate() {
self.y_coefficients[i] += coeff;
}
for (i, coeffs) in other.yx_coefficients.iter().enumerate() {
for (j, coeff) in coeffs.iter().enumerate() {
self.yx_coefficients[i][j] += coeff;
}
}
for (i, coeff) in other.x_coefficients.iter().enumerate() {
self.x_coefficients[i] += coeff;
}
self.zero_coefficient += other.zero_coefficient;
self.tidy();
self
}
}
impl<F: PrimeField + From<u64>> Neg for Poly<F> {
type Output = Self;
fn neg(mut self) -> Self {
for y_coeff in self.y_coefficients.iter_mut() {
*y_coeff = -*y_coeff;
}
for yx_coeffs in self.yx_coefficients.iter_mut() {
for yx_coeff in yx_coeffs.iter_mut() {
*yx_coeff = -*yx_coeff;
}
}
for x_coeff in self.x_coefficients.iter_mut() {
*x_coeff = -*x_coeff;
}
self.zero_coefficient = -self.zero_coefficient;
self
}
}
impl<F: PrimeField + From<u64>> Sub for Poly<F> {
type Output = Self;
fn sub(self, other: Self) -> Self {
self + &-other
}
}
impl<F: PrimeField + From<u64>> Mul<F> for Poly<F> {
type Output = Self;
fn mul(mut self, scalar: F) -> Self {
if scalar == F::ZERO {
return Poly::zero();
}
for y_coeff in self.y_coefficients.iter_mut() {
*y_coeff *= scalar;
}
for coeffs in self.yx_coefficients.iter_mut() {
for coeff in coeffs.iter_mut() {
*coeff *= scalar;
}
}
for x_coeff in self.x_coefficients.iter_mut() {
*x_coeff *= scalar;
}
self.zero_coefficient *= scalar;
self
}
}
impl<F: PrimeField + From<u64>> Poly<F> {
#[must_use]
fn shift_by_x(mut self, power_of_x: usize) -> Self {
if power_of_x == 0 {
return self;
}
// Shift up every x coefficient
for _ in 0 .. power_of_x {
self.x_coefficients.insert(0, F::ZERO);
for yx_coeffs in &mut self.yx_coefficients {
yx_coeffs.insert(0, F::ZERO);
}
}
// Move the zero coefficient
self.x_coefficients[power_of_x - 1] = self.zero_coefficient;
self.zero_coefficient = F::ZERO;
// Move the y coefficients
// Start by creating yx coefficients with the necessary powers of x
let mut yx_coefficients_to_push = vec![];
while yx_coefficients_to_push.len() < power_of_x {
yx_coefficients_to_push.push(F::ZERO);
}
// Now, ensure the yx coefficients has the slots for the y coefficients we're moving
while self.yx_coefficients.len() < self.y_coefficients.len() {
self.yx_coefficients.push(yx_coefficients_to_push.clone());
}
// Perform the move
for (i, y_coeff) in self.y_coefficients.drain(..).enumerate() {
self.yx_coefficients[i][power_of_x - 1] = y_coeff;
}
self
}
#[must_use]
fn shift_by_y(mut self, power_of_y: usize) -> Self {
if power_of_y == 0 {
return self;
}
// Shift up every y coefficient
for _ in 0 .. power_of_y {
self.y_coefficients.insert(0, F::ZERO);
self.yx_coefficients.insert(0, vec![]);
}
// Move the zero coefficient
self.y_coefficients[power_of_y - 1] = self.zero_coefficient;
self.zero_coefficient = F::ZERO;
// Move the x coefficients
self.yx_coefficients[power_of_y - 1] = self.x_coefficients;
self.x_coefficients = vec![];
self
}
}
impl<F: PrimeField + From<u64>> Mul for Poly<F> {
type Output = Self;
fn mul(self, other: Self) -> Self {
let mut res = self.clone() * other.zero_coefficient;
for (i, y_coeff) in other.y_coefficients.iter().enumerate() {
let scaled = self.clone() * *y_coeff;
res = res + &scaled.shift_by_y(i + 1);
}
for (y_i, yx_coeffs) in other.yx_coefficients.iter().enumerate() {
for (x_i, yx_coeff) in yx_coeffs.iter().enumerate() {
let scaled = self.clone() * *yx_coeff;
res = res + &scaled.shift_by_y(y_i + 1).shift_by_x(x_i + 1);
}
}
for (i, x_coeff) in other.x_coefficients.iter().enumerate() {
let scaled = self.clone() * *x_coeff;
res = res + &scaled.shift_by_x(i + 1);
}
res.tidy();
res
}
}
impl<F: PrimeField + From<u64>> Poly<F> {
/// Perform multiplication mod `modulus`.
#[must_use]
pub fn mul_mod(self, other: Self, modulus: &Self) -> Self {
((self % modulus) * (other % modulus)) % modulus
}
/// Perform division, returning the result and remainder.
///
/// Panics upon division by zero, with undefined behavior if a non-tidy divisor is used.
#[must_use]
pub fn div_rem(self, divisor: &Self) -> (Self, Self) {
// The leading y coefficient and associated x coefficient.
let leading_y = |poly: &Self| -> (_, _) {
if poly.y_coefficients.len() > poly.yx_coefficients.len() {
(poly.y_coefficients.len(), 0)
} else if !poly.yx_coefficients.is_empty() {
(poly.yx_coefficients.len(), poly.yx_coefficients.last().unwrap().len())
} else {
(0, poly.x_coefficients.len())
}
};
let (div_y, div_x) = leading_y(divisor);
// If this divisor is actually a scalar, don't perform long division
if (div_y == 0) && (div_x == 0) {
return (self * divisor.zero_coefficient.invert().unwrap(), Poly::zero());
}
// Remove leading terms until the value is less than the divisor
let mut quotient: Poly<F> = Poly::zero();
let mut remainder = self.clone();
loop {
// If there's nothing left to divide, return
if remainder == Poly::zero() {
break;
}
let (rem_y, rem_x) = leading_y(&remainder);
if (rem_y < div_y) || (rem_x < div_x) {
break;
}
let get = |poly: &Poly<F>, y_pow: usize, x_pow: usize| -> F {
if (y_pow == 0) && (x_pow == 0) {
poly.zero_coefficient
} else if x_pow == 0 {
poly.y_coefficients[y_pow - 1]
} else if y_pow == 0 {
poly.x_coefficients[x_pow - 1]
} else {
poly.yx_coefficients[y_pow - 1][x_pow - 1]
}
};
let coeff_numerator = get(&remainder, rem_y, rem_x);
let coeff_denominator = get(divisor, div_y, div_x);
// We want coeff_denominator scaled by x to equal coeff_numerator
// x * d = n
// n / d = x
let mut quotient_term = Poly::zero();
// Because this is the coefficient for the leading term of a tidied polynomial, it must be
// non-zero
quotient_term.zero_coefficient = coeff_numerator * coeff_denominator.invert().unwrap();
// Add the necessary yx powers
let delta_y = rem_y - div_y;
let delta_x = rem_x - div_x;
let quotient_term = quotient_term.shift_by_y(delta_y).shift_by_x(delta_x);
let to_remove = quotient_term.clone() * divisor.clone();
debug_assert_eq!(get(&to_remove, rem_y, rem_x), coeff_numerator);
remainder = remainder - to_remove;
quotient = quotient + &quotient_term;
}
debug_assert_eq!((quotient.clone() * divisor.clone()) + &remainder, self);
(quotient, remainder)
}
}
impl<F: PrimeField + From<u64>> Rem<&Self> for Poly<F> {
type Output = Self;
fn rem(self, modulus: &Self) -> Self {
self.div_rem(modulus).1
}
}
impl<F: PrimeField + From<u64>> Poly<F> {
/// Evaluate this polynomial with the specified x/y values.
///
/// Panics on polynomials with terms whose powers exceed 2**64.
#[must_use]
pub fn eval(&self, x: F, y: F) -> F {
let mut res = self.zero_coefficient;
for (pow, coeff) in
self.y_coefficients.iter().enumerate().map(|(i, v)| (u64::try_from(i + 1).unwrap(), v))
{
res += y.pow([pow]) * coeff;
}
for (y_pow, coeffs) in
self.yx_coefficients.iter().enumerate().map(|(i, v)| (u64::try_from(i + 1).unwrap(), v))
{
let y_pow = y.pow([y_pow]);
for (x_pow, coeff) in
coeffs.iter().enumerate().map(|(i, v)| (u64::try_from(i + 1).unwrap(), v))
{
res += y_pow * x.pow([x_pow]) * coeff;
}
}
for (pow, coeff) in
self.x_coefficients.iter().enumerate().map(|(i, v)| (u64::try_from(i + 1).unwrap(), v))
{
res += x.pow([pow]) * coeff;
}
res
}
/// Differentiate a polynomial, reduced by a modulus with a leading y term y**2 x**0, by x and y.
///
/// This function panics if a y**2 term is present within the polynomial.
#[must_use]
pub fn differentiate(&self) -> (Poly<F>, Poly<F>) {
assert!(self.y_coefficients.len() <= 1);
assert!(self.yx_coefficients.len() <= 1);
// Differentation by x practically involves:
// - Dropping everything without an x component
// - Shifting everything down a power of x
// - Multiplying the new coefficient by the power it prior was used with
let diff_x = {
let mut diff_x = Poly {
y_coefficients: vec![],
yx_coefficients: vec![],
x_coefficients: vec![],
zero_coefficient: F::ZERO,
};
if !self.x_coefficients.is_empty() {
let mut x_coeffs = self.x_coefficients.clone();
diff_x.zero_coefficient = x_coeffs.remove(0);
diff_x.x_coefficients = x_coeffs;
let mut prior_x_power = F::from(2);
for x_coeff in &mut diff_x.x_coefficients {
*x_coeff *= prior_x_power;
prior_x_power += F::ONE;
}
}
if !self.yx_coefficients.is_empty() {
let mut yx_coeffs = self.yx_coefficients[0].clone();
diff_x.y_coefficients = vec![yx_coeffs.remove(0)];
diff_x.yx_coefficients = vec![yx_coeffs];
let mut prior_x_power = F::from(2);
for yx_coeff in &mut diff_x.yx_coefficients[0] {
*yx_coeff *= prior_x_power;
prior_x_power += F::ONE;
}
}
diff_x.tidy();
diff_x
};
// Differentation by y is trivial
// It's the y coefficient as the zero coefficient, and the yx coefficients as the x
// coefficients
// This is thanks to any y term over y^2 being reduced out
let diff_y = Poly {
y_coefficients: vec![],
yx_coefficients: vec![],
x_coefficients: self.yx_coefficients.first().cloned().unwrap_or(vec![]),
zero_coefficient: self.y_coefficients.first().cloned().unwrap_or(F::ZERO),
};
(diff_x, diff_y)
}
/// Normalize the x coefficient to 1.
///
/// Panics if there is no x coefficient to normalize or if it cannot be normalized to 1.
#[must_use]
pub fn normalize_x_coefficient(self) -> Self {
let scalar = self.x_coefficients[0].invert().unwrap();
self * scalar
}
}

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crypto/evrf/divisors/src/tests/mod.rs Normal file
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use rand_core::OsRng;
use group::{ff::Field, Group};
use dalek_ff_group::EdwardsPoint;
use pasta_curves::{Ep, Eq};
use crate::{DivisorCurve, Poly, new_divisor};
// Equation 4 in the security proofs
fn check_divisor<C: DivisorCurve>(points: Vec<C>) {
// Create the divisor
let divisor = new_divisor::<C>(&points).unwrap();
let eval = |c| {
let (x, y) = C::to_xy(c).unwrap();
divisor.eval(x, y)
};
// Decide challgenges
let c0 = C::random(&mut OsRng);
let c1 = C::random(&mut OsRng);
let c2 = -(c0 + c1);
let (slope, intercept) = crate::slope_intercept::<C>(c0, c1);
let mut rhs = <C as DivisorCurve>::FieldElement::ONE;
for point in points {
let (x, y) = C::to_xy(point).unwrap();
rhs *= intercept - (y - (slope * x));
}
assert_eq!(eval(c0) * eval(c1) * eval(c2), rhs);
}
fn test_divisor<C: DivisorCurve>() {
for i in 1 ..= 255 {
println!("Test iteration {i}");
// Select points
let mut points = vec![];
for _ in 0 .. i {
points.push(C::random(&mut OsRng));
}
points.push(-points.iter().sum::<C>());
println!("Points {}", points.len());
// Perform the original check
check_divisor(points.clone());
// Create the divisor
let divisor = new_divisor::<C>(&points).unwrap();
// For a divisor interpolating 256 points, as one does when interpreting a 255-bit discrete log
// with the result of its scalar multiplication against a fixed generator, the lengths of the
// yx/x coefficients shouldn't supersede the following bounds
assert!((divisor.yx_coefficients.first().unwrap_or(&vec![]).len()) <= 126);
assert!((divisor.x_coefficients.len() - 1) <= 127);
assert!(
(1 + divisor.yx_coefficients.first().unwrap_or(&vec![]).len() +
(divisor.x_coefficients.len() - 1) +
1) <=
255
);
// Decide challgenges
let c0 = C::random(&mut OsRng);
let c1 = C::random(&mut OsRng);
let c2 = -(c0 + c1);
let (slope, intercept) = crate::slope_intercept::<C>(c0, c1);
// Perform the Logarithmic derivative check
{
let dx_over_dz = {
let dx = Poly {
y_coefficients: vec![],
yx_coefficients: vec![],
x_coefficients: vec![C::FieldElement::ZERO, C::FieldElement::from(3)],
zero_coefficient: C::a(),
};
let dy = Poly {
y_coefficients: vec![C::FieldElement::from(2)],
yx_coefficients: vec![],
x_coefficients: vec![],
zero_coefficient: C::FieldElement::ZERO,
};
let dz = (dy.clone() * -slope) + &dx;
// We want dx/dz, and dz/dx is equal to dy/dx - slope
// Sagemath claims this, dy / dz, is the proper inverse
(dy, dz)
};
{
let sanity_eval = |c| {
let (x, y) = C::to_xy(c).unwrap();
dx_over_dz.0.eval(x, y) * dx_over_dz.1.eval(x, y).invert().unwrap()
};
let sanity = sanity_eval(c0) + sanity_eval(c1) + sanity_eval(c2);
// This verifies the dx/dz polynomial is correct
assert_eq!(sanity, C::FieldElement::ZERO);
}
// Logarithmic derivative check
let test = |divisor: Poly<_>| {
let (dx, dy) = divisor.differentiate();
let lhs = |c| {
let (x, y) = C::to_xy(c).unwrap();
let n_0 = (C::FieldElement::from(3) * (x * x)) + C::a();
let d_0 = (C::FieldElement::from(2) * y).invert().unwrap();
let p_0_n_0 = n_0 * d_0;
let n_1 = dy.eval(x, y);
let first = p_0_n_0 * n_1;
let second = dx.eval(x, y);
let d_1 = divisor.eval(x, y);
let fraction_1_n = first + second;
let fraction_1_d = d_1;
let fraction_2_n = dx_over_dz.0.eval(x, y);
let fraction_2_d = dx_over_dz.1.eval(x, y);
fraction_1_n * fraction_2_n * (fraction_1_d * fraction_2_d).invert().unwrap()
};
let lhs = lhs(c0) + lhs(c1) + lhs(c2);
let mut rhs = C::FieldElement::ZERO;
for point in &points {
let (x, y) = <C as DivisorCurve>::to_xy(*point).unwrap();
rhs += (intercept - (y - (slope * x))).invert().unwrap();
}
assert_eq!(lhs, rhs);
};
// Test the divisor and the divisor with a normalized x coefficient
test(divisor.clone());
test(divisor.normalize_x_coefficient());
}
}
}
fn test_same_point<C: DivisorCurve>() {
let mut points = vec![C::random(&mut OsRng)];
points.push(points[0]);
points.push(-points.iter().sum::<C>());
check_divisor(points);
}
fn test_subset_sum_to_infinity<C: DivisorCurve>() {
// Internally, a binary tree algorithm is used
// This executes the first pass to end up with [0, 0] for further reductions
{
let mut points = vec![C::random(&mut OsRng)];
points.push(-points[0]);
let next = C::random(&mut OsRng);
points.push(next);
points.push(-next);
check_divisor(points);
}
// This executes the first pass to end up with [0, X, -X, 0]
{
let mut points = vec![C::random(&mut OsRng)];
points.push(-points[0]);
let x_1 = C::random(&mut OsRng);
let x_2 = C::random(&mut OsRng);
points.push(x_1);
points.push(x_2);
points.push(-x_1);
points.push(-x_2);
let next = C::random(&mut OsRng);
points.push(next);
points.push(-next);
check_divisor(points);
}
}
#[test]
fn test_divisor_pallas() {
test_divisor::<Ep>();
test_same_point::<Ep>();
test_subset_sum_to_infinity::<Ep>();
}
#[test]
fn test_divisor_vesta() {
test_divisor::<Eq>();
test_same_point::<Eq>();
test_subset_sum_to_infinity::<Eq>();
}
#[test]
fn test_divisor_ed25519() {
// Since we're implementing Wei25519 ourselves, check the isomorphism works as expected
{
let incomplete_add = |p1, p2| {
let (x1, y1) = EdwardsPoint::to_xy(p1).unwrap();
let (x2, y2) = EdwardsPoint::to_xy(p2).unwrap();
// mmadd-1998-cmo
let u = y2 - y1;
let uu = u * u;
let v = x2 - x1;
let vv = v * v;
let vvv = v * vv;
let R = vv * x1;
let A = uu - vvv - R.double();
let x3 = v * A;
let y3 = (u * (R - A)) - (vvv * y1);
let z3 = vvv;
// Normalize from XYZ to XY
let x3 = x3 * z3.invert().unwrap();
let y3 = y3 * z3.invert().unwrap();
// Edwards addition -> Wei25519 coordinates should be equivalent to Wei25519 addition
assert_eq!(EdwardsPoint::to_xy(p1 + p2).unwrap(), (x3, y3));
};
for _ in 0 .. 256 {
incomplete_add(EdwardsPoint::random(&mut OsRng), EdwardsPoint::random(&mut OsRng));
}
}
test_divisor::<EdwardsPoint>();
test_same_point::<EdwardsPoint>();
test_subset_sum_to_infinity::<EdwardsPoint>();
}

129
crypto/evrf/divisors/src/tests/poly.rs Normal file
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use group::ff::Field;
use pasta_curves::Ep;
use crate::{DivisorCurve, Poly};
type F = <Ep as DivisorCurve>::FieldElement;
#[test]
fn test_poly() {
let zero = F::ZERO;
let one = F::ONE;
{
let mut poly = Poly::zero();
poly.y_coefficients = vec![zero, one];
let mut modulus = Poly::zero();
modulus.y_coefficients = vec![one];
assert_eq!(poly % &modulus, Poly::zero());
}
{
let mut poly = Poly::zero();
poly.y_coefficients = vec![zero, one];
let mut squared = Poly::zero();
squared.y_coefficients = vec![zero, zero, zero, one];
assert_eq!(poly.clone() * poly.clone(), squared);
}
{
let mut a = Poly::zero();
a.zero_coefficient = F::from(2u64);
let mut b = Poly::zero();
b.zero_coefficient = F::from(3u64);
let mut res = Poly::zero();
res.zero_coefficient = F::from(6u64);
assert_eq!(a.clone() * b.clone(), res);
b.y_coefficients = vec![F::from(4u64)];
res.y_coefficients = vec![F::from(8u64)];
assert_eq!(a.clone() * b.clone(), res);
assert_eq!(b.clone() * a.clone(), res);
a.x_coefficients = vec![F::from(5u64)];
res.x_coefficients = vec![F::from(15u64)];
res.yx_coefficients = vec![vec![F::from(20u64)]];
assert_eq!(a.clone() * b.clone(), res);
assert_eq!(b * a.clone(), res);
// res is now 20xy + 8*y + 15*x + 6
// res ** 2 =
// 400*x^2*y^2 + 320*x*y^2 + 64*y^2 + 600*x^2*y + 480*x*y + 96*y + 225*x^2 + 180*x + 36
let mut squared = Poly::zero();
squared.y_coefficients = vec![F::from(96u64), F::from(64u64)];
squared.yx_coefficients =
vec![vec![F::from(480u64), F::from(600u64)], vec![F::from(320u64), F::from(400u64)]];
squared.x_coefficients = vec![F::from(180u64), F::from(225u64)];
squared.zero_coefficient = F::from(36u64);
assert_eq!(res.clone() * res, squared);
}
}
#[test]
fn test_differentation() {
let random = || F::random(&mut OsRng);
let input = Poly {
y_coefficients: vec![random()],
yx_coefficients: vec![vec![random()]],
x_coefficients: vec![random(), random(), random()],
zero_coefficient: random(),
};
let (diff_x, diff_y) = input.differentiate();
assert_eq!(
diff_x,
Poly {
y_coefficients: vec![input.yx_coefficients[0][0]],
yx_coefficients: vec![],
x_coefficients: vec![
F::from(2) * input.x_coefficients[1],
F::from(3) * input.x_coefficients[2]
],
zero_coefficient: input.x_coefficients[0],
}
);
assert_eq!(
diff_y,
Poly {
y_coefficients: vec![],
yx_coefficients: vec![],
x_coefficients: vec![input.yx_coefficients[0][0]],
zero_coefficient: input.y_coefficients[0],
}
);
let input = Poly {
y_coefficients: vec![random()],
yx_coefficients: vec![vec![random(), random()]],
x_coefficients: vec![random(), random(), random(), random()],
zero_coefficient: random(),
};
let (diff_x, diff_y) = input.differentiate();
assert_eq!(
diff_x,
Poly {
y_coefficients: vec![input.yx_coefficients[0][0]],
yx_coefficients: vec![vec![F::from(2) * input.yx_coefficients[0][1]]],
x_coefficients: vec![
F::from(2) * input.x_coefficients[1],
F::from(3) * input.x_coefficients[2],
F::from(4) * input.x_coefficients[3],
],
zero_coefficient: input.x_coefficients[0],
}
);
assert_eq!(
diff_y,
Poly {
y_coefficients: vec![],
yx_coefficients: vec![],
x_coefficients: vec![input.yx_coefficients[0][0], input.yx_coefficients[0][1]],
zero_coefficient: input.y_coefficients[0],
}
);
}

20
crypto/evrf/ec-gadgets/Cargo.toml Normal file
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@@ -0,0 +1,20 @@
[package]
name = "generalized-bulletproofs-ec-gadgets"
version = "0.1.0"
description = "Gadgets for working with an embedded Elliptic Curve in a Generalized Bulletproofs circuit"
license = "MIT"
repository = "https://github.com/serai-dex/serai/tree/develop/crypto/evrf/ec-gadgets"
authors = ["Luke Parker <lukeparker5132@gmail.com>"]
keywords = ["bulletproofs", "circuit", "divisors"]
edition = "2021"
[package.metadata.docs.rs]
all-features = true
rustdoc-args = ["--cfg", "docsrs"]
[dependencies]
generic-array = { version = "1", default-features = false, features = ["alloc"] }
ciphersuite = { path = "../../ciphersuite", version = "0.4", default-features = false, features = ["std"] }
generalized-bulletproofs-circuit-abstraction = { path = "../circuit-abstraction" }

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MIT License
Copyright (c) 2024 Luke Parker
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.

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# Generalized Bulletproofs Circuit Abstraction
A circuit abstraction around `generalized-bulletproofs`.

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use core::fmt;
use ciphersuite::{
group::ff::{Field, PrimeField, BatchInverter},
Ciphersuite,
};
use generalized_bulletproofs_circuit_abstraction::*;
use crate::*;
/// Parameters for a discrete logarithm proof.
///
/// This isn't required to be implemented by the Field/Group/Ciphersuite, solely a struct, to
/// enable parameterization of discrete log proofs to the bitlength of the discrete logarithm.
/// While that may be F::NUM_BITS, a discrete log proof a for a full scalar, it could also be 64,
/// a discrete log proof for a u64 (such as if opening a Pedersen commitment in-circuit).
pub trait DiscreteLogParameters {
/// The amount of bits used to represent a scalar.
type ScalarBits: ArrayLength;
/// The amount of x**i coefficients in a divisor.
///
/// This is the amount of points in a divisor (the amount of bits in a scalar, plus one) divided
/// by two.
type XCoefficients: ArrayLength;
/// The amount of x**i coefficients in a divisor, minus one.
type XCoefficientsMinusOne: ArrayLength;
/// The amount of y x**i coefficients in a divisor.
///
/// This is the amount of points in a divisor (the amount of bits in a scalar, plus one) plus
/// one, divided by two, minus two.
type YxCoefficients: ArrayLength;
}
/// A tabled generator for proving/verifying discrete logarithm claims.
#[derive(Clone)]
pub struct GeneratorTable<F: PrimeField, Parameters: DiscreteLogParameters>(
GenericArray<(F, F), Parameters::ScalarBits>,
);
impl<F: PrimeField, Parameters: DiscreteLogParameters> fmt::Debug
for GeneratorTable<F, Parameters>
{
fn fmt(&self, fmt: &mut fmt::Formatter<'_>) -> fmt::Result {
fmt
.debug_struct("GeneratorTable")
.field("x", &self.0[0].0)
.field("y", &self.0[0].1)
.finish_non_exhaustive()
}
}
impl<F: PrimeField, Parameters: DiscreteLogParameters> GeneratorTable<F, Parameters> {
/// Create a new table for this generator.
///
/// The generator is assumed to be well-formed and on-curve. This function may panic if it's not.
pub fn new(curve: &CurveSpec<F>, generator_x: F, generator_y: F) -> Self {
// mdbl-2007-bl
fn dbl<F: PrimeField>(a: F, x1: F, y1: F) -> (F, F) {
let xx = x1 * x1;
let w = a + (xx + xx.double());
let y1y1 = y1 * y1;
let r = y1y1 + y1y1;
let sss = (y1 * r).double().double();
let rr = r * r;
let b = x1 + r;
let b = (b * b) - xx - rr;
let h = (w * w) - b.double();
let x3 = h.double() * y1;
let y3 = (w * (b - h)) - rr.double();
let z3 = sss;
// Normalize from XYZ to XY
let z3_inv = z3.invert().unwrap();
let x3 = x3 * z3_inv;
let y3 = y3 * z3_inv;
(x3, y3)
}
let mut res = Self(GenericArray::default());
res.0[0] = (generator_x, generator_y);
for i in 1 .. Parameters::ScalarBits::USIZE {
let last = res.0[i - 1];
res.0[i] = dbl(curve.a, last.0, last.1);
}
res
}
}
/// A representation of the divisor.
///
/// The coefficient for x**1 is explicitly excluded as it's expected to be normalized to 1.
#[derive(Clone)]
pub struct Divisor<Parameters: DiscreteLogParameters> {
/// The coefficient for the `y` term of the divisor.
///
/// There is never more than one `y**i x**0` coefficient as the leading term of the modulus is
/// `y**2`. It's assumed the coefficient is non-zero (and present) as it will be for any divisor
/// exceeding trivial complexity.
pub y: Variable,
/// The coefficients for the `y**1 x**i` terms of the polynomial.
// This subtraction enforces the divisor to have at least 4 points which is acceptable.
// TODO: Double check these constants
pub yx: GenericArray<Variable, Parameters::YxCoefficients>,
/// The coefficients for the `x**i` terms of the polynomial, skipping x**1.
///
/// x**1 is skipped as it's expected to be normalized to 1, and therefore constant, in order to
/// ensure the divisor is non-zero (as necessary for the proof to be complete).
// Subtract 1 from the length due to skipping the coefficient for x**1
pub x_from_power_of_2: GenericArray<Variable, Parameters::XCoefficientsMinusOne>,
/// The constant term in the polynomial (alternatively, the coefficient for y**0 x**0).
pub zero: Variable,
}
/// A point, its discrete logarithm, and the divisor to prove it.
#[derive(Clone)]
pub struct PointWithDlog<Parameters: DiscreteLogParameters> {
/// The point which is supposedly the result of scaling the generator by the discrete logarithm.
pub point: (Variable, Variable),
/// The discrete logarithm, represented as coefficients of a polynomial of 2**i.
pub dlog: GenericArray<Variable, Parameters::ScalarBits>,
/// The divisor interpolating the relevant doublings of generator with the inverse of the point.
pub divisor: Divisor<Parameters>,
}
/// A struct containing a point used for the evaluation of a divisor.
///
/// Preprocesses and caches as much of the calculation as possible to minimize work upon reuse of
/// challenge points.
struct ChallengePoint<F: PrimeField, Parameters: DiscreteLogParameters> {
y: F,
yx: GenericArray<F, Parameters::YxCoefficients>,
x: GenericArray<F, Parameters::XCoefficients>,
p_0_n_0: F,
x_p_0_n_0: GenericArray<F, Parameters::YxCoefficients>,
p_1_n: F,
p_1_d: F,
}
impl<F: PrimeField, Parameters: DiscreteLogParameters> ChallengePoint<F, Parameters> {
fn new(
curve: &CurveSpec<F>,
// The slope between all of the challenge points
slope: F,
// The x and y coordinates
x: F,
y: F,
// The inversion of twice the y coordinate
// We accept this as an argument so that the caller can calculcate these with a batch inversion
inv_two_y: F,
) -> Self {
// Powers of x, skipping x**0
let divisor_x_len = Parameters::XCoefficients::USIZE;
let mut x_pows = GenericArray::default();
x_pows[0] = x;
for i in 1 .. divisor_x_len {
let last = x_pows[i - 1];
x_pows[i] = last * x;
}
// Powers of x multiplied by y
let divisor_yx_len = Parameters::YxCoefficients::USIZE;
let mut yx = GenericArray::default();
// Skips x**0
yx[0] = y * x;
for i in 1 .. divisor_yx_len {
let last = yx[i - 1];
yx[i] = last * x;
}
let x_sq = x.square();
let three_x_sq = x_sq.double() + x_sq;
let three_x_sq_plus_a = three_x_sq + curve.a;
let two_y = y.double();
// p_0_n_0 from `DivisorChallenge`
let p_0_n_0 = three_x_sq_plus_a * inv_two_y;
let mut x_p_0_n_0 = GenericArray::default();
// Since this iterates over x, which skips x**0, this also skips p_0_n_0 x**0
for (i, x) in x_pows.iter().take(divisor_yx_len).enumerate() {
x_p_0_n_0[i] = p_0_n_0 * x;
}
// p_1_n from `DivisorChallenge`
let p_1_n = two_y;
// p_1_d from `DivisorChallenge`
let p_1_d = (-slope * p_1_n) + three_x_sq_plus_a;
ChallengePoint { x: x_pows, y, yx, p_0_n_0, x_p_0_n_0, p_1_n, p_1_d }
}
}
// `DivisorChallenge` from the section `Discrete Log Proof`
fn divisor_challenge_eval<C: Ciphersuite, Parameters: DiscreteLogParameters>(
circuit: &mut Circuit<C>,
divisor: &Divisor<Parameters>,
challenge: &ChallengePoint<C::F, Parameters>,
) -> Variable {
// The evaluation of the divisor differentiated by y, further multiplied by p_0_n_0
// Differentation drops everything without a y coefficient, and drops what remains by a power
// of y
// (y**1 -> y**0, yx**i -> x**i)
// This aligns with p_0_n_1 from `DivisorChallenge`
let p_0_n_1 = {
let mut p_0_n_1 = LinComb::empty().term(challenge.p_0_n_0, divisor.y);
for (j, var) in divisor.yx.iter().enumerate() {
// This does not raise by `j + 1` as x_p_0_n_0 omits x**0
p_0_n_1 = p_0_n_1.term(challenge.x_p_0_n_0[j], *var);
}
p_0_n_1
};
// The evaluation of the divisor differentiated by x
// This aligns with p_0_n_2 from `DivisorChallenge`
let p_0_n_2 = {
// The coefficient for x**1 is 1, so 1 becomes the new zero coefficient
let mut p_0_n_2 = LinComb::empty().constant(C::F::ONE);
// Handle the new y coefficient
p_0_n_2 = p_0_n_2.term(challenge.y, divisor.yx[0]);
// Handle the new yx coefficients
for (j, yx) in divisor.yx.iter().enumerate().skip(1) {
// For the power which was shifted down, we multiply this coefficient
// 3 x**2 -> 2 * 3 x**1
let original_power_of_x = C::F::from(u64::try_from(j + 1).unwrap());
// `j - 1` so `j = 1` indexes yx[0] as yx[0] is the y x**1
// (yx omits y x**0)
let this_weight = original_power_of_x * challenge.yx[j - 1];
p_0_n_2 = p_0_n_2.term(this_weight, *yx);
}
// Handle the x coefficients
// We don't skip the first one as `x_from_power_of_2` already omits x**1
for (i, x) in divisor.x_from_power_of_2.iter().enumerate() {
// i + 2 as the paper expects i to start from 1 and be + 1, yet we start from 0
let original_power_of_x = C::F::from(u64::try_from(i + 2).unwrap());
// Still x[i] as x[0] is x**1
let this_weight = original_power_of_x * challenge.x[i];
p_0_n_2 = p_0_n_2.term(this_weight, *x);
}
p_0_n_2
};
// p_0_n from `DivisorChallenge`
let p_0_n = p_0_n_1 + &p_0_n_2;
// Evaluation of the divisor
// p_0_d from `DivisorChallenge`
let p_0_d = {
let mut p_0_d = LinComb::empty().term(challenge.y, divisor.y);
for (var, c_yx) in divisor.yx.iter().zip(&challenge.yx) {
p_0_d = p_0_d.term(*c_yx, *var);
}
for (i, var) in divisor.x_from_power_of_2.iter().enumerate() {
// This `i+1` is preserved, despite most not being as x omits x**0, as this assumes we
// start with `i=1`
p_0_d = p_0_d.term(challenge.x[i + 1], *var);
}
// Adding x effectively adds a `1 x` term, ensuring the divisor isn't 0
p_0_d.term(C::F::ONE, divisor.zero).constant(challenge.x[0])
};
// Calculate the joint numerator
// p_n from `DivisorChallenge`
let p_n = p_0_n * challenge.p_1_n;
// Calculate the joint denominator
// p_d from `DivisorChallenge`
let p_d = p_0_d * challenge.p_1_d;
// We want `n / d = o`
// `n / d = o` == `n = d * o`
// These are safe unwraps as they're solely done by the prover and should always be non-zero
let witness =
circuit.eval(&p_d).map(|p_d| (p_d, circuit.eval(&p_n).unwrap() * p_d.invert().unwrap()));
let (_l, o, n_claim) = circuit.mul(Some(p_d), None, witness);
circuit.equality(p_n, &n_claim.into());
o
}
/// A challenge to evaluate divisors with.
///
/// This challenge must be sampled after writing the commitments to the transcript. This challenge
/// is reusable across various divisors.
pub struct DiscreteLogChallenge<F: PrimeField, Parameters: DiscreteLogParameters> {
c0: ChallengePoint<F, Parameters>,
c1: ChallengePoint<F, Parameters>,
c2: ChallengePoint<F, Parameters>,
slope: F,
intercept: F,
}
/// A generator which has been challenged and is ready for use in evaluating discrete logarithm
/// claims.
pub struct ChallengedGenerator<F: PrimeField, Parameters: DiscreteLogParameters>(
GenericArray<F, Parameters::ScalarBits>,
);
/// Gadgets for proving the discrete logarithm of points on an elliptic curve defined over the
/// scalar field of the curve of the Bulletproof.
pub trait EcDlogGadgets<C: Ciphersuite> {
/// Sample a challenge for a series of discrete logarithm claims.
///
/// This must be called after writing the commitments to the transcript.
///
/// The generators are assumed to be non-empty. They are not transcripted. If your generators are
/// dynamic, they must be properly transcripted into the context.
///
/// May panic/have undefined behavior if an assumption is broken.
#[allow(clippy::type_complexity)]
fn discrete_log_challenge<T: Transcript, Parameters: DiscreteLogParameters>(
&self,
transcript: &mut T,
curve: &CurveSpec<C::F>,
generators: &[GeneratorTable<C::F, Parameters>],
) -> (DiscreteLogChallenge<C::F, Parameters>, Vec<ChallengedGenerator<C::F, Parameters>>);
/// Prove this point has the specified discrete logarithm over the specified generator.
///
/// The discrete logarithm is not validated to be in a canonical form. The only guarantee made on
/// it is that it's a consistent representation of _a_ discrete logarithm (reuse won't enable
/// re-interpretation as a distinct discrete logarithm).
///
/// This does ensure the point is on-curve.
///
/// This MUST only be called with `Variable`s present within commitments.
///
/// May panic/have undefined behavior if an assumption is broken, or if passed an invalid
/// witness.
fn discrete_log<Parameters: DiscreteLogParameters>(
&mut self,
curve: &CurveSpec<C::F>,
point: PointWithDlog<Parameters>,
challenge: &DiscreteLogChallenge<C::F, Parameters>,
challenged_generator: &ChallengedGenerator<C::F, Parameters>,
) -> OnCurve;
}
impl<C: Ciphersuite> EcDlogGadgets<C> for Circuit<C> {
// This is part of `DiscreteLog` from `Discrete Log Proof`, specifically, the challenges and
// the calculations dependent solely on them
fn discrete_log_challenge<T: Transcript, Parameters: DiscreteLogParameters>(
&self,
transcript: &mut T,
curve: &CurveSpec<C::F>,
generators: &[GeneratorTable<C::F, Parameters>],
) -> (DiscreteLogChallenge<C::F, Parameters>, Vec<ChallengedGenerator<C::F, Parameters>>) {
// Get the challenge points
// TODO: Implement a proper hash to curve
let (c0_x, c0_y) = loop {
let c0_x: C::F = transcript.challenge();
let Some(c0_y) =
Option::<C::F>::from(((c0_x.square() * c0_x) + (curve.a * c0_x) + curve.b).sqrt())
else {
continue;
};
// Takes the even y coordinate as to not be dependent on whatever root the above sqrt
// happens to returns
// TODO: Randomly select which to take
break (c0_x, if bool::from(c0_y.is_odd()) { -c0_y } else { c0_y });
};
let (c1_x, c1_y) = loop {
let c1_x: C::F = transcript.challenge();
let Some(c1_y) =
Option::<C::F>::from(((c1_x.square() * c1_x) + (curve.a * c1_x) + curve.b).sqrt())
else {
continue;
};
break (c1_x, if bool::from(c1_y.is_odd()) { -c1_y } else { c1_y });
};
// mmadd-1998-cmo
fn incomplete_add<F: PrimeField>(x1: F, y1: F, x2: F, y2: F) -> Option<(F, F)> {
if x1 == x2 {
None?
}
let u = y2 - y1;
let uu = u * u;
let v = x2 - x1;
let vv = v * v;
let vvv = v * vv;
let r = vv * x1;
let a = uu - vvv - r.double();
let x3 = v * a;
let y3 = (u * (r - a)) - (vvv * y1);
let z3 = vvv;
// Normalize from XYZ to XY
let z3_inv = Option::<F>::from(z3.invert())?;
let x3 = x3 * z3_inv;
let y3 = y3 * z3_inv;
Some((x3, y3))
}
let (c2_x, c2_y) = incomplete_add::<C::F>(c0_x, c0_y, c1_x, c1_y)
.expect("randomly selected points shared an x coordinate");
// We want C0, C1, C2 = -(C0 + C1)
let c2_y = -c2_y;
// Calculate the slope and intercept
// Safe invert as these x coordinates must be distinct due to passing the above incomplete_add
let slope = (c1_y - c0_y) * (c1_x - c0_x).invert().unwrap();
let intercept = c0_y - (slope * c0_x);
// Calculate the inversions for 2 c_y (for each c) and all of the challenged generators
let mut inversions = vec![C::F::ZERO; 3 + (generators.len() * Parameters::ScalarBits::USIZE)];
// Needed for the left-hand side eval
{
inversions[0] = c0_y.double();
inversions[1] = c1_y.double();
inversions[2] = c2_y.double();
}
// Perform the inversions for the generators
for (i, generator) in generators.iter().enumerate() {
// Needed for the right-hand side eval
for (j, generator) in generator.0.iter().enumerate() {
// `DiscreteLog` has weights of `(mu - (G_i.y + (slope * G_i.x)))**-1` in its last line
inversions[3 + (i * Parameters::ScalarBits::USIZE) + j] =
intercept - (generator.1 - (slope * generator.0));
}
}
for challenge_inversion in &inversions {
// This should be unreachable barring negligible probability
if challenge_inversion.is_zero().into() {
panic!("trying to invert 0");
}
}
let mut scratch = vec![C::F::ZERO; inversions.len()];
let _ = BatchInverter::invert_with_external_scratch(&mut inversions, &mut scratch);
let mut inversions = inversions.into_iter();
let inv_c0_two_y = inversions.next().unwrap();
let inv_c1_two_y = inversions.next().unwrap();
let inv_c2_two_y = inversions.next().unwrap();
let c0 = ChallengePoint::new(curve, slope, c0_x, c0_y, inv_c0_two_y);
let c1 = ChallengePoint::new(curve, slope, c1_x, c1_y, inv_c1_two_y);
let c2 = ChallengePoint::new(curve, slope, c2_x, c2_y, inv_c2_two_y);
// Fill in the inverted values
let mut challenged_generators = Vec::with_capacity(generators.len());
for _ in 0 .. generators.len() {
let mut challenged_generator = GenericArray::default();
for i in 0 .. Parameters::ScalarBits::USIZE {
challenged_generator[i] = inversions.next().unwrap();
}
challenged_generators.push(ChallengedGenerator(challenged_generator));
}
(DiscreteLogChallenge { c0, c1, c2, slope, intercept }, challenged_generators)
}
// `DiscreteLog` from `Discrete Log Proof`
fn discrete_log<Parameters: DiscreteLogParameters>(
&mut self,
curve: &CurveSpec<C::F>,
point: PointWithDlog<Parameters>,
challenge: &DiscreteLogChallenge<C::F, Parameters>,
challenged_generator: &ChallengedGenerator<C::F, Parameters>,
) -> OnCurve {
let PointWithDlog { divisor, dlog, point } = point;
// Ensure this is being safely called
let arg_iter = [point.0, point.1, divisor.y, divisor.zero];
let arg_iter = arg_iter.iter().chain(divisor.yx.iter());
let arg_iter = arg_iter.chain(divisor.x_from_power_of_2.iter());
let arg_iter = arg_iter.chain(dlog.iter());
for variable in arg_iter {
debug_assert!(
matches!(variable, Variable::CG { .. } | Variable::CH { .. } | Variable::V(_)),
"discrete log proofs requires all arguments belong to commitments",
);
}
// Check the point is on curve
let point = self.on_curve(curve, point);
// The challenge has already been sampled so those lines aren't necessary
// lhs from the paper, evaluating the divisor
let lhs_eval = LinComb::from(divisor_challenge_eval(self, &divisor, &challenge.c0)) +
&LinComb::from(divisor_challenge_eval(self, &divisor, &challenge.c1)) +
&LinComb::from(divisor_challenge_eval(self, &divisor, &challenge.c2));
// Interpolate the doublings of the generator
let mut rhs_eval = LinComb::empty();
// We call this `bit` yet it's not constrained to being a bit
// It's presumed to be yet may be malleated
for (bit, weight) in dlog.into_iter().zip(&challenged_generator.0) {
rhs_eval = rhs_eval.term(*weight, bit);
}
// Interpolate the output point
// intercept - (y - (slope * x))
// intercept - y + (slope * x)
// -y + (slope * x) + intercept
// EXCEPT the output point we're proving the discrete log for isn't the one interpolated
// Its negative is, so -y becomes y
// y + (slope * x) + intercept
let output_interpolation = LinComb::empty()
.constant(challenge.intercept)
.term(C::F::ONE, point.y)
.term(challenge.slope, point.x);
let output_interpolation_eval = self.eval(&output_interpolation);
let (_output_interpolation, inverse) =
self.inverse(Some(output_interpolation), output_interpolation_eval);
rhs_eval = rhs_eval.term(C::F::ONE, inverse);
self.equality(lhs_eval, &rhs_eval);
point
}
}

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#![cfg_attr(docsrs, feature(doc_auto_cfg))]
#![doc = include_str!("../README.md")]
#![deny(missing_docs)]
#![allow(non_snake_case)]
use generic_array::{typenum::Unsigned, ArrayLength, GenericArray};
use ciphersuite::{group::ff::Field, Ciphersuite};
use generalized_bulletproofs_circuit_abstraction::*;
mod dlog;
pub use dlog::*;
/// The specification of a short Weierstrass curve over the field `F`.
///
/// The short Weierstrass curve is defined via the formula `y**2 = x**3 + a*x + b`.
#[derive(Clone, Copy, PartialEq, Eq, Debug)]
pub struct CurveSpec<F> {
/// The `a` constant in the curve formula.
pub a: F,
/// The `b` constant in the curve formula.
pub b: F,
}
/// A struct for a point on a towered curve which has been confirmed to be on-curve.
#[derive(Clone, Copy, PartialEq, Eq, Debug)]
pub struct OnCurve {
pub(crate) x: Variable,
pub(crate) y: Variable,
}
impl OnCurve {
/// The variable for the x-coordinate.
pub fn x(&self) -> Variable {
self.x
}
/// The variable for the y-coordinate.
pub fn y(&self) -> Variable {
self.y
}
}
/// Gadgets for working with points on an elliptic curve defined over the scalar field of the curve
/// of the Bulletproof.
pub trait EcGadgets<C: Ciphersuite> {
/// Constrain an x and y coordinate as being on the specified curve.
///
/// The specified curve is defined over the scalar field of the curve this proof is performed
/// over, offering efficient arithmetic.
///
/// May panic if the prover and the point is not actually on-curve.
fn on_curve(&mut self, curve: &CurveSpec<C::F>, point: (Variable, Variable)) -> OnCurve;
/// Perform incomplete addition for a fixed point and an on-curve point.
///
/// `a` is the x and y coordinates of the fixed point, assumed to be on-curve.
///
/// `b` is a point prior checked to be on-curve.
///
/// `c` is a point prior checked to be on-curve, constrained to be the sum of `a` and `b`.
///
/// `a` and `b` are checked to have distinct x coordinates.
///
/// This function may panic if `a` is malformed or if the prover and `c` is not actually the sum
/// of `a` and `b`.
fn incomplete_add_fixed(&mut self, a: (C::F, C::F), b: OnCurve, c: OnCurve) -> OnCurve;
}
impl<C: Ciphersuite> EcGadgets<C> for Circuit<C> {
fn on_curve(&mut self, curve: &CurveSpec<C::F>, (x, y): (Variable, Variable)) -> OnCurve {
let x_eval = self.eval(&LinComb::from(x));
let (_x, _x_2, x2) =
self.mul(Some(LinComb::from(x)), Some(LinComb::from(x)), x_eval.map(|x| (x, x)));
let (_x, _x_2, x3) =
self.mul(Some(LinComb::from(x2)), Some(LinComb::from(x)), x_eval.map(|x| (x * x, x)));
let expected_y2 = LinComb::from(x3).term(curve.a, x).constant(curve.b);
let y_eval = self.eval(&LinComb::from(y));
let (_y, _y_2, y2) =
self.mul(Some(LinComb::from(y)), Some(LinComb::from(y)), y_eval.map(|y| (y, y)));
self.equality(y2.into(), &expected_y2);
OnCurve { x, y }
}
fn incomplete_add_fixed(&mut self, a: (C::F, C::F), b: OnCurve, c: OnCurve) -> OnCurve {
// Check b.x != a.0
{
let bx_lincomb = LinComb::from(b.x);
let bx_eval = self.eval(&bx_lincomb);
self.inequality(bx_lincomb, &LinComb::empty().constant(a.0), bx_eval.map(|bx| (bx, a.0)));
}
let (x0, y0) = (a.0, a.1);
let (x1, y1) = (b.x, b.y);
let (x2, y2) = (c.x, c.y);
let slope_eval = self.eval(&LinComb::from(x1)).map(|x1| {
let y1 = self.eval(&LinComb::from(b.y)).unwrap();
(y1 - y0) * (x1 - x0).invert().unwrap()
});
// slope * (x1 - x0) = y1 - y0
let x1_minus_x0 = LinComb::from(x1).constant(-x0);
let x1_minus_x0_eval = self.eval(&x1_minus_x0);
let (slope, _r, o) =
self.mul(None, Some(x1_minus_x0), slope_eval.map(|slope| (slope, x1_minus_x0_eval.unwrap())));
self.equality(LinComb::from(o), &LinComb::from(y1).constant(-y0));
// slope * (x2 - x0) = -y2 - y0
let x2_minus_x0 = LinComb::from(x2).constant(-x0);
let x2_minus_x0_eval = self.eval(&x2_minus_x0);
let (_slope, _x2_minus_x0, o) = self.mul(
Some(slope.into()),
Some(x2_minus_x0),
slope_eval.map(|slope| (slope, x2_minus_x0_eval.unwrap())),
);
self.equality(o.into(), &LinComb::empty().term(-C::F::ONE, y2).constant(-y0));
// slope * slope = x0 + x1 + x2
let (_slope, _slope_2, o) =
self.mul(Some(slope.into()), Some(slope.into()), slope_eval.map(|slope| (slope, slope)));
self.equality(o.into(), &LinComb::from(x1).term(C::F::ONE, x2).constant(x0));
OnCurve { x: x2, y: y2 }
}
}

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[package]
name = "embedwards25519"
version = "0.1.0"
description = "A curve defined over the Ed25519 scalar field"
license = "MIT"
repository = "https://github.com/serai-dex/serai/tree/develop/crypto/evrf/embedwards25519"
authors = ["Luke Parker <lukeparker5132@gmail.com>"]
keywords = ["curve25519", "ed25519", "ristretto255", "group"]
edition = "2021"
[package.metadata.docs.rs]
all-features = true
rustdoc-args = ["--cfg", "docsrs"]
[dependencies]
rustversion = "1"
hex-literal = { version = "0.4", default-features = false }
rand_core = { version = "0.6", default-features = false, features = ["std"] }
zeroize = { version = "^1.5", default-features = false, features = ["std", "zeroize_derive"] }
subtle = { version = "^2.4", default-features = false, features = ["std"] }
generic-array = { version = "0.14", default-features = false }
crypto-bigint = { version = "0.5", default-features = false, features = ["zeroize"] }
dalek-ff-group = { path = "../../dalek-ff-group", version = "0.4", default-features = false }
blake2 = { version = "0.10", default-features = false, features = ["std"] }
ciphersuite = { path = "../../ciphersuite", version = "0.4", default-features = false, features = ["std"] }
ec-divisors = { path = "../divisors" }
generalized-bulletproofs-ec-gadgets = { path = "../ec-gadgets" }
[dev-dependencies]
hex = "0.4"
rand_core = { version = "0.6", features = ["std"] }
ff-group-tests = { path = "../../ff-group-tests" }

21
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MIT License
Copyright (c) 2022-2024 Luke Parker
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.

21
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# embedwards25519
A curve defined over the Ed25519 scalar field.
This curve was found via
[tevador's script](https://gist.github.com/tevador/4524c2092178df08996487d4e272b096)
for finding curves (specifically, curve cycles), modified to search for curves
whose field is the Ed25519 scalar field (not the Ed25519 field).
```
p = 0x1000000000000000000000000000000014def9dea2f79cd65812631a5cf5d3ed
q = 0x0fffffffffffffffffffffffffffffffe53f4debb78ff96877063f0306eef96b
D = -420435
y^2 = x^3 - 3*x + 4188043517836764736459661287169077812555441231147410753119540549773825148767
```
The embedding degree is `(q-1)/2`.
This curve should not be used with single-coordinate ladders, and points should
always be represented in a compressed form (preventing receiving off-curve
points).

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use zeroize::Zeroize;
// Use black_box when possible
#[rustversion::since(1.66)]
use core::hint::black_box;
#[rustversion::before(1.66)]
fn black_box<T>(val: T) -> T {
val
}
pub(crate) fn u8_from_bool(bit_ref: &mut bool) -> u8 {
let bit_ref = black_box(bit_ref);
let mut bit = black_box(*bit_ref);
let res = black_box(bit as u8);
bit.zeroize();
debug_assert!((res | 1) == 1);
bit_ref.zeroize();
res
}
macro_rules! math_op {
(
$Value: ident,
$Other: ident,
$Op: ident,
$op_fn: ident,
$Assign: ident,
$assign_fn: ident,
$function: expr
) => {
impl $Op<$Other> for $Value {
type Output = $Value;
fn $op_fn(self, other: $Other) -> Self::Output {
Self($function(self.0, other.0))
}
}
impl $Assign<$Other> for $Value {
fn $assign_fn(&mut self, other: $Other) {
self.0 = $function(self.0, other.0);
}
}
impl<'a> $Op<&'a $Other> for $Value {
type Output = $Value;
fn $op_fn(self, other: &'a $Other) -> Self::Output {
Self($function(self.0, other.0))
}
}
impl<'a> $Assign<&'a $Other> for $Value {
fn $assign_fn(&mut self, other: &'a $Other) {
self.0 = $function(self.0, other.0);
}
}
};
}
macro_rules! from_wrapper {
($wrapper: ident, $inner: ident, $uint: ident) => {
impl From<$uint> for $wrapper {
fn from(a: $uint) -> $wrapper {
Self(Residue::new(&$inner::from(a)))
}
}
};
}
macro_rules! field {
(
$FieldName: ident,
$ResidueType: ident,
$MODULUS_STR: ident,
$MODULUS: ident,
$WIDE_MODULUS: ident,
$NUM_BITS: literal,
$MULTIPLICATIVE_GENERATOR: literal,
$S: literal,
$ROOT_OF_UNITY: literal,
$DELTA: literal,
) => {
use core::{
ops::{DerefMut, Add, AddAssign, Neg, Sub, SubAssign, Mul, MulAssign},
iter::{Sum, Product},
};
use subtle::{Choice, CtOption, ConstantTimeEq, ConstantTimeLess, ConditionallySelectable};
use rand_core::RngCore;
use crypto_bigint::{Integer, NonZero, Encoding, impl_modulus};
use ciphersuite::group::ff::{
Field, PrimeField, FieldBits, PrimeFieldBits, helpers::sqrt_ratio_generic,
};
use $crate::backend::u8_from_bool;
fn reduce(x: U512) -> U256 {
U256::from_le_slice(&x.rem(&NonZero::new($WIDE_MODULUS).unwrap()).to_le_bytes()[.. 32])
}
impl ConstantTimeEq for $FieldName {
fn ct_eq(&self, other: &Self) -> Choice {
self.0.ct_eq(&other.0)
}
}
impl ConditionallySelectable for $FieldName {
fn conditional_select(a: &Self, b: &Self, choice: Choice) -> Self {
$FieldName(Residue::conditional_select(&a.0, &b.0, choice))
}
}
math_op!($FieldName, $FieldName, Add, add, AddAssign, add_assign, |x: $ResidueType, y| x
.add(&y));
math_op!($FieldName, $FieldName, Sub, sub, SubAssign, sub_assign, |x: $ResidueType, y| x
.sub(&y));
math_op!($FieldName, $FieldName, Mul, mul, MulAssign, mul_assign, |x: $ResidueType, y| x
.mul(&y));
from_wrapper!($FieldName, U256, u8);
from_wrapper!($FieldName, U256, u16);
from_wrapper!($FieldName, U256, u32);
from_wrapper!($FieldName, U256, u64);
from_wrapper!($FieldName, U256, u128);
impl Neg for $FieldName {
type Output = $FieldName;
fn neg(self) -> $FieldName {
Self(self.0.neg())
}
}
impl<'a> Neg for &'a $FieldName {
type Output = $FieldName;
fn neg(self) -> Self::Output {
(*self).neg()
}
}
impl $FieldName {
/// Perform an exponentation.
pub fn pow(&self, other: $FieldName) -> $FieldName {
let mut table = [Self(Residue::ONE); 16];
table[1] = *self;
for i in 2 .. 16 {
table[i] = table[i - 1] * self;
}
let mut res = Self(Residue::ONE);
let mut bits = 0;
for (i, mut bit) in other.to_le_bits().iter_mut().rev().enumerate() {
bits <<= 1;
let mut bit = u8_from_bool(bit.deref_mut());
bits |= bit;
bit.zeroize();
if ((i + 1) % 4) == 0 {
if i != 3 {
for _ in 0 .. 4 {
res *= res;
}
}
let mut factor = table[0];
for (j, candidate) in table[1 ..].iter().enumerate() {
let j = j + 1;
factor = Self::conditional_select(&factor, &candidate, usize::from(bits).ct_eq(&j));
}
res *= factor;
bits = 0;
}
}
res
}
}
impl Field for $FieldName {
const ZERO: Self = Self(Residue::ZERO);
const ONE: Self = Self(Residue::ONE);
fn random(mut rng: impl RngCore) -> Self {
let mut bytes = [0; 64];
rng.fill_bytes(&mut bytes);
$FieldName(Residue::new(&reduce(U512::from_le_slice(bytes.as_ref()))))
}
fn square(&self) -> Self {
Self(self.0.square())
}
fn double(&self) -> Self {
*self + self
}
fn invert(&self) -> CtOption<Self> {
let res = self.0.invert();
CtOption::new(Self(res.0), res.1.into())
}
fn sqrt(&self) -> CtOption<Self> {
// (p + 1) // 4, as valid since p % 4 == 3
let mod_plus_one_div_four = $MODULUS.saturating_add(&U256::ONE).wrapping_div(&(4u8.into()));
let res = self.pow(Self($ResidueType::new_checked(&mod_plus_one_div_four).unwrap()));
CtOption::new(res, res.square().ct_eq(self))
}
fn sqrt_ratio(num: &Self, div: &Self) -> (Choice, Self) {
sqrt_ratio_generic(num, div)
}
}
impl PrimeField for $FieldName {
type Repr = [u8; 32];
const MODULUS: &'static str = $MODULUS_STR;
const NUM_BITS: u32 = $NUM_BITS;
const CAPACITY: u32 = $NUM_BITS - 1;
const TWO_INV: Self = $FieldName($ResidueType::new(&U256::from_u8(2)).invert().0);
const MULTIPLICATIVE_GENERATOR: Self =
Self(Residue::new(&U256::from_u8($MULTIPLICATIVE_GENERATOR)));
const S: u32 = $S;
const ROOT_OF_UNITY: Self = $FieldName(Residue::new(&U256::from_be_hex($ROOT_OF_UNITY)));
const ROOT_OF_UNITY_INV: Self = Self(Self::ROOT_OF_UNITY.0.invert().0);
const DELTA: Self = $FieldName(Residue::new(&U256::from_be_hex($DELTA)));
fn from_repr(bytes: Self::Repr) -> CtOption<Self> {
let res = U256::from_le_slice(&bytes);
CtOption::new($FieldName(Residue::new(&res)), res.ct_lt(&$MODULUS))
}
fn to_repr(&self) -> Self::Repr {
let mut repr = [0; 32];
repr.copy_from_slice(&self.0.retrieve().to_le_bytes());
repr
}
fn is_odd(&self) -> Choice {
self.0.retrieve().is_odd()
}
}
impl PrimeFieldBits for $FieldName {
type ReprBits = [u8; 32];
fn to_le_bits(&self) -> FieldBits<Self::ReprBits> {
self.to_repr().into()
}
fn char_le_bits() -> FieldBits<Self::ReprBits> {
let mut repr = [0; 32];
repr.copy_from_slice(&MODULUS.to_le_bytes());
repr.into()
}
}
impl Sum<$FieldName> for $FieldName {
fn sum<I: Iterator<Item = $FieldName>>(iter: I) -> $FieldName {
let mut res = $FieldName::ZERO;
for item in iter {
res += item;
}
res
}
}
impl<'a> Sum<&'a $FieldName> for $FieldName {
fn sum<I: Iterator<Item = &'a $FieldName>>(iter: I) -> $FieldName {
iter.cloned().sum()
}
}
impl Product<$FieldName> for $FieldName {
fn product<I: Iterator<Item = $FieldName>>(iter: I) -> $FieldName {
let mut res = $FieldName::ONE;
for item in iter {
res *= item;
}
res
}
}
impl<'a> Product<&'a $FieldName> for $FieldName {
fn product<I: Iterator<Item = &'a $FieldName>>(iter: I) -> $FieldName {
iter.cloned().product()
}
}
};
}

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#![cfg_attr(docsrs, feature(doc_auto_cfg))]
#![doc = include_str!("../README.md")]
use generic_array::typenum::{Sum, Diff, Quot, U, U1, U2};
use ciphersuite::group::{ff::PrimeField, Group};
#[macro_use]
mod backend;
mod scalar;
pub use scalar::Scalar;
pub use dalek_ff_group::Scalar as FieldElement;
mod point;
pub use point::Point;
/// Ciphersuite for Embedwards25519.
///
/// hash_to_F is implemented with a naive concatenation of the dst and data, allowing transposition
/// between the two. This means `dst: b"abc", data: b"def"`, will produce the same scalar as
/// `dst: "abcdef", data: b""`. Please use carefully, not letting dsts be substrings of each other.
#[derive(Clone, Copy, PartialEq, Eq, Debug, zeroize::Zeroize)]
pub struct Embedwards25519;
impl ciphersuite::Ciphersuite for Embedwards25519 {
type F = Scalar;
type G = Point;
type H = blake2::Blake2b512;
const ID: &'static [u8] = b"embedwards25519";
fn generator() -> Self::G {
Point::generator()
}
fn hash_to_F(dst: &[u8], data: &[u8]) -> Self::F {
use blake2::Digest;
Scalar::wide_reduce(Self::H::digest([dst, data].concat()).as_slice().try_into().unwrap())
}
}
impl generalized_bulletproofs_ec_gadgets::DiscreteLogParameters for Embedwards25519 {
type ScalarBits = U<{ Scalar::NUM_BITS as usize }>;
type XCoefficients = Quot<Sum<Self::ScalarBits, U1>, U2>;
type XCoefficientsMinusOne = Diff<Self::XCoefficients, U1>;
type YxCoefficients = Diff<Quot<Sum<Sum<Self::ScalarBits, U1>, U1>, U2>, U2>;
}

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use core::{
ops::{DerefMut, Add, AddAssign, Neg, Sub, SubAssign, Mul, MulAssign},
iter::Sum,
};
use rand_core::RngCore;
use zeroize::Zeroize;
use subtle::{Choice, CtOption, ConstantTimeEq, ConditionallySelectable};
use ciphersuite::group::{
ff::{Field, PrimeField, PrimeFieldBits},
Group, GroupEncoding,
prime::PrimeGroup,
};
use crate::{backend::u8_from_bool, Scalar, FieldElement};
#[allow(non_snake_case)]
fn B() -> FieldElement {
FieldElement::from_repr(hex_literal::hex!(
"5f07603a853f20370b682036210d463e64903a23ea669d07ca26cfc13f594209"
))
.unwrap()
}
fn recover_y(x: FieldElement) -> CtOption<FieldElement> {
// x**3 - 3 * x + B
((x.square() * x) - (x.double() + x) + B()).sqrt()
}
/// Point.
#[derive(Clone, Copy, Debug, Zeroize)]
#[repr(C)]
pub struct Point {
x: FieldElement, // / Z
y: FieldElement, // / Z
z: FieldElement,
}
impl ConstantTimeEq for Point {
fn ct_eq(&self, other: &Self) -> Choice {
let x1 = self.x * other.z;
let x2 = other.x * self.z;
let y1 = self.y * other.z;
let y2 = other.y * self.z;
(self.x.is_zero() & other.x.is_zero()) | (x1.ct_eq(&x2) & y1.ct_eq(&y2))
}
}
impl PartialEq for Point {
fn eq(&self, other: &Point) -> bool {
self.ct_eq(other).into()
}
}
impl Eq for Point {}
impl ConditionallySelectable for Point {
fn conditional_select(a: &Self, b: &Self, choice: Choice) -> Self {
Point {
x: FieldElement::conditional_select(&a.x, &b.x, choice),
y: FieldElement::conditional_select(&a.y, &b.y, choice),
z: FieldElement::conditional_select(&a.z, &b.z, choice),
}
}
}
impl Add for Point {
type Output = Point;
#[allow(non_snake_case)]
fn add(self, other: Self) -> Self {
// add-2015-rcb
let a = -FieldElement::from(3u64);
let B = B();
let b3 = B + B + B;
let X1 = self.x;
let Y1 = self.y;
let Z1 = self.z;
let X2 = other.x;
let Y2 = other.y;
let Z2 = other.z;
let t0 = X1 * X2;
let t1 = Y1 * Y2;
let t2 = Z1 * Z2;
let t3 = X1 + Y1;
let t4 = X2 + Y2;
let t3 = t3 * t4;
let t4 = t0 + t1;
let t3 = t3 - t4;
let t4 = X1 + Z1;
let t5 = X2 + Z2;
let t4 = t4 * t5;
let t5 = t0 + t2;
let t4 = t4 - t5;
let t5 = Y1 + Z1;
let X3 = Y2 + Z2;
let t5 = t5 * X3;
let X3 = t1 + t2;
let t5 = t5 - X3;
let Z3 = a * t4;
let X3 = b3 * t2;
let Z3 = X3 + Z3;
let X3 = t1 - Z3;
let Z3 = t1 + Z3;
let Y3 = X3 * Z3;
let t1 = t0 + t0;
let t1 = t1 + t0;
let t2 = a * t2;
let t4 = b3 * t4;
let t1 = t1 + t2;
let t2 = t0 - t2;
let t2 = a * t2;
let t4 = t4 + t2;
let t0 = t1 * t4;
let Y3 = Y3 + t0;
let t0 = t5 * t4;
let X3 = t3 * X3;
let X3 = X3 - t0;
let t0 = t3 * t1;
let Z3 = t5 * Z3;
let Z3 = Z3 + t0;
Point { x: X3, y: Y3, z: Z3 }
}
}
impl AddAssign for Point {
fn add_assign(&mut self, other: Point) {
*self = *self + other;
}
}
impl Add<&Point> for Point {
type Output = Point;
fn add(self, other: &Point) -> Point {
self + *other
}
}
impl AddAssign<&Point> for Point {
fn add_assign(&mut self, other: &Point) {
*self += *other;
}
}
impl Neg for Point {
type Output = Point;
fn neg(self) -> Self {
Point { x: self.x, y: -self.y, z: self.z }
}
}
impl Sub for Point {
type Output = Point;
#[allow(clippy::suspicious_arithmetic_impl)]
fn sub(self, other: Self) -> Self {
self + other.neg()
}
}
impl SubAssign for Point {
fn sub_assign(&mut self, other: Point) {
*self = *self - other;
}
}
impl Sub<&Point> for Point {
type Output = Point;
fn sub(self, other: &Point) -> Point {
self - *other
}
}
impl SubAssign<&Point> for Point {
fn sub_assign(&mut self, other: &Point) {
*self -= *other;
}
}
impl Group for Point {
type Scalar = Scalar;
fn random(mut rng: impl RngCore) -> Self {
loop {
let mut bytes = [0; 32];
rng.fill_bytes(bytes.as_mut());
let opt = Self::from_bytes(&bytes);
if opt.is_some().into() {
return opt.unwrap();
}
}
}
fn identity() -> Self {
Point { x: FieldElement::ZERO, y: FieldElement::ONE, z: FieldElement::ZERO }
}
fn generator() -> Self {
Point {
x: FieldElement::from_repr(hex_literal::hex!(
"0100000000000000000000000000000000000000000000000000000000000000"
))
.unwrap(),
y: FieldElement::from_repr(hex_literal::hex!(
"2e4118080a484a3dfbafe2199a0e36b7193581d676c0dadfa376b0265616020c"
))
.unwrap(),
z: FieldElement::ONE,
}
}
fn is_identity(&self) -> Choice {
self.z.ct_eq(&FieldElement::ZERO)
}
#[allow(non_snake_case)]
fn double(&self) -> Self {
// dbl-2007-bl-2
let X1 = self.x;
let Y1 = self.y;
let Z1 = self.z;
let w = (X1 - Z1) * (X1 + Z1);
let w = w.double() + w;
let s = (Y1 * Z1).double();
let ss = s.square();
let sss = s * ss;
let R = Y1 * s;
let RR = R.square();
let B_ = (X1 * R).double();
let h = w.square() - B_.double();
let X3 = h * s;
let Y3 = w * (B_ - h) - RR.double();
let Z3 = sss;
let res = Self { x: X3, y: Y3, z: Z3 };
// If self is identity, res will not be well-formed
// Accordingly, we return self if self was the identity
Self::conditional_select(&res, self, self.is_identity())
}
}
impl Sum<Point> for Point {
fn sum<I: Iterator<Item = Point>>(iter: I) -> Point {
let mut res = Self::identity();
for i in iter {
res += i;
}
res
}
}
impl<'a> Sum<&'a Point> for Point {
fn sum<I: Iterator<Item = &'a Point>>(iter: I) -> Point {
Point::sum(iter.cloned())
}
}
impl Mul<Scalar> for Point {
type Output = Point;
fn mul(self, mut other: Scalar) -> Point {
// Precompute the optimal amount that's a multiple of 2
let mut table = [Point::identity(); 16];
table[1] = self;
for i in 2 .. 16 {
table[i] = table[i - 1] + self;
}
let mut res = Self::identity();
let mut bits = 0;
for (i, mut bit) in other.to_le_bits().iter_mut().rev().enumerate() {
bits <<= 1;
let mut bit = u8_from_bool(bit.deref_mut());
bits |= bit;
bit.zeroize();
if ((i + 1) % 4) == 0 {
if i != 3 {
for _ in 0 .. 4 {
res = res.double();
}
}
let mut term = table[0];
for (j, candidate) in table[1 ..].iter().enumerate() {
let j = j + 1;
term = Self::conditional_select(&term, candidate, usize::from(bits).ct_eq(&j));
}
res += term;
bits = 0;
}
}
other.zeroize();
res
}
}
impl MulAssign<Scalar> for Point {
fn mul_assign(&mut self, other: Scalar) {
*self = *self * other;
}
}
impl Mul<&Scalar> for Point {
type Output = Point;
fn mul(self, other: &Scalar) -> Point {
self * *other
}
}
impl MulAssign<&Scalar> for Point {
fn mul_assign(&mut self, other: &Scalar) {
*self *= *other;
}
}
impl GroupEncoding for Point {
type Repr = [u8; 32];
fn from_bytes(bytes: &Self::Repr) -> CtOption<Self> {
// Extract and clear the sign bit
let mut bytes = *bytes;
let sign = Choice::from(bytes[31] >> 7);
bytes[31] &= u8::MAX >> 1;
// Parse x, recover y
FieldElement::from_repr(bytes).and_then(|x| {
let is_identity = x.is_zero();
let y = recover_y(x).map(|mut y| {
y = <_>::conditional_select(&y, &-y, y.is_odd().ct_eq(&!sign));
y
});
// If this the identity, set y to 1
let y =
CtOption::conditional_select(&y, &CtOption::new(FieldElement::ONE, 1.into()), is_identity);
// Create the point if we have a y solution
let point = y.map(|y| Point { x, y, z: FieldElement::ONE });
let not_negative_zero = !(is_identity & sign);
// Only return the point if it isn't -0
CtOption::conditional_select(
&CtOption::new(Point::identity(), 0.into()),
&point,
not_negative_zero,
)
})
}
fn from_bytes_unchecked(bytes: &Self::Repr) -> CtOption<Self> {
Point::from_bytes(bytes)
}
fn to_bytes(&self) -> Self::Repr {
let Some(z) = Option::<FieldElement>::from(self.z.invert()) else {
return [0; 32];
};
let x = self.x * z;
let y = self.y * z;
let mut res = [0; 32];
res.as_mut().copy_from_slice(&x.to_repr());
// The following conditional select normalizes the sign to 0 when x is 0
let y_sign = u8::conditional_select(&y.is_odd().unwrap_u8(), &0, x.ct_eq(&FieldElement::ZERO));
res[31] |= y_sign << 7;
res
}
}
impl PrimeGroup for Point {}
impl ec_divisors::DivisorCurve for Point {
type FieldElement = FieldElement;
fn a() -> Self::FieldElement {
-FieldElement::from(3u64)
}
fn b() -> Self::FieldElement {
B()
}
fn to_xy(point: Self) -> Option<(Self::FieldElement, Self::FieldElement)> {
let z: Self::FieldElement = Option::from(point.z.invert())?;
Some((point.x * z, point.y * z))
}
}
#[test]
fn test_curve() {
ff_group_tests::group::test_prime_group_bits::<_, Point>(&mut rand_core::OsRng);
}
#[test]
fn generator() {
assert_eq!(
Point::generator(),
Point::from_bytes(&hex_literal::hex!(
"0100000000000000000000000000000000000000000000000000000000000000"
))
.unwrap()
);
}
#[test]
fn zero_x_is_invalid() {
assert!(Option::<FieldElement>::from(recover_y(FieldElement::ZERO)).is_none());
}
// Checks random won't infinitely loop
#[test]
fn random() {
Point::random(&mut rand_core::OsRng);
}

52
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use zeroize::{DefaultIsZeroes, Zeroize};
use crypto_bigint::{
U256, U512,
modular::constant_mod::{ResidueParams, Residue},
};
const MODULUS_STR: &str = "0fffffffffffffffffffffffffffffffe53f4debb78ff96877063f0306eef96b";
impl_modulus!(EmbedwardsQ, U256, MODULUS_STR);
type ResidueType = Residue<EmbedwardsQ, { EmbedwardsQ::LIMBS }>;
/// The Scalar field of Embedwards25519.
///
/// This is equivalent to the field secp256k1 is defined over.
#[derive(Clone, Copy, PartialEq, Eq, Default, Debug)]
#[repr(C)]
pub struct Scalar(pub(crate) ResidueType);
impl DefaultIsZeroes for Scalar {}
pub(crate) const MODULUS: U256 = U256::from_be_hex(MODULUS_STR);
const WIDE_MODULUS: U512 = U512::from_be_hex(concat!(
"0000000000000000000000000000000000000000000000000000000000000000",
"0fffffffffffffffffffffffffffffffe53f4debb78ff96877063f0306eef96b",
));
field!(
Scalar,
ResidueType,
MODULUS_STR,
MODULUS,
WIDE_MODULUS,
252,
10,
1,
"0fffffffffffffffffffffffffffffffe53f4debb78ff96877063f0306eef96a",
"0000000000000000000000000000000000000000000000000000000000000064",
);
impl Scalar {
/// Perform a wide reduction, presumably to obtain a non-biased Scalar field element.
pub fn wide_reduce(bytes: [u8; 64]) -> Scalar {
Scalar(Residue::new(&reduce(U512::from_le_slice(bytes.as_ref()))))
}
}
#[test]
fn test_scalar_field() {
ff_group_tests::prime_field::test_prime_field_bits::<_, Scalar>(&mut rand_core::OsRng);
}

33
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[package]
name = "generalized-bulletproofs"
version = "0.1.0"
description = "Generalized Bulletproofs"
license = "MIT"
repository = "https://github.com/serai-dex/serai/tree/develop/crypto/evrf/generalized-bulletproofs"
authors = ["Luke Parker <lukeparker5132@gmail.com>"]
keywords = ["ciphersuite", "ff", "group"]
edition = "2021"
[package.metadata.docs.rs]
all-features = true
rustdoc-args = ["--cfg", "docsrs"]
[dependencies]
rand_core = { version = "0.6", default-features = false, features = ["std"] }
zeroize = { version = "^1.5", default-features = false, features = ["std", "zeroize_derive"] }
blake2 = { version = "0.10", default-features = false, features = ["std"] }
multiexp = { path = "../../multiexp", version = "0.4", default-features = false, features = ["std", "batch"] }
ciphersuite = { path = "../../ciphersuite", version = "0.4", default-features = false, features = ["std"] }
[dev-dependencies]
rand_core = { version = "0.6", features = ["getrandom"] }
transcript = { package = "flexible-transcript", path = "../../transcript", features = ["recommended"] }
ciphersuite = { path = "../../ciphersuite", features = ["ristretto"] }
[features]
tests = []

21
crypto/evrf/generalized-bulletproofs/LICENSE Normal file
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MIT License
Copyright (c) 2021-2024 Luke Parker
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.

6
crypto/evrf/generalized-bulletproofs/README.md Normal file
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# Generalized Bulletproofs
An implementation of
[Generalized Bulletproofs](https://repo.getmonero.org/monero-project/ccs-proposals/uploads/a9baa50c38c6312efc0fea5c6a188bb9/gbp.pdf),
a variant of the Bulletproofs arithmetic circuit statement to support Pedersen
vector commitments.

679
crypto/evrf/generalized-bulletproofs/src/arithmetic_circuit_proof.rs Normal file
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use rand_core::{RngCore, CryptoRng};
use zeroize::{Zeroize, ZeroizeOnDrop};
use multiexp::{multiexp, multiexp_vartime};
use ciphersuite::{group::ff::Field, Ciphersuite};
use crate::{
ScalarVector, PointVector, ProofGenerators, PedersenCommitment, PedersenVectorCommitment,
BatchVerifier,
transcript::*,
lincomb::accumulate_vector,
inner_product::{IpError, IpStatement, IpWitness, P},
};
pub use crate::lincomb::{Variable, LinComb};
/// An Arithmetic Circuit Statement.
///
/// Bulletproofs' constraints are of the form
/// `aL * aR = aO, WL * aL + WR * aR + WO * aO = WV * V + c`.
///
/// Generalized Bulletproofs modifies this to
/// `aL * aR = aO, WL * aL + WR * aR + WO * aO + WCG * C_G + WCH * C_H = WV * V + c`.
///
/// We implement the latter, yet represented (for simplicity) as
/// `aL * aR = aO, WL * aL + WR * aR + WO * aO + WCG * C_G + WCH * C_H + WV * V + c = 0`.
#[derive(Clone, Debug)]
pub struct ArithmeticCircuitStatement<'a, C: Ciphersuite> {
generators: ProofGenerators<'a, C>,
constraints: Vec<LinComb<C::F>>,
C: PointVector<C>,
V: PointVector<C>,
}
impl<'a, C: Ciphersuite> Zeroize for ArithmeticCircuitStatement<'a, C> {
fn zeroize(&mut self) {
self.constraints.zeroize();
self.C.zeroize();
self.V.zeroize();
}
}
/// The witness for an arithmetic circuit statement.
#[derive(Clone, Debug, Zeroize, ZeroizeOnDrop)]
pub struct ArithmeticCircuitWitness<C: Ciphersuite> {
aL: ScalarVector<C::F>,
aR: ScalarVector<C::F>,
aO: ScalarVector<C::F>,
c: Vec<PedersenVectorCommitment<C>>,
v: Vec<PedersenCommitment<C>>,
}
/// An error incurred during arithmetic circuit proof operations.
#[derive(Clone, Copy, PartialEq, Eq, Debug)]
pub enum AcError {
/// The vectors of scalars which are multiplied against each other were of different lengths.
DifferingLrLengths,
/// The matrices of constraints are of different lengths.
InconsistentAmountOfConstraints,
/// A constraint referred to a non-existent term.
ConstrainedNonExistentTerm,
/// A constraint referred to a non-existent commitment.
ConstrainedNonExistentCommitment,
/// There weren't enough generators to prove for this statement.
NotEnoughGenerators,
/// The witness was inconsistent to the statement.
///
/// Sanity checks on the witness are always performed. If the library is compiled with debug
/// assertions on, the satisfaction of all constraints and validity of the commitmentsd is
/// additionally checked.
InconsistentWitness,
/// There was an error from the inner-product proof.
Ip(IpError),
/// The proof wasn't complete and the necessary values could not be read from the transcript.
IncompleteProof,
}
impl<C: Ciphersuite> ArithmeticCircuitWitness<C> {
/// Constructs a new witness instance.
pub fn new(
aL: ScalarVector<C::F>,
aR: ScalarVector<C::F>,
c: Vec<PedersenVectorCommitment<C>>,
v: Vec<PedersenCommitment<C>>,
) -> Result<Self, AcError> {
if aL.len() != aR.len() {
Err(AcError::DifferingLrLengths)?;
}
// The Pedersen Vector Commitments don't have their variables' lengths checked as they aren't
// paired off with each other as aL, aR are
// The PVC commit function ensures there's enough generators for their amount of terms
// If there aren't enough/the same generators when this is proven for, it'll trigger
// InconsistentWitness
let aO = aL.clone() * &aR;
Ok(ArithmeticCircuitWitness { aL, aR, aO, c, v })
}
}
struct YzChallenges<C: Ciphersuite> {
y_inv: ScalarVector<C::F>,
z: ScalarVector<C::F>,
}
impl<'a, C: Ciphersuite> ArithmeticCircuitStatement<'a, C> {
// The amount of multiplications performed.
fn n(&self) -> usize {
self.generators.len()
}
// The amount of constraints.
fn q(&self) -> usize {
self.constraints.len()
}
// The amount of Pedersen vector commitments.
fn c(&self) -> usize {
self.C.len()
}
// The amount of Pedersen commitments.
fn m(&self) -> usize {
self.V.len()
}
/// Create a new ArithmeticCircuitStatement for the specified relationship.
///
/// The `LinComb`s passed as `constraints` will be bound to evaluate to 0.
///
/// The constraints are not transcripted. They're expected to be deterministic from the context
/// and higher-level statement. If your constraints are variable, you MUST transcript them before
/// calling prove/verify.
///
/// The commitments are expected to have been transcripted extenally to this statement's
/// invocation. That's practically ensured by taking a `Commitments` struct here, which is only
/// obtainable via a transcript.
pub fn new(
generators: ProofGenerators<'a, C>,
constraints: Vec<LinComb<C::F>>,
commitments: Commitments<C>,
) -> Result<Self, AcError> {
let Commitments { C, V } = commitments;
for constraint in &constraints {
if Some(generators.len()) <= constraint.highest_a_index {
Err(AcError::ConstrainedNonExistentTerm)?;
}
if Some(C.len()) <= constraint.highest_c_index {
Err(AcError::ConstrainedNonExistentCommitment)?;
}
if Some(V.len()) <= constraint.highest_v_index {
Err(AcError::ConstrainedNonExistentCommitment)?;
}
}
Ok(Self { generators, constraints, C, V })
}
fn yz_challenges(&self, y: C::F, z_1: C::F) -> YzChallenges<C> {
let y_inv = y.invert().unwrap();
let y_inv = ScalarVector::powers(y_inv, self.n());
// Powers of z *starting with z**1*
// We could reuse powers and remove the first element, yet this is cheaper than the shift that
// would require
let q = self.q();
let mut z = ScalarVector(Vec::with_capacity(q));
z.0.push(z_1);
for _ in 1 .. q {
z.0.push(*z.0.last().unwrap() * z_1);
}
z.0.truncate(q);
YzChallenges { y_inv, z }
}
/// Prove for this statement/witness.
pub fn prove<R: RngCore + CryptoRng>(
self,
rng: &mut R,
transcript: &mut Transcript,
mut witness: ArithmeticCircuitWitness<C>,
) -> Result<(), AcError> {
let n = self.n();
let c = self.c();
let m = self.m();
// Check the witness length and pad it to the necessary power of two
if witness.aL.len() > n {
Err(AcError::NotEnoughGenerators)?;
}
while witness.aL.len() < n {
witness.aL.0.push(C::F::ZERO);
witness.aR.0.push(C::F::ZERO);
witness.aO.0.push(C::F::ZERO);
}
for c in &mut witness.c {
if c.g_values.len() > n {
Err(AcError::NotEnoughGenerators)?;
}
if c.h_values.len() > n {
Err(AcError::NotEnoughGenerators)?;
}
// The Pedersen vector commitments internally have n terms
while c.g_values.len() < n {
c.g_values.0.push(C::F::ZERO);
}
while c.h_values.len() < n {
c.h_values.0.push(C::F::ZERO);
}
}
// Check the witness's consistency with the statement
if (c != witness.c.len()) || (m != witness.v.len()) {
Err(AcError::InconsistentWitness)?;
}
#[cfg(debug_assertions)]
{
for (commitment, opening) in self.V.0.iter().zip(witness.v.iter()) {
if *commitment != opening.commit(self.generators.g(), self.generators.h()) {
Err(AcError::InconsistentWitness)?;
}
}
for (commitment, opening) in self.C.0.iter().zip(witness.c.iter()) {
if Some(*commitment) !=
opening.commit(
self.generators.g_bold_slice(),
self.generators.h_bold_slice(),
self.generators.h(),
)
{
Err(AcError::InconsistentWitness)?;
}
}
for constraint in &self.constraints {
let eval =
constraint
.WL
.iter()
.map(|(i, weight)| *weight * witness.aL[*i])
.chain(constraint.WR.iter().map(|(i, weight)| *weight * witness.aR[*i]))
.chain(constraint.WO.iter().map(|(i, weight)| *weight * witness.aO[*i]))
.chain(
constraint.WCG.iter().zip(&witness.c).flat_map(|(weights, c)| {
weights.iter().map(|(j, weight)| *weight * c.g_values[*j])
}),
)
.chain(
constraint.WCH.iter().zip(&witness.c).flat_map(|(weights, c)| {
weights.iter().map(|(j, weight)| *weight * c.h_values[*j])
}),
)
.chain(constraint.WV.iter().map(|(i, weight)| *weight * witness.v[*i].value))
.chain(core::iter::once(constraint.c))
.sum::<C::F>();
if eval != C::F::ZERO {
Err(AcError::InconsistentWitness)?;
}
}
}
let alpha = C::F::random(&mut *rng);
let beta = C::F::random(&mut *rng);
let rho = C::F::random(&mut *rng);
let AI = {
let alg = witness.aL.0.iter().enumerate().map(|(i, aL)| (*aL, self.generators.g_bold(i)));
let arh = witness.aR.0.iter().enumerate().map(|(i, aR)| (*aR, self.generators.h_bold(i)));
let ah = core::iter::once((alpha, self.generators.h()));
let mut AI_terms = alg.chain(arh).chain(ah).collect::<Vec<_>>();
let AI = multiexp(&AI_terms);
AI_terms.zeroize();
AI
};
let AO = {
let aog = witness.aO.0.iter().enumerate().map(|(i, aO)| (*aO, self.generators.g_bold(i)));
let bh = core::iter::once((beta, self.generators.h()));
let mut AO_terms = aog.chain(bh).collect::<Vec<_>>();
let AO = multiexp(&AO_terms);
AO_terms.zeroize();
AO
};
let mut sL = ScalarVector(Vec::with_capacity(n));
let mut sR = ScalarVector(Vec::with_capacity(n));
for _ in 0 .. n {
sL.0.push(C::F::random(&mut *rng));
sR.0.push(C::F::random(&mut *rng));
}
let S = {
let slg = sL.0.iter().enumerate().map(|(i, sL)| (*sL, self.generators.g_bold(i)));
let srh = sR.0.iter().enumerate().map(|(i, sR)| (*sR, self.generators.h_bold(i)));
let rh = core::iter::once((rho, self.generators.h()));
let mut S_terms = slg.chain(srh).chain(rh).collect::<Vec<_>>();
let S = multiexp(&S_terms);
S_terms.zeroize();
S
};
transcript.push_point(AI);
transcript.push_point(AO);
transcript.push_point(S);
let y = transcript.challenge();
let z = transcript.challenge();
let YzChallenges { y_inv, z } = self.yz_challenges(y, z);
let y = ScalarVector::powers(y, n);
// t is a n'-term polynomial
// While Bulletproofs discuss it as a 6-term polynomial, Generalized Bulletproofs re-defines it
// as `2(n' + 1)`-term, where `n'` is `2 (c + 1)`.
// When `c = 0`, `n' = 2`, and t is `6` (which lines up with Bulletproofs having a 6-term
// polynomial).
// ni = n'
let ni = 2 * (c + 1);
// These indexes are from the Generalized Bulletproofs paper
#[rustfmt::skip]
let ilr = ni / 2; // 1 if c = 0
#[rustfmt::skip]
let io = ni; // 2 if c = 0
#[rustfmt::skip]
let is = ni + 1; // 3 if c = 0
#[rustfmt::skip]
let jlr = ni / 2; // 1 if c = 0
#[rustfmt::skip]
let jo = 0; // 0 if c = 0
#[rustfmt::skip]
let js = ni + 1; // 3 if c = 0
// If c = 0, these indexes perfectly align with the stated powers of X from the Bulletproofs
// paper for the following coefficients
// Declare the l and r polynomials, assigning the traditional coefficients to their positions
let mut l = vec![];
let mut r = vec![];
for _ in 0 .. (is + 1) {
l.push(ScalarVector::new(0));
r.push(ScalarVector::new(0));
}
let mut l_weights = ScalarVector::new(n);
let mut r_weights = ScalarVector::new(n);
let mut o_weights = ScalarVector::new(n);
for (constraint, z) in self.constraints.iter().zip(&z.0) {
accumulate_vector(&mut l_weights, &constraint.WL, *z);
accumulate_vector(&mut r_weights, &constraint.WR, *z);
accumulate_vector(&mut o_weights, &constraint.WO, *z);
}
l[ilr] = (r_weights * &y_inv) + &witness.aL;
l[io] = witness.aO.clone();
l[is] = sL;
r[jlr] = l_weights + &(witness.aR.clone() * &y);
r[jo] = o_weights - &y;
r[js] = sR * &y;
// Pad as expected
for l in &mut l {
debug_assert!((l.len() == 0) || (l.len() == n));
if l.len() == 0 {
*l = ScalarVector::new(n);
}
}
for r in &mut r {
debug_assert!((r.len() == 0) || (r.len() == n));
if r.len() == 0 {
*r = ScalarVector::new(n);
}
}
// We now fill in the vector commitments
// We use unused coefficients of l increasing from 0 (skipping ilr), and unused coefficients of
// r decreasing from n' (skipping jlr)
let mut cg_weights = Vec::with_capacity(witness.c.len());
let mut ch_weights = Vec::with_capacity(witness.c.len());
for i in 0 .. witness.c.len() {
let mut cg = ScalarVector::new(n);
let mut ch = ScalarVector::new(n);
for (constraint, z) in self.constraints.iter().zip(&z.0) {
if let Some(WCG) = constraint.WCG.get(i) {
accumulate_vector(&mut cg, WCG, *z);
}
if let Some(WCH) = constraint.WCH.get(i) {
accumulate_vector(&mut ch, WCH, *z);
}
}
cg_weights.push(cg);
ch_weights.push(ch);
}
for (i, (c, (cg_weights, ch_weights))) in
witness.c.iter().zip(cg_weights.into_iter().zip(ch_weights)).enumerate()
{
let i = i + 1;
let j = ni - i;
l[i] = c.g_values.clone();
l[j] = ch_weights * &y_inv;
r[j] = cg_weights;
r[i] = (c.h_values.clone() * &y) + &r[i];
}
// Multiply them to obtain t
let mut t = ScalarVector::new(1 + (2 * (l.len() - 1)));
for (i, l) in l.iter().enumerate() {
for (j, r) in r.iter().enumerate() {
let new_coeff = i + j;
t[new_coeff] += l.inner_product(r.0.iter());
}
}
// Per Bulletproofs, calculate masks tau for each t where (i > 0) && (i != 2)
// Per Generalized Bulletproofs, calculate masks tau for each t where i != n'
// With Bulletproofs, t[0] is zero, hence its omission, yet Generalized Bulletproofs uses it
let mut tau_before_ni = vec![];
for _ in 0 .. ni {
tau_before_ni.push(C::F::random(&mut *rng));
}
let mut tau_after_ni = vec![];
for _ in 0 .. t.0[(ni + 1) ..].len() {
tau_after_ni.push(C::F::random(&mut *rng));
}
// Calculate commitments to the coefficients of t, blinded by tau
debug_assert_eq!(t.0[0 .. ni].len(), tau_before_ni.len());
for (t, tau) in t.0[0 .. ni].iter().zip(tau_before_ni.iter()) {
transcript.push_point(multiexp(&[(*t, self.generators.g()), (*tau, self.generators.h())]));
}
debug_assert_eq!(t.0[(ni + 1) ..].len(), tau_after_ni.len());
for (t, tau) in t.0[(ni + 1) ..].iter().zip(tau_after_ni.iter()) {
transcript.push_point(multiexp(&[(*t, self.generators.g()), (*tau, self.generators.h())]));
}
let x: ScalarVector<C::F> = ScalarVector::powers(transcript.challenge(), t.len());
let poly_eval = |poly: &[ScalarVector<C::F>], x: &ScalarVector<_>| -> ScalarVector<_> {
let mut res = ScalarVector::<C::F>::new(poly[0].0.len());
for (i, coeff) in poly.iter().enumerate() {
res = res + &(coeff.clone() * x[i]);
}
res
};
let l = poly_eval(&l, &x);
let r = poly_eval(&r, &x);
let t_caret = l.inner_product(r.0.iter());
let mut V_weights = ScalarVector::new(self.V.len());
for (constraint, z) in self.constraints.iter().zip(&z.0) {
// We use `-z`, not `z`, as we write our constraint as `... + WV V = 0` not `= WV V + ..`
// This means we need to subtract `WV V` from both sides, which we accomplish here
accumulate_vector(&mut V_weights, &constraint.WV, -*z);
}
let tau_x = {
let mut tau_x_poly = vec![];
tau_x_poly.extend(tau_before_ni);
tau_x_poly.push(V_weights.inner_product(witness.v.iter().map(|v| &v.mask)));
tau_x_poly.extend(tau_after_ni);
let mut tau_x = C::F::ZERO;
for (i, coeff) in tau_x_poly.into_iter().enumerate() {
tau_x += coeff * x[i];
}
tau_x
};
// Calculate u for the powers of x variable to ilr/io/is
let u = {
// Calculate the first part of u
let mut u = (alpha * x[ilr]) + (beta * x[io]) + (rho * x[is]);
// Incorporate the commitment masks multiplied by the associated power of x
for (i, commitment) in witness.c.iter().enumerate() {
let i = i + 1;
u += x[i] * commitment.mask;
}
u
};
// Use the Inner-Product argument to prove for this
// P = t_caret * g + l * g_bold + r * (y_inv * h_bold)
let mut P_terms = Vec::with_capacity(1 + (2 * self.generators.len()));
debug_assert_eq!(l.len(), r.len());
for (i, (l, r)) in l.0.iter().zip(r.0.iter()).enumerate() {
P_terms.push((*l, self.generators.g_bold(i)));
P_terms.push((y_inv[i] * r, self.generators.h_bold(i)));
}
// Protocol 1, inlined, since our IpStatement is for Protocol 2
transcript.push_scalar(tau_x);
transcript.push_scalar(u);
transcript.push_scalar(t_caret);
let ip_x = transcript.challenge();
P_terms.push((ip_x * t_caret, self.generators.g()));
IpStatement::new(
self.generators,
y_inv,
ip_x,
// Safe since IpStatement isn't a ZK proof
P::Prover(multiexp_vartime(&P_terms)),
)
.unwrap()
.prove(transcript, IpWitness::new(l, r).unwrap())
.map_err(AcError::Ip)
}
/// Verify a proof for this statement.
pub fn verify<R: RngCore + CryptoRng>(
self,
rng: &mut R,
verifier: &mut BatchVerifier<C>,
transcript: &mut VerifierTranscript,
) -> Result<(), AcError> {
let n = self.n();
let c = self.c();
let ni = 2 * (c + 1);
let ilr = ni / 2;
let io = ni;
let is = ni + 1;
let jlr = ni / 2;
let l_r_poly_len = 1 + ni + 1;
let t_poly_len = (2 * l_r_poly_len) - 1;
let AI = transcript.read_point::<C>().map_err(|_| AcError::IncompleteProof)?;
let AO = transcript.read_point::<C>().map_err(|_| AcError::IncompleteProof)?;
let S = transcript.read_point::<C>().map_err(|_| AcError::IncompleteProof)?;
let y = transcript.challenge();
let z = transcript.challenge();
let YzChallenges { y_inv, z } = self.yz_challenges(y, z);
let mut l_weights = ScalarVector::new(n);
let mut r_weights = ScalarVector::new(n);
let mut o_weights = ScalarVector::new(n);
for (constraint, z) in self.constraints.iter().zip(&z.0) {
accumulate_vector(&mut l_weights, &constraint.WL, *z);
accumulate_vector(&mut r_weights, &constraint.WR, *z);
accumulate_vector(&mut o_weights, &constraint.WO, *z);
}
let r_weights = r_weights * &y_inv;
let delta = r_weights.inner_product(l_weights.0.iter());
let mut T_before_ni = Vec::with_capacity(ni);
let mut T_after_ni = Vec::with_capacity(t_poly_len - ni - 1);
for _ in 0 .. ni {
T_before_ni.push(transcript.read_point::<C>().map_err(|_| AcError::IncompleteProof)?);
}
for _ in 0 .. (t_poly_len - ni - 1) {
T_after_ni.push(transcript.read_point::<C>().map_err(|_| AcError::IncompleteProof)?);
}
let x: ScalarVector<C::F> = ScalarVector::powers(transcript.challenge(), t_poly_len);
let tau_x = transcript.read_scalar::<C>().map_err(|_| AcError::IncompleteProof)?;
let u = transcript.read_scalar::<C>().map_err(|_| AcError::IncompleteProof)?;
let t_caret = transcript.read_scalar::<C>().map_err(|_| AcError::IncompleteProof)?;
// Lines 88-90, modified per Generalized Bulletproofs as needed w.r.t. t
{
let verifier_weight = C::F::random(&mut *rng);
// lhs of the equation, weighted to enable batch verification
verifier.g += t_caret * verifier_weight;
verifier.h += tau_x * verifier_weight;
let mut V_weights = ScalarVector::new(self.V.len());
for (constraint, z) in self.constraints.iter().zip(&z.0) {
// We use `-z`, not `z`, as we write our constraint as `... + WV V = 0` not `= WV V + ..`
// This means we need to subtract `WV V` from both sides, which we accomplish here
accumulate_vector(&mut V_weights, &constraint.WV, -*z);
}
V_weights = V_weights * x[ni];
// rhs of the equation, negated to cause a sum to zero
// `delta - z...`, instead of `delta + z...`, is done for the same reason as in the above WV
// matrix transform
verifier.g -= verifier_weight *
x[ni] *
(delta - z.inner_product(self.constraints.iter().map(|constraint| &constraint.c)));
for pair in V_weights.0.into_iter().zip(self.V.0) {
verifier.additional.push((-verifier_weight * pair.0, pair.1));
}
for (i, T) in T_before_ni.into_iter().enumerate() {
verifier.additional.push((-verifier_weight * x[i], T));
}
for (i, T) in T_after_ni.into_iter().enumerate() {
verifier.additional.push((-verifier_weight * x[ni + 1 + i], T));
}
}
let verifier_weight = C::F::random(&mut *rng);
// Multiply `x` by `verifier_weight` as this effects `verifier_weight` onto most scalars and
// saves a notable amount of operations
let x = x * verifier_weight;
// This following block effectively calculates P, within the multiexp
{
verifier.additional.push((x[ilr], AI));
verifier.additional.push((x[io], AO));
// h' ** y is equivalent to h as h' is h ** y_inv
let mut log2_n = 0;
while (1 << log2_n) != n {
log2_n += 1;
}
verifier.h_sum[log2_n] -= verifier_weight;
verifier.additional.push((x[is], S));
// Lines 85-87 calculate WL, WR, WO
// We preserve them in terms of g_bold and h_bold for a more efficient multiexp
let mut h_bold_scalars = l_weights * x[jlr];
for (i, wr) in (r_weights * x[jlr]).0.into_iter().enumerate() {
verifier.g_bold[i] += wr;
}
// WO is weighted by x**jo where jo == 0, hence why we can ignore the x term
h_bold_scalars = h_bold_scalars + &(o_weights * verifier_weight);
let mut cg_weights = Vec::with_capacity(self.C.len());
let mut ch_weights = Vec::with_capacity(self.C.len());
for i in 0 .. self.C.len() {
let mut cg = ScalarVector::new(n);
let mut ch = ScalarVector::new(n);
for (constraint, z) in self.constraints.iter().zip(&z.0) {
if let Some(WCG) = constraint.WCG.get(i) {
accumulate_vector(&mut cg, WCG, *z);
}
if let Some(WCH) = constraint.WCH.get(i) {
accumulate_vector(&mut ch, WCH, *z);
}
}
cg_weights.push(cg);
ch_weights.push(ch);
}
// Push the terms for C, which increment from 0, and the terms for WC, which decrement from
// n'
for (i, (C, (WCG, WCH))) in
self.C.0.into_iter().zip(cg_weights.into_iter().zip(ch_weights)).enumerate()
{
let i = i + 1;
let j = ni - i;
verifier.additional.push((x[i], C));
h_bold_scalars = h_bold_scalars + &(WCG * x[j]);
for (i, scalar) in (WCH * &y_inv * x[j]).0.into_iter().enumerate() {
verifier.g_bold[i] += scalar;
}
}
// All terms for h_bold here have actually been for h_bold', h_bold * y_inv
h_bold_scalars = h_bold_scalars * &y_inv;
for (i, scalar) in h_bold_scalars.0.into_iter().enumerate() {
verifier.h_bold[i] += scalar;
}
// Remove u * h from P
verifier.h -= verifier_weight * u;
}
// Prove for lines 88, 92 with an Inner-Product statement
// This inlines Protocol 1, as our IpStatement implements Protocol 2
let ip_x = transcript.challenge();
// P is amended with this additional term
verifier.g += verifier_weight * ip_x * t_caret;
IpStatement::new(self.generators, y_inv, ip_x, P::Verifier { verifier_weight })
.unwrap()
.verify(verifier, transcript)
.map_err(AcError::Ip)?;
Ok(())
}
}

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use multiexp::multiexp_vartime;
use ciphersuite::{group::ff::Field, Ciphersuite};
#[rustfmt::skip]
use crate::{ScalarVector, PointVector, ProofGenerators, BatchVerifier, transcript::*, padded_pow_of_2};
/// An error from proving/verifying Inner-Product statements.
#[derive(Clone, Copy, PartialEq, Eq, Debug)]
pub enum IpError {
/// An incorrect amount of generators was provided.
IncorrectAmountOfGenerators,
/// The witness was inconsistent to the statement.
///
/// Sanity checks on the witness are always performed. If the library is compiled with debug
/// assertions on, whether or not this witness actually opens `P` is checked.
InconsistentWitness,
/// The proof wasn't complete and the necessary values could not be read from the transcript.
IncompleteProof,
}
#[derive(Clone, PartialEq, Eq, Debug)]
pub(crate) enum P<C: Ciphersuite> {
Verifier { verifier_weight: C::F },
Prover(C::G),
}
/// The Bulletproofs Inner-Product statement.
///
/// This is for usage with Protocol 2 from the Bulletproofs paper.
#[derive(Clone, Debug)]
pub(crate) struct IpStatement<'a, C: Ciphersuite> {
generators: ProofGenerators<'a, C>,
// Weights for h_bold
h_bold_weights: ScalarVector<C::F>,
// u as the discrete logarithm of G
u: C::F,
// P
P: P<C>,
}
/// The witness for the Bulletproofs Inner-Product statement.
#[derive(Clone, Debug)]
pub(crate) struct IpWitness<C: Ciphersuite> {
// a
a: ScalarVector<C::F>,
// b
b: ScalarVector<C::F>,
}
impl<C: Ciphersuite> IpWitness<C> {
/// Construct a new witness for an Inner-Product statement.
///
/// If the witness is less than a power of two, it is padded to the nearest power of two.
///
/// This functions return None if the lengths of a, b are mismatched or either are empty.
pub(crate) fn new(mut a: ScalarVector<C::F>, mut b: ScalarVector<C::F>) -> Option<Self> {
if a.0.is_empty() || (a.len() != b.len()) {
None?;
}
// Pad to the nearest power of 2
let missing = padded_pow_of_2(a.len()) - a.len();
a.0.reserve(missing);
b.0.reserve(missing);
for _ in 0 .. missing {
a.0.push(C::F::ZERO);
b.0.push(C::F::ZERO);
}
Some(Self { a, b })
}
}
impl<'a, C: Ciphersuite> IpStatement<'a, C> {
/// Create a new Inner-Product statement.
///
/// This does not perform any transcripting of any variables within this statement. They must be
/// deterministic to the existing transcript.
pub(crate) fn new(
generators: ProofGenerators<'a, C>,
h_bold_weights: ScalarVector<C::F>,
u: C::F,
P: P<C>,
) -> Result<Self, IpError> {
if generators.h_bold_slice().len() != h_bold_weights.len() {
Err(IpError::IncorrectAmountOfGenerators)?
}
Ok(Self { generators, h_bold_weights, u, P })
}
/// Prove for this Inner-Product statement.
///
/// Returns an error if this statement couldn't be proven for (such as if the witness isn't
/// consistent).
pub(crate) fn prove(
self,
transcript: &mut Transcript,
witness: IpWitness<C>,
) -> Result<(), IpError> {
let (mut g_bold, mut h_bold, u, mut P, mut a, mut b) = {
let IpStatement { generators, h_bold_weights, u, P } = self;
let u = generators.g() * u;
// Ensure we have the exact amount of generators
if generators.g_bold_slice().len() != witness.a.len() {
Err(IpError::IncorrectAmountOfGenerators)?;
}
// Acquire a local copy of the generators
let g_bold = PointVector::<C>(generators.g_bold_slice().to_vec());
let h_bold = PointVector::<C>(generators.h_bold_slice().to_vec()).mul_vec(&h_bold_weights);
let IpWitness { a, b } = witness;
let P = match P {
P::Prover(point) => point,
P::Verifier { .. } => {
panic!("prove called with a P specification which was for the verifier")
}
};
// Ensure this witness actually opens this statement
#[cfg(debug_assertions)]
{
let ag = a.0.iter().cloned().zip(g_bold.0.iter().cloned());
let bh = b.0.iter().cloned().zip(h_bold.0.iter().cloned());
let cu = core::iter::once((a.inner_product(b.0.iter()), u));
if P != multiexp_vartime(&ag.chain(bh).chain(cu).collect::<Vec<_>>()) {
Err(IpError::InconsistentWitness)?;
}
}
(g_bold, h_bold, u, P, a, b)
};
// `else: (n > 1)` case, lines 18-35 of the Bulletproofs paper
// This interprets `g_bold.len()` as `n`
while g_bold.len() > 1 {
// Split a, b, g_bold, h_bold as needed for lines 20-24
let (a1, a2) = a.clone().split();
let (b1, b2) = b.clone().split();
let (g_bold1, g_bold2) = g_bold.split();
let (h_bold1, h_bold2) = h_bold.split();
let n_hat = g_bold1.len();
// Sanity
debug_assert_eq!(a1.len(), n_hat);
debug_assert_eq!(a2.len(), n_hat);
debug_assert_eq!(b1.len(), n_hat);
debug_assert_eq!(b2.len(), n_hat);
debug_assert_eq!(g_bold1.len(), n_hat);
debug_assert_eq!(g_bold2.len(), n_hat);
debug_assert_eq!(h_bold1.len(), n_hat);
debug_assert_eq!(h_bold2.len(), n_hat);
// cl, cr, lines 21-22
let cl = a1.inner_product(b2.0.iter());
let cr = a2.inner_product(b1.0.iter());
let L = {
let mut L_terms = Vec::with_capacity(1 + (2 * g_bold1.len()));
for (a, g) in a1.0.iter().zip(g_bold2.0.iter()) {
L_terms.push((*a, *g));
}
for (b, h) in b2.0.iter().zip(h_bold1.0.iter()) {
L_terms.push((*b, *h));
}
L_terms.push((cl, u));
// Uses vartime since this isn't a ZK proof
multiexp_vartime(&L_terms)
};
let R = {
let mut R_terms = Vec::with_capacity(1 + (2 * g_bold1.len()));
for (a, g) in a2.0.iter().zip(g_bold1.0.iter()) {
R_terms.push((*a, *g));
}
for (b, h) in b1.0.iter().zip(h_bold2.0.iter()) {
R_terms.push((*b, *h));
}
R_terms.push((cr, u));
multiexp_vartime(&R_terms)
};
// Now that we've calculate L, R, transcript them to receive x (26-27)
transcript.push_point(L);
transcript.push_point(R);
let x: C::F = transcript.challenge();
let x_inv = x.invert().unwrap();
// The prover and verifier now calculate the following (28-31)
g_bold = PointVector(Vec::with_capacity(g_bold1.len()));
for (a, b) in g_bold1.0.into_iter().zip(g_bold2.0.into_iter()) {
g_bold.0.push(multiexp_vartime(&[(x_inv, a), (x, b)]));
}
h_bold = PointVector(Vec::with_capacity(h_bold1.len()));
for (a, b) in h_bold1.0.into_iter().zip(h_bold2.0.into_iter()) {
h_bold.0.push(multiexp_vartime(&[(x, a), (x_inv, b)]));
}
P = (L * (x * x)) + P + (R * (x_inv * x_inv));
// 32-34
a = (a1 * x) + &(a2 * x_inv);
b = (b1 * x_inv) + &(b2 * x);
}
// `if n = 1` case from line 14-17
// Sanity
debug_assert_eq!(g_bold.len(), 1);
debug_assert_eq!(h_bold.len(), 1);
debug_assert_eq!(a.len(), 1);
debug_assert_eq!(b.len(), 1);
// We simply send a/b
transcript.push_scalar(a[0]);
transcript.push_scalar(b[0]);
Ok(())
}
/*
This has room for optimization worth investigating further. It currently takes
an iterative approach. It can be optimized further via divide and conquer.
Assume there are 4 challenges.
Iterative approach (current):
1. Do the optimal multiplications across challenge column 0 and 1.
2. Do the optimal multiplications across that result and column 2.
3. Do the optimal multiplications across that result and column 3.
Divide and conquer (worth investigating further):
1. Do the optimal multiplications across challenge column 0 and 1.
2. Do the optimal multiplications across challenge column 2 and 3.
3. Multiply both results together.
When there are 4 challenges (n=16), the iterative approach does 28 multiplications
versus divide and conquer's 24.
*/
fn challenge_products(challenges: &[(C::F, C::F)]) -> Vec<C::F> {
let mut products = vec![C::F::ONE; 1 << challenges.len()];
if !challenges.is_empty() {
products[0] = challenges[0].1;
products[1] = challenges[0].0;
for (j, challenge) in challenges.iter().enumerate().skip(1) {
let mut slots = (1 << (j + 1)) - 1;
while slots > 0 {
products[slots] = products[slots / 2] * challenge.0;
products[slots - 1] = products[slots / 2] * challenge.1;
slots = slots.saturating_sub(2);
}
}
// Sanity check since if the above failed to populate, it'd be critical
for product in &products {
debug_assert!(!bool::from(product.is_zero()));
}
}
products
}
/// Queue an Inner-Product proof for batch verification.
///
/// This will return Err if there is an error. This will return Ok if the proof was successfully
/// queued for batch verification. The caller is required to verify the batch in order to ensure
/// the proof is actually correct.
pub(crate) fn verify(
self,
verifier: &mut BatchVerifier<C>,
transcript: &mut VerifierTranscript,
) -> Result<(), IpError> {
let IpStatement { generators, h_bold_weights, u, P } = self;
// Calculate the discrete log w.r.t. 2 for the amount of generators present
let mut lr_len = 0;
while (1 << lr_len) < generators.g_bold_slice().len() {
lr_len += 1;
}
let weight = match P {
P::Prover(_) => panic!("prove called with a P specification which was for the prover"),
P::Verifier { verifier_weight } => verifier_weight,
};
// Again, we start with the `else: (n > 1)` case
// We need x, x_inv per lines 25-27 for lines 28-31
let mut L = Vec::with_capacity(lr_len);
let mut R = Vec::with_capacity(lr_len);
let mut xs: Vec<C::F> = Vec::with_capacity(lr_len);
for _ in 0 .. lr_len {
L.push(transcript.read_point::<C>().map_err(|_| IpError::IncompleteProof)?);
R.push(transcript.read_point::<C>().map_err(|_| IpError::IncompleteProof)?);
xs.push(transcript.challenge());
}
// We calculate their inverse in batch
let mut x_invs = xs.clone();
{
let mut scratch = vec![C::F::ZERO; x_invs.len()];
ciphersuite::group::ff::BatchInverter::invert_with_external_scratch(
&mut x_invs,
&mut scratch,
);
}
// Now, with x and x_inv, we need to calculate g_bold', h_bold', P'
//
// For the sake of performance, we solely want to calculate all of these in terms of scalings
// for g_bold, h_bold, P, and don't want to actually perform intermediary scalings of the
// points
//
// L and R are easy, as it's simply x**2, x**-2
//
// For the series of g_bold, h_bold, we use the `challenge_products` function
// For how that works, please see its own documentation
let product_cache = {
let mut challenges = Vec::with_capacity(lr_len);
let x_iter = xs.into_iter().zip(x_invs);
let lr_iter = L.into_iter().zip(R);
for ((x, x_inv), (L, R)) in x_iter.zip(lr_iter) {
challenges.push((x, x_inv));
verifier.additional.push((weight * x.square(), L));
verifier.additional.push((weight * x_inv.square(), R));
}
Self::challenge_products(&challenges)
};
// And now for the `if n = 1` case
let a = transcript.read_scalar::<C>().map_err(|_| IpError::IncompleteProof)?;
let b = transcript.read_scalar::<C>().map_err(|_| IpError::IncompleteProof)?;
let c = a * b;
// The multiexp of these terms equate to the final permutation of P
// We now add terms for a * g_bold' + b * h_bold' b + c * u, with the scalars negative such
// that the terms sum to 0 for an honest prover
// The g_bold * a term case from line 16
#[allow(clippy::needless_range_loop)]
for i in 0 .. generators.g_bold_slice().len() {
verifier.g_bold[i] -= weight * product_cache[i] * a;
}
// The h_bold * b term case from line 16
for i in 0 .. generators.h_bold_slice().len() {
verifier.h_bold[i] -=
weight * product_cache[product_cache.len() - 1 - i] * b * h_bold_weights[i];
}
// The c * u term case from line 16
verifier.g -= weight * c * u;
Ok(())
}
}

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#![cfg_attr(docsrs, feature(doc_auto_cfg))]
#![doc = include_str!("../README.md")]
#![deny(missing_docs)]
#![allow(non_snake_case)]
use core::fmt;
use std::collections::HashSet;
use zeroize::Zeroize;
use multiexp::{multiexp, multiexp_vartime};
use ciphersuite::{
group::{ff::Field, Group, GroupEncoding},
Ciphersuite,
};
mod scalar_vector;
pub use scalar_vector::ScalarVector;
mod point_vector;
pub use point_vector::PointVector;
/// The transcript formats.
pub mod transcript;
pub(crate) mod inner_product;
pub(crate) mod lincomb;
/// The arithmetic circuit proof.
pub mod arithmetic_circuit_proof;
/// Functionlity useful when testing.
#[cfg(any(test, feature = "tests"))]
pub mod tests;
/// Calculate the nearest power of two greater than or equivalent to the argument.
pub(crate) fn padded_pow_of_2(i: usize) -> usize {
let mut next_pow_of_2 = 1;
while next_pow_of_2 < i {
next_pow_of_2 <<= 1;
}
next_pow_of_2
}
/// An error from working with generators.
#[derive(Clone, Copy, PartialEq, Eq, Debug)]
pub enum GeneratorsError {
/// The provided list of generators for `g` (bold) was empty.
GBoldEmpty,
/// The provided list of generators for `h` (bold) did not match `g` (bold) in length.
DifferingGhBoldLengths,
/// The amount of provided generators were not a power of two.
NotPowerOfTwo,
/// A generator was used multiple times.
DuplicatedGenerator,
}
/// A full set of generators.
#[derive(Clone)]
pub struct Generators<C: Ciphersuite> {
g: C::G,
h: C::G,
g_bold: Vec<C::G>,
h_bold: Vec<C::G>,
h_sum: Vec<C::G>,
}
/// A batch verifier of proofs.
#[must_use]
#[derive(Clone)]
pub struct BatchVerifier<C: Ciphersuite> {
g: C::F,
h: C::F,
g_bold: Vec<C::F>,
h_bold: Vec<C::F>,
h_sum: Vec<C::F>,
additional: Vec<(C::F, C::G)>,
}
impl<C: Ciphersuite> fmt::Debug for Generators<C> {
fn fmt(&self, fmt: &mut fmt::Formatter<'_>) -> fmt::Result {
let g = self.g.to_bytes();
let g: &[u8] = g.as_ref();
let h = self.h.to_bytes();
let h: &[u8] = h.as_ref();
fmt.debug_struct("Generators").field("g", &g).field("h", &h).finish_non_exhaustive()
}
}
/// The generators for a specific proof.
///
/// This potentially have been reduced in size from the original set of generators, as beneficial
/// to performance.
#[derive(Copy, Clone)]
pub struct ProofGenerators<'a, C: Ciphersuite> {
g: &'a C::G,
h: &'a C::G,
g_bold: &'a [C::G],
h_bold: &'a [C::G],
}
impl<C: Ciphersuite> fmt::Debug for ProofGenerators<'_, C> {
fn fmt(&self, fmt: &mut fmt::Formatter<'_>) -> fmt::Result {
let g = self.g.to_bytes();
let g: &[u8] = g.as_ref();
let h = self.h.to_bytes();
let h: &[u8] = h.as_ref();
fmt.debug_struct("ProofGenerators").field("g", &g).field("h", &h).finish_non_exhaustive()
}
}
impl<C: Ciphersuite> Generators<C> {
/// Construct an instance of Generators for usage with Bulletproofs.
pub fn new(
g: C::G,
h: C::G,
g_bold: Vec<C::G>,
h_bold: Vec<C::G>,
) -> Result<Self, GeneratorsError> {
if g_bold.is_empty() {
Err(GeneratorsError::GBoldEmpty)?;
}
if g_bold.len() != h_bold.len() {
Err(GeneratorsError::DifferingGhBoldLengths)?;
}
if padded_pow_of_2(g_bold.len()) != g_bold.len() {
Err(GeneratorsError::NotPowerOfTwo)?;
}
let mut set = HashSet::new();
let mut add_generator = |generator: &C::G| {
assert!(!bool::from(generator.is_identity()));
let bytes = generator.to_bytes();
!set.insert(bytes.as_ref().to_vec())
};
assert!(!add_generator(&g), "g was prior present in empty set");
if add_generator(&h) {
Err(GeneratorsError::DuplicatedGenerator)?;
}
for g in &g_bold {
if add_generator(g) {
Err(GeneratorsError::DuplicatedGenerator)?;
}
}
for h in &h_bold {
if add_generator(h) {
Err(GeneratorsError::DuplicatedGenerator)?;
}
}
let mut running_h_sum = C::G::identity();
let mut h_sum = vec![];
let mut next_pow_of_2 = 1;
for (i, h) in h_bold.iter().enumerate() {
running_h_sum += h;
if (i + 1) == next_pow_of_2 {
h_sum.push(running_h_sum);
next_pow_of_2 *= 2;
}
}
Ok(Generators { g, h, g_bold, h_bold, h_sum })
}
/// Create a BatchVerifier for proofs which use these generators.
pub fn batch_verifier(&self) -> BatchVerifier<C> {
BatchVerifier {
g: C::F::ZERO,
h: C::F::ZERO,
g_bold: vec![C::F::ZERO; self.g_bold.len()],
h_bold: vec![C::F::ZERO; self.h_bold.len()],
h_sum: vec![C::F::ZERO; self.h_sum.len()],
additional: Vec::with_capacity(128),
}
}
/// Verify all proofs queued for batch verification in this BatchVerifier.
#[must_use]
pub fn verify(&self, verifier: BatchVerifier<C>) -> bool {
multiexp_vartime(
&[(verifier.g, self.g), (verifier.h, self.h)]
.into_iter()
.chain(verifier.g_bold.into_iter().zip(self.g_bold.iter().cloned()))
.chain(verifier.h_bold.into_iter().zip(self.h_bold.iter().cloned()))
.chain(verifier.h_sum.into_iter().zip(self.h_sum.iter().cloned()))
.chain(verifier.additional)
.collect::<Vec<_>>(),
)
.is_identity()
.into()
}
/// The `g` generator.
pub fn g(&self) -> C::G {
self.g
}
/// The `h` generator.
pub fn h(&self) -> C::G {
self.h
}
/// A slice to view the `g` (bold) generators.
pub fn g_bold_slice(&self) -> &[C::G] {
&self.g_bold
}
/// A slice to view the `h` (bold) generators.
pub fn h_bold_slice(&self) -> &[C::G] {
&self.h_bold
}
/// Reduce a set of generators to the quantity necessary to support a certain amount of
/// in-circuit multiplications/terms in a Pedersen vector commitment.
///
/// Returns None if reducing to 0 or if the generators reduced are insufficient to provide this
/// many generators.
pub fn reduce(&self, generators: usize) -> Option<ProofGenerators<'_, C>> {
if generators == 0 {
None?;
}
// Round to the nearest power of 2
let generators = padded_pow_of_2(generators);
if generators > self.g_bold.len() {
None?;
}
Some(ProofGenerators {
g: &self.g,
h: &self.h,
g_bold: &self.g_bold[.. generators],
h_bold: &self.h_bold[.. generators],
})
}
}
impl<'a, C: Ciphersuite> ProofGenerators<'a, C> {
pub(crate) fn len(&self) -> usize {
self.g_bold.len()
}
pub(crate) fn g(&self) -> C::G {
*self.g
}
pub(crate) fn h(&self) -> C::G {
*self.h
}
pub(crate) fn g_bold(&self, i: usize) -> C::G {
self.g_bold[i]
}
pub(crate) fn h_bold(&self, i: usize) -> C::G {
self.h_bold[i]
}
pub(crate) fn g_bold_slice(&self) -> &[C::G] {
self.g_bold
}
pub(crate) fn h_bold_slice(&self) -> &[C::G] {
self.h_bold
}
}
/// The opening of a Pedersen commitment.
#[derive(Clone, Copy, PartialEq, Eq, Debug, Zeroize)]
pub struct PedersenCommitment<C: Ciphersuite> {
/// The value committed to.
pub value: C::F,
/// The mask blinding the value committed to.
pub mask: C::F,
}
impl<C: Ciphersuite> PedersenCommitment<C> {
/// Commit to this value, yielding the Pedersen commitment.
pub fn commit(&self, g: C::G, h: C::G) -> C::G {
multiexp(&[(self.value, g), (self.mask, h)])
}
}
/// The opening of a Pedersen vector commitment.
#[derive(Clone, PartialEq, Eq, Debug, Zeroize)]
pub struct PedersenVectorCommitment<C: Ciphersuite> {
/// The values committed to across the `g` (bold) generators.
pub g_values: ScalarVector<C::F>,
/// The values committed to across the `h` (bold) generators.
pub h_values: ScalarVector<C::F>,
/// The mask blinding the values committed to.
pub mask: C::F,
}
impl<C: Ciphersuite> PedersenVectorCommitment<C> {
/// Commit to the vectors of values.
///
/// This function returns None if the amount of generators is less than the amount of values
/// within the relevant vector.
pub fn commit(&self, g_bold: &[C::G], h_bold: &[C::G], h: C::G) -> Option<C::G> {
if (g_bold.len() < self.g_values.len()) || (h_bold.len() < self.h_values.len()) {
None?;
};
let mut terms = vec![(self.mask, h)];
for pair in self.g_values.0.iter().cloned().zip(g_bold.iter().cloned()) {
terms.push(pair);
}
for pair in self.h_values.0.iter().cloned().zip(h_bold.iter().cloned()) {
terms.push(pair);
}
let res = multiexp(&terms);
terms.zeroize();
Some(res)
}
}

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use core::ops::{Add, Sub, Mul};
use zeroize::Zeroize;
use ciphersuite::group::ff::PrimeField;
use crate::ScalarVector;
/// A reference to a variable usable within linear combinations.
#[derive(Clone, Copy, PartialEq, Eq, Debug)]
#[allow(non_camel_case_types)]
pub enum Variable {
/// A variable within the left vector of vectors multiplied against each other.
aL(usize),
/// A variable within the right vector of vectors multiplied against each other.
aR(usize),
/// A variable within the output vector of the left vector multiplied by the right vector.
aO(usize),
/// A variable within a Pedersen vector commitment, committed to with a generator from `g` (bold).
CG {
/// The commitment being indexed.
commitment: usize,
/// The index of the variable.
index: usize,
},
/// A variable within a Pedersen vector commitment, committed to with a generator from `h` (bold).
CH {
/// The commitment being indexed.
commitment: usize,
/// The index of the variable.
index: usize,
},
/// A variable within a Pedersen commitment.
V(usize),
}
// Does a NOP as there shouldn't be anything critical here
impl Zeroize for Variable {
fn zeroize(&mut self) {}
}
/// A linear combination.
///
/// Specifically, `WL aL + WR aR + WO aO + WCG C_G + WCH C_H + WV V + c`.
#[derive(Clone, PartialEq, Eq, Debug, Zeroize)]
#[must_use]
pub struct LinComb<F: PrimeField> {
pub(crate) highest_a_index: Option<usize>,
pub(crate) highest_c_index: Option<usize>,
pub(crate) highest_v_index: Option<usize>,
// Sparse representation of WL/WR/WO
pub(crate) WL: Vec<(usize, F)>,
pub(crate) WR: Vec<(usize, F)>,
pub(crate) WO: Vec<(usize, F)>,
// Sparse representation once within a commitment
pub(crate) WCG: Vec<Vec<(usize, F)>>,
pub(crate) WCH: Vec<Vec<(usize, F)>>,
// Sparse representation of WV
pub(crate) WV: Vec<(usize, F)>,
pub(crate) c: F,
}
impl<F: PrimeField> From<Variable> for LinComb<F> {
fn from(constrainable: Variable) -> LinComb<F> {
LinComb::empty().term(F::ONE, constrainable)
}
}
impl<F: PrimeField> Add<&LinComb<F>> for LinComb<F> {
type Output = Self;
fn add(mut self, constraint: &Self) -> Self {
self.highest_a_index = self.highest_a_index.max(constraint.highest_a_index);
self.highest_c_index = self.highest_c_index.max(constraint.highest_c_index);
self.highest_v_index = self.highest_v_index.max(constraint.highest_v_index);
self.WL.extend(&constraint.WL);
self.WR.extend(&constraint.WR);
self.WO.extend(&constraint.WO);
while self.WCG.len() < constraint.WCG.len() {
self.WCG.push(vec![]);
}
while self.WCH.len() < constraint.WCH.len() {
self.WCH.push(vec![]);
}
for (sWC, cWC) in self.WCG.iter_mut().zip(&constraint.WCG) {
sWC.extend(cWC);
}
for (sWC, cWC) in self.WCH.iter_mut().zip(&constraint.WCH) {
sWC.extend(cWC);
}
self.WV.extend(&constraint.WV);
self.c += constraint.c;
self
}
}
impl<F: PrimeField> Sub<&LinComb<F>> for LinComb<F> {
type Output = Self;
fn sub(mut self, constraint: &Self) -> Self {
self.highest_a_index = self.highest_a_index.max(constraint.highest_a_index);
self.highest_c_index = self.highest_c_index.max(constraint.highest_c_index);
self.highest_v_index = self.highest_v_index.max(constraint.highest_v_index);
self.WL.extend(constraint.WL.iter().map(|(i, weight)| (*i, -*weight)));
self.WR.extend(constraint.WR.iter().map(|(i, weight)| (*i, -*weight)));
self.WO.extend(constraint.WO.iter().map(|(i, weight)| (*i, -*weight)));
while self.WCG.len() < constraint.WCG.len() {
self.WCG.push(vec![]);
}
while self.WCH.len() < constraint.WCH.len() {
self.WCH.push(vec![]);
}
for (sWC, cWC) in self.WCG.iter_mut().zip(&constraint.WCG) {
sWC.extend(cWC.iter().map(|(i, weight)| (*i, -*weight)));
}
for (sWC, cWC) in self.WCH.iter_mut().zip(&constraint.WCH) {
sWC.extend(cWC.iter().map(|(i, weight)| (*i, -*weight)));
}
self.WV.extend(constraint.WV.iter().map(|(i, weight)| (*i, -*weight)));
self.c -= constraint.c;
self
}
}
impl<F: PrimeField> Mul<F> for LinComb<F> {
type Output = Self;
fn mul(mut self, scalar: F) -> Self {
for (_, weight) in self.WL.iter_mut() {
*weight *= scalar;
}
for (_, weight) in self.WR.iter_mut() {
*weight *= scalar;
}
for (_, weight) in self.WO.iter_mut() {
*weight *= scalar;
}
for WC in self.WCG.iter_mut() {
for (_, weight) in WC {
*weight *= scalar;
}
}
for WC in self.WCH.iter_mut() {
for (_, weight) in WC {
*weight *= scalar;
}
}
for (_, weight) in self.WV.iter_mut() {
*weight *= scalar;
}
self.c *= scalar;
self
}
}
impl<F: PrimeField> LinComb<F> {
/// Create an empty linear combination.
pub fn empty() -> Self {
Self {
highest_a_index: None,
highest_c_index: None,
highest_v_index: None,
WL: vec![],
WR: vec![],
WO: vec![],
WCG: vec![],
WCH: vec![],
WV: vec![],
c: F::ZERO,
}
}
/// Add a new instance of a term to this linear combination.
pub fn term(mut self, scalar: F, constrainable: Variable) -> Self {
match constrainable {
Variable::aL(i) => {
self.highest_a_index = self.highest_a_index.max(Some(i));
self.WL.push((i, scalar))
}
Variable::aR(i) => {
self.highest_a_index = self.highest_a_index.max(Some(i));
self.WR.push((i, scalar))
}
Variable::aO(i) => {
self.highest_a_index = self.highest_a_index.max(Some(i));
self.WO.push((i, scalar))
}
Variable::CG { commitment: i, index: j } => {
self.highest_c_index = self.highest_c_index.max(Some(i));
self.highest_a_index = self.highest_a_index.max(Some(j));
while self.WCG.len() <= i {
self.WCG.push(vec![]);
}
self.WCG[i].push((j, scalar))
}
Variable::CH { commitment: i, index: j } => {
self.highest_c_index = self.highest_c_index.max(Some(i));
self.highest_a_index = self.highest_a_index.max(Some(j));
while self.WCH.len() <= i {
self.WCH.push(vec![]);
}
self.WCH[i].push((j, scalar))
}
Variable::V(i) => {
self.highest_v_index = self.highest_v_index.max(Some(i));
self.WV.push((i, scalar));
}
};
self
}
/// Add to the constant c.
pub fn constant(mut self, scalar: F) -> Self {
self.c += scalar;
self
}
/// View the current weights for aL.
pub fn WL(&self) -> &[(usize, F)] {
&self.WL
}
/// View the current weights for aR.
pub fn WR(&self) -> &[(usize, F)] {
&self.WR
}
/// View the current weights for aO.
pub fn WO(&self) -> &[(usize, F)] {
&self.WO
}
/// View the current weights for CG.
pub fn WCG(&self) -> &[Vec<(usize, F)>] {
&self.WCG
}
/// View the current weights for CH.
pub fn WCH(&self) -> &[Vec<(usize, F)>] {
&self.WCH
}
/// View the current weights for V.
pub fn WV(&self) -> &[(usize, F)] {
&self.WV
}
/// View the current constant.
pub fn c(&self) -> F {
self.c
}
}
pub(crate) fn accumulate_vector<F: PrimeField>(
accumulator: &mut ScalarVector<F>,
values: &[(usize, F)],
weight: F,
) {
for (i, coeff) in values {
accumulator[*i] += *coeff * weight;
}
}

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use core::ops::{Index, IndexMut};
use zeroize::Zeroize;
use ciphersuite::Ciphersuite;
#[cfg(test)]
use multiexp::multiexp;
use crate::ScalarVector;
/// A point vector struct with the functionality necessary for Bulletproofs.
///
/// The math operations for this panic upon any invalid operation, such as if vectors of different
/// lengths are added. The full extent of invalidity is not fully defined. Only field access is
/// guaranteed to have a safe, public API.
#[derive(Clone, PartialEq, Eq, Debug, Zeroize)]
pub struct PointVector<C: Ciphersuite>(pub(crate) Vec<C::G>);
impl<C: Ciphersuite> Index<usize> for PointVector<C> {
type Output = C::G;
fn index(&self, index: usize) -> &C::G {
&self.0[index]
}
}
impl<C: Ciphersuite> IndexMut<usize> for PointVector<C> {
fn index_mut(&mut self, index: usize) -> &mut C::G {
&mut self.0[index]
}
}
impl<C: Ciphersuite> PointVector<C> {
/*
pub(crate) fn add(&self, point: impl AsRef<C::G>) -> Self {
let mut res = self.clone();
for val in res.0.iter_mut() {
*val += point.as_ref();
}
res
}
pub(crate) fn sub(&self, point: impl AsRef<C::G>) -> Self {
let mut res = self.clone();
for val in res.0.iter_mut() {
*val -= point.as_ref();
}
res
}
pub(crate) fn mul(&self, scalar: impl core::borrow::Borrow<C::F>) -> Self {
let mut res = self.clone();
for val in res.0.iter_mut() {
*val *= scalar.borrow();
}
res
}
pub(crate) fn add_vec(&self, vector: &Self) -> Self {
debug_assert_eq!(self.len(), vector.len());
let mut res = self.clone();
for (i, val) in res.0.iter_mut().enumerate() {
*val += vector.0[i];
}
res
}
pub(crate) fn sub_vec(&self, vector: &Self) -> Self {
debug_assert_eq!(self.len(), vector.len());
let mut res = self.clone();
for (i, val) in res.0.iter_mut().enumerate() {
*val -= vector.0[i];
}
res
}
*/
pub(crate) fn mul_vec(&self, vector: &ScalarVector<C::F>) -> Self {
debug_assert_eq!(self.len(), vector.len());
let mut res = self.clone();
for (i, val) in res.0.iter_mut().enumerate() {
*val *= vector.0[i];
}
res
}
#[cfg(test)]
pub(crate) fn multiexp(&self, vector: &crate::ScalarVector<C::F>) -> C::G {
debug_assert_eq!(self.len(), vector.len());
let mut res = Vec::with_capacity(self.len());
for (point, scalar) in self.0.iter().copied().zip(vector.0.iter().copied()) {
res.push((scalar, point));
}
multiexp(&res)
}
/*
pub(crate) fn multiexp_vartime(&self, vector: &ScalarVector<C::F>) -> C::G {
debug_assert_eq!(self.len(), vector.len());
let mut res = Vec::with_capacity(self.len());
for (point, scalar) in self.0.iter().copied().zip(vector.0.iter().copied()) {
res.push((scalar, point));
}
multiexp_vartime(&res)
}
pub(crate) fn sum(&self) -> C::G {
self.0.iter().sum()
}
*/
pub(crate) fn len(&self) -> usize {
self.0.len()
}
pub(crate) fn split(mut self) -> (Self, Self) {
assert!(self.len() > 1);
let r = self.0.split_off(self.0.len() / 2);
debug_assert_eq!(self.len(), r.len());
(self, PointVector(r))
}
}

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crypto/evrf/generalized-bulletproofs/src/scalar_vector.rs Normal file
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use core::ops::{Index, IndexMut, Add, Sub, Mul};
use zeroize::Zeroize;
use ciphersuite::group::ff::PrimeField;
/// A scalar vector struct with the functionality necessary for Bulletproofs.
///
/// The math operations for this panic upon any invalid operation, such as if vectors of different
/// lengths are added. The full extent of invalidity is not fully defined. Only `new`, `len`,
/// and field access is guaranteed to have a safe, public API.
#[derive(Clone, PartialEq, Eq, Debug)]
pub struct ScalarVector<F: PrimeField>(pub(crate) Vec<F>);
impl<F: PrimeField + Zeroize> Zeroize for ScalarVector<F> {
fn zeroize(&mut self) {
self.0.zeroize()
}
}
impl<F: PrimeField> Index<usize> for ScalarVector<F> {
type Output = F;
fn index(&self, index: usize) -> &F {
&self.0[index]
}
}
impl<F: PrimeField> IndexMut<usize> for ScalarVector<F> {
fn index_mut(&mut self, index: usize) -> &mut F {
&mut self.0[index]
}
}
impl<F: PrimeField> Add<F> for ScalarVector<F> {
type Output = ScalarVector<F>;
fn add(mut self, scalar: F) -> Self {
for s in &mut self.0 {
*s += scalar;
}
self
}
}
impl<F: PrimeField> Sub<F> for ScalarVector<F> {
type Output = ScalarVector<F>;
fn sub(mut self, scalar: F) -> Self {
for s in &mut self.0 {
*s -= scalar;
}
self
}
}
impl<F: PrimeField> Mul<F> for ScalarVector<F> {
type Output = ScalarVector<F>;
fn mul(mut self, scalar: F) -> Self {
for s in &mut self.0 {
*s *= scalar;
}
self
}
}
impl<F: PrimeField> Add<&ScalarVector<F>> for ScalarVector<F> {
type Output = ScalarVector<F>;
fn add(mut self, other: &ScalarVector<F>) -> Self {
assert_eq!(self.len(), other.len());
for (s, o) in self.0.iter_mut().zip(other.0.iter()) {
*s += o;
}
self
}
}
impl<F: PrimeField> Sub<&ScalarVector<F>> for ScalarVector<F> {
type Output = ScalarVector<F>;
fn sub(mut self, other: &ScalarVector<F>) -> Self {
assert_eq!(self.len(), other.len());
for (s, o) in self.0.iter_mut().zip(other.0.iter()) {
*s -= o;
}
self
}
}
impl<F: PrimeField> Mul<&ScalarVector<F>> for ScalarVector<F> {
type Output = ScalarVector<F>;
fn mul(mut self, other: &ScalarVector<F>) -> Self {
assert_eq!(self.len(), other.len());
for (s, o) in self.0.iter_mut().zip(other.0.iter()) {
*s *= o;
}
self
}
}
impl<F: PrimeField> ScalarVector<F> {
/// Create a new scalar vector, initialized with `len` zero scalars.
pub fn new(len: usize) -> Self {
ScalarVector(vec![F::ZERO; len])
}
pub(crate) fn powers(x: F, len: usize) -> Self {
assert!(len != 0);
let mut res = Vec::with_capacity(len);
res.push(F::ONE);
res.push(x);
for i in 2 .. len {
res.push(res[i - 1] * x);
}
res.truncate(len);
ScalarVector(res)
}
/// The length of this scalar vector.
#[allow(clippy::len_without_is_empty)]
pub fn len(&self) -> usize {
self.0.len()
}
/*
pub(crate) fn sum(mut self) -> F {
self.0.drain(..).sum()
}
*/
pub(crate) fn inner_product<'a, V: Iterator<Item = &'a F>>(&self, vector: V) -> F {
let mut count = 0;
let mut res = F::ZERO;
for (a, b) in self.0.iter().zip(vector) {
res += *a * b;
count += 1;
}
debug_assert_eq!(self.len(), count);
res
}
pub(crate) fn split(mut self) -> (Self, Self) {
assert!(self.len() > 1);
let r = self.0.split_off(self.0.len() / 2);
debug_assert_eq!(self.len(), r.len());
(self, ScalarVector(r))
}
}
impl<F: PrimeField> From<Vec<F>> for ScalarVector<F> {
fn from(vec: Vec<F>) -> Self {
Self(vec)
}
}

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crypto/evrf/generalized-bulletproofs/src/tests/arithmetic_circuit_proof.rs Normal file
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use rand_core::{RngCore, OsRng};
use ciphersuite::{group::ff::Field, Ciphersuite, Ristretto};
use crate::{
ScalarVector, PedersenCommitment, PedersenVectorCommitment,
transcript::*,
arithmetic_circuit_proof::{
Variable, LinComb, ArithmeticCircuitStatement, ArithmeticCircuitWitness,
},
tests::generators,
};
#[test]
fn test_zero_arithmetic_circuit() {
let generators = generators(1);
let value = <Ristretto as Ciphersuite>::F::random(&mut OsRng);
let gamma = <Ristretto as Ciphersuite>::F::random(&mut OsRng);
let commitment = (generators.g() * value) + (generators.h() * gamma);
let V = vec![commitment];
let aL = ScalarVector::<<Ristretto as Ciphersuite>::F>(vec![<Ristretto as Ciphersuite>::F::ZERO]);
let aR = aL.clone();
let mut transcript = Transcript::new([0; 32]);
let commitments = transcript.write_commitments(vec![], V);
let statement = ArithmeticCircuitStatement::<Ristretto>::new(
generators.reduce(1).unwrap(),
vec![],
commitments.clone(),
)
.unwrap();
let witness = ArithmeticCircuitWitness::<Ristretto>::new(
aL,
aR,
vec![],
vec![PedersenCommitment { value, mask: gamma }],
)
.unwrap();
let proof = {
statement.clone().prove(&mut OsRng, &mut transcript, witness).unwrap();
transcript.complete()
};
let mut verifier = generators.batch_verifier();
let mut transcript = VerifierTranscript::new([0; 32], &proof);
let verifier_commmitments = transcript.read_commitments(0, 1);
assert_eq!(commitments, verifier_commmitments.unwrap());
statement.verify(&mut OsRng, &mut verifier, &mut transcript).unwrap();
assert!(generators.verify(verifier));
}
#[test]
fn test_vector_commitment_arithmetic_circuit() {
let generators = generators(2);
let reduced = generators.reduce(2).unwrap();
let v1 = <Ristretto as Ciphersuite>::F::random(&mut OsRng);
let v2 = <Ristretto as Ciphersuite>::F::random(&mut OsRng);
let v3 = <Ristretto as Ciphersuite>::F::random(&mut OsRng);
let v4 = <Ristretto as Ciphersuite>::F::random(&mut OsRng);
let gamma = <Ristretto as Ciphersuite>::F::random(&mut OsRng);
let commitment = (reduced.g_bold(0) * v1) +
(reduced.g_bold(1) * v2) +
(reduced.h_bold(0) * v3) +
(reduced.h_bold(1) * v4) +
(generators.h() * gamma);
let V = vec![];
let C = vec![commitment];
let zero_vec =
|| ScalarVector::<<Ristretto as Ciphersuite>::F>(vec![<Ristretto as Ciphersuite>::F::ZERO]);
let aL = zero_vec();
let aR = zero_vec();
let mut transcript = Transcript::new([0; 32]);
let commitments = transcript.write_commitments(C, V);
let statement = ArithmeticCircuitStatement::<Ristretto>::new(
reduced,
vec![LinComb::empty()
.term(<Ristretto as Ciphersuite>::F::ONE, Variable::CG { commitment: 0, index: 0 })
.term(<Ristretto as Ciphersuite>::F::from(2u64), Variable::CG { commitment: 0, index: 1 })
.term(<Ristretto as Ciphersuite>::F::from(3u64), Variable::CH { commitment: 0, index: 0 })
.term(<Ristretto as Ciphersuite>::F::from(4u64), Variable::CH { commitment: 0, index: 1 })
.constant(-(v1 + (v2 + v2) + (v3 + v3 + v3) + (v4 + v4 + v4 + v4)))],
commitments.clone(),
)
.unwrap();
let witness = ArithmeticCircuitWitness::<Ristretto>::new(
aL,
aR,
vec![PedersenVectorCommitment {
g_values: ScalarVector(vec![v1, v2]),
h_values: ScalarVector(vec![v3, v4]),
mask: gamma,
}],
vec![],
)
.unwrap();
let proof = {
statement.clone().prove(&mut OsRng, &mut transcript, witness).unwrap();
transcript.complete()
};
let mut verifier = generators.batch_verifier();
let mut transcript = VerifierTranscript::new([0; 32], &proof);
let verifier_commmitments = transcript.read_commitments(1, 0);
assert_eq!(commitments, verifier_commmitments.unwrap());
statement.verify(&mut OsRng, &mut verifier, &mut transcript).unwrap();
assert!(generators.verify(verifier));
}
#[test]
fn fuzz_test_arithmetic_circuit() {
let generators = generators(32);
for i in 0 .. 100 {
dbg!(i);
// Create aL, aR, aO
let mut aL = ScalarVector(vec![]);
let mut aR = ScalarVector(vec![]);
while aL.len() < ((OsRng.next_u64() % 8) + 1).try_into().unwrap() {
aL.0.push(<Ristretto as Ciphersuite>::F::random(&mut OsRng));
}
while aR.len() < aL.len() {
aR.0.push(<Ristretto as Ciphersuite>::F::random(&mut OsRng));
}
let aO = aL.clone() * &aR;
// Create C
let mut C = vec![];
while C.len() < (OsRng.next_u64() % 16).try_into().unwrap() {
let mut g_values = ScalarVector(vec![]);
while g_values.0.len() < ((OsRng.next_u64() % 8) + 1).try_into().unwrap() {
g_values.0.push(<Ristretto as Ciphersuite>::F::random(&mut OsRng));
}
let mut h_values = ScalarVector(vec![]);
while h_values.0.len() < ((OsRng.next_u64() % 8) + 1).try_into().unwrap() {
h_values.0.push(<Ristretto as Ciphersuite>::F::random(&mut OsRng));
}
C.push(PedersenVectorCommitment {
g_values,
h_values,
mask: <Ristretto as Ciphersuite>::F::random(&mut OsRng),
});
}
// Create V
let mut V = vec![];
while V.len() < (OsRng.next_u64() % 4).try_into().unwrap() {
V.push(PedersenCommitment {
value: <Ristretto as Ciphersuite>::F::random(&mut OsRng),
mask: <Ristretto as Ciphersuite>::F::random(&mut OsRng),
});
}
// Generate random constraints
let mut constraints = vec![];
for _ in 0 .. (OsRng.next_u64() % 8).try_into().unwrap() {
let mut eval = <Ristretto as Ciphersuite>::F::ZERO;
let mut constraint = LinComb::empty();
for _ in 0 .. (OsRng.next_u64() % 4) {
let index = usize::try_from(OsRng.next_u64()).unwrap() % aL.len();
let weight = <Ristretto as Ciphersuite>::F::random(&mut OsRng);
constraint = constraint.term(weight, Variable::aL(index));
eval += weight * aL[index];
}
for _ in 0 .. (OsRng.next_u64() % 4) {
let index = usize::try_from(OsRng.next_u64()).unwrap() % aR.len();
let weight = <Ristretto as Ciphersuite>::F::random(&mut OsRng);
constraint = constraint.term(weight, Variable::aR(index));
eval += weight * aR[index];
}
for _ in 0 .. (OsRng.next_u64() % 4) {
let index = usize::try_from(OsRng.next_u64()).unwrap() % aO.len();
let weight = <Ristretto as Ciphersuite>::F::random(&mut OsRng);
constraint = constraint.term(weight, Variable::aO(index));
eval += weight * aO[index];
}
for (commitment, C) in C.iter().enumerate() {
for _ in 0 .. (OsRng.next_u64() % 4) {
let index = usize::try_from(OsRng.next_u64()).unwrap() % C.g_values.len();
let weight = <Ristretto as Ciphersuite>::F::random(&mut OsRng);
constraint = constraint.term(weight, Variable::CG { commitment, index });
eval += weight * C.g_values[index];
}
for _ in 0 .. (OsRng.next_u64() % 4) {
let index = usize::try_from(OsRng.next_u64()).unwrap() % C.h_values.len();
let weight = <Ristretto as Ciphersuite>::F::random(&mut OsRng);
constraint = constraint.term(weight, Variable::CH { commitment, index });
eval += weight * C.h_values[index];
}
}
if !V.is_empty() {
for _ in 0 .. (OsRng.next_u64() % 4) {
let index = usize::try_from(OsRng.next_u64()).unwrap() % V.len();
let weight = <Ristretto as Ciphersuite>::F::random(&mut OsRng);
constraint = constraint.term(weight, Variable::V(index));
eval += weight * V[index].value;
}
}
constraint = constraint.constant(-eval);
constraints.push(constraint);
}
let mut transcript = Transcript::new([0; 32]);
let commitments = transcript.write_commitments(
C.iter()
.map(|C| {
C.commit(generators.g_bold_slice(), generators.h_bold_slice(), generators.h()).unwrap()
})
.collect(),
V.iter().map(|V| V.commit(generators.g(), generators.h())).collect(),
);
let statement = ArithmeticCircuitStatement::<Ristretto>::new(
generators.reduce(16).unwrap(),
constraints,
commitments.clone(),
)
.unwrap();
let witness = ArithmeticCircuitWitness::<Ristretto>::new(aL, aR, C.clone(), V.clone()).unwrap();
let proof = {
statement.clone().prove(&mut OsRng, &mut transcript, witness).unwrap();
transcript.complete()
};
let mut verifier = generators.batch_verifier();
let mut transcript = VerifierTranscript::new([0; 32], &proof);
let verifier_commmitments = transcript.read_commitments(C.len(), V.len());
assert_eq!(commitments, verifier_commmitments.unwrap());
statement.verify(&mut OsRng, &mut verifier, &mut transcript).unwrap();
assert!(generators.verify(verifier));
}
}

113
crypto/evrf/generalized-bulletproofs/src/tests/inner_product.rs Normal file
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// The inner product relation is P = sum(g_bold * a, h_bold * b, g * (a * b))
use rand_core::OsRng;
use ciphersuite::{
group::{ff::Field, Group},
Ciphersuite, Ristretto,
};
use crate::{
ScalarVector, PointVector,
transcript::*,
inner_product::{P, IpStatement, IpWitness},
tests::generators,
};
#[test]
fn test_zero_inner_product() {
let P = <Ristretto as Ciphersuite>::G::identity();
let generators = generators::<Ristretto>(1);
let reduced = generators.reduce(1).unwrap();
let witness = IpWitness::<Ristretto>::new(
ScalarVector::<<Ristretto as Ciphersuite>::F>::new(1),
ScalarVector::<<Ristretto as Ciphersuite>::F>::new(1),
)
.unwrap();
let proof = {
let mut transcript = Transcript::new([0; 32]);
IpStatement::<Ristretto>::new(
reduced,
ScalarVector(vec![<Ristretto as Ciphersuite>::F::ONE; 1]),
<Ristretto as Ciphersuite>::F::ONE,
P::Prover(P),
)
.unwrap()
.clone()
.prove(&mut transcript, witness)
.unwrap();
transcript.complete()
};
let mut verifier = generators.batch_verifier();
IpStatement::<Ristretto>::new(
reduced,
ScalarVector(vec![<Ristretto as Ciphersuite>::F::ONE; 1]),
<Ristretto as Ciphersuite>::F::ONE,
P::Verifier { verifier_weight: <Ristretto as Ciphersuite>::F::ONE },
)
.unwrap()
.verify(&mut verifier, &mut VerifierTranscript::new([0; 32], &proof))
.unwrap();
assert!(generators.verify(verifier));
}
#[test]
fn test_inner_product() {
// P = sum(g_bold * a, h_bold * b)
let generators = generators::<Ristretto>(32);
let mut verifier = generators.batch_verifier();
for i in [1, 2, 4, 8, 16, 32] {
let generators = generators.reduce(i).unwrap();
let g = generators.g();
assert_eq!(generators.len(), i);
let mut g_bold = vec![];
let mut h_bold = vec![];
for i in 0 .. i {
g_bold.push(generators.g_bold(i));
h_bold.push(generators.h_bold(i));
}
let g_bold = PointVector::<Ristretto>(g_bold);
let h_bold = PointVector::<Ristretto>(h_bold);
let mut a = ScalarVector::<<Ristretto as Ciphersuite>::F>::new(i);
let mut b = ScalarVector::<<Ristretto as Ciphersuite>::F>::new(i);
for i in 0 .. i {
a[i] = <Ristretto as Ciphersuite>::F::random(&mut OsRng);
b[i] = <Ristretto as Ciphersuite>::F::random(&mut OsRng);
}
let P = g_bold.multiexp(&a) + h_bold.multiexp(&b) + (g * a.inner_product(b.0.iter()));
let witness = IpWitness::<Ristretto>::new(a, b).unwrap();
let proof = {
let mut transcript = Transcript::new([0; 32]);
IpStatement::<Ristretto>::new(
generators,
ScalarVector(vec![<Ristretto as Ciphersuite>::F::ONE; i]),
<Ristretto as Ciphersuite>::F::ONE,
P::Prover(P),
)
.unwrap()
.prove(&mut transcript, witness)
.unwrap();
transcript.complete()
};
verifier.additional.push((<Ristretto as Ciphersuite>::F::ONE, P));
IpStatement::<Ristretto>::new(
generators,
ScalarVector(vec![<Ristretto as Ciphersuite>::F::ONE; i]),
<Ristretto as Ciphersuite>::F::ONE,
P::Verifier { verifier_weight: <Ristretto as Ciphersuite>::F::ONE },
)
.unwrap()
.verify(&mut verifier, &mut VerifierTranscript::new([0; 32], &proof))
.unwrap();
}
assert!(generators.verify(verifier));
}

27
crypto/evrf/generalized-bulletproofs/src/tests/mod.rs Normal file
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use rand_core::OsRng;
use ciphersuite::{group::Group, Ciphersuite};
use crate::{Generators, padded_pow_of_2};
#[cfg(test)]
mod inner_product;
#[cfg(test)]
mod arithmetic_circuit_proof;
/// Generate a set of generators for testing purposes.
///
/// This should not be considered secure.
pub fn generators<C: Ciphersuite>(n: usize) -> Generators<C> {
assert_eq!(padded_pow_of_2(n), n, "amount of generators wasn't a power of 2");
let gens = || {
let mut res = Vec::with_capacity(n);
for _ in 0 .. n {
res.push(C::G::random(&mut OsRng));
}
res
};
Generators::new(C::G::random(&mut OsRng), C::G::random(&mut OsRng), gens(), gens()).unwrap()
}

188
crypto/evrf/generalized-bulletproofs/src/transcript.rs Normal file
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use std::io;
use blake2::{Digest, Blake2b512};
use ciphersuite::{
group::{ff::PrimeField, GroupEncoding},
Ciphersuite,
};
use crate::PointVector;
const SCALAR: u8 = 0;
const POINT: u8 = 1;
const CHALLENGE: u8 = 2;
fn challenge<F: PrimeField>(digest: &mut Blake2b512) -> F {
// Panic if this is such a wide field, we won't successfully perform a reduction into an unbiased
// scalar
debug_assert!((F::NUM_BITS + 128) < 512);
digest.update([CHALLENGE]);
let chl = digest.clone().finalize();
let mut res = F::ZERO;
for (i, mut byte) in chl.iter().cloned().enumerate() {
for j in 0 .. 8 {
let lsb = byte & 1;
let mut bit = F::from(u64::from(lsb));
for _ in 0 .. ((i * 8) + j) {
bit = bit.double();
}
res += bit;
byte >>= 1;
}
}
// Negligible probability
if bool::from(res.is_zero()) {
panic!("zero challenge");
}
res
}
/// Commitments written to/read from a transcript.
// We use a dedicated type for this to coerce the caller into transcripting the commitments as
// expected.
#[cfg_attr(test, derive(Clone, PartialEq, Debug))]
pub struct Commitments<C: Ciphersuite> {
pub(crate) C: PointVector<C>,
pub(crate) V: PointVector<C>,
}
impl<C: Ciphersuite> Commitments<C> {
/// The vector commitments.
pub fn C(&self) -> &[C::G] {
&self.C.0
}
/// The non-vector commitments.
pub fn V(&self) -> &[C::G] {
&self.V.0
}
}
/// A transcript for proving proofs.
pub struct Transcript {
digest: Blake2b512,
transcript: Vec<u8>,
}
/*
We define our proofs as Vec<u8> and derive our transcripts from the values we deserialize from
them. This format assumes the order of the values read, their size, and their quantity are
constant to the context.
*/
impl Transcript {
/// Create a new transcript off some context.
pub fn new(context: [u8; 32]) -> Self {
let mut digest = Blake2b512::new();
digest.update(context);
Self { digest, transcript: Vec::with_capacity(1024) }
}
/// Push a scalar onto the transcript.
pub fn push_scalar(&mut self, scalar: impl PrimeField) {
self.digest.update([SCALAR]);
let bytes = scalar.to_repr();
self.digest.update(bytes);
self.transcript.extend(bytes.as_ref());
}
/// Push a point onto the transcript.
pub fn push_point(&mut self, point: impl GroupEncoding) {
self.digest.update([POINT]);
let bytes = point.to_bytes();
self.digest.update(bytes);
self.transcript.extend(bytes.as_ref());
}
/// Write the Pedersen (vector) commitments to this transcript.
pub fn write_commitments<C: Ciphersuite>(
&mut self,
C: Vec<C::G>,
V: Vec<C::G>,
) -> Commitments<C> {
for C in &C {
self.push_point(*C);
}
for V in &V {
self.push_point(*V);
}
Commitments { C: PointVector(C), V: PointVector(V) }
}
/// Sample a challenge.
pub fn challenge<F: PrimeField>(&mut self) -> F {
challenge(&mut self.digest)
}
/// Complete a transcript, yielding the fully serialized proof.
pub fn complete(self) -> Vec<u8> {
self.transcript
}
}
/// A transcript for verifying proofs.
pub struct VerifierTranscript<'a> {
digest: Blake2b512,
transcript: &'a [u8],
}
impl<'a> VerifierTranscript<'a> {
/// Create a new transcript to verify a proof with.
pub fn new(context: [u8; 32], proof: &'a [u8]) -> Self {
let mut digest = Blake2b512::new();
digest.update(context);
Self { digest, transcript: proof }
}
/// Read a scalar from the transcript.
pub fn read_scalar<C: Ciphersuite>(&mut self) -> io::Result<C::F> {
let scalar = C::read_F(&mut self.transcript)?;
self.digest.update([SCALAR]);
let bytes = scalar.to_repr();
self.digest.update(bytes);
Ok(scalar)
}
/// Read a point from the transcript.
pub fn read_point<C: Ciphersuite>(&mut self) -> io::Result<C::G> {
let point = C::read_G(&mut self.transcript)?;
self.digest.update([POINT]);
let bytes = point.to_bytes();
self.digest.update(bytes);
Ok(point)
}
/// Read the Pedersen (Vector) Commitments from the transcript.
///
/// The lengths of the vectors are not transcripted.
#[allow(clippy::type_complexity)]
pub fn read_commitments<C: Ciphersuite>(
&mut self,
C: usize,
V: usize,
) -> io::Result<Commitments<C>> {
let mut C_vec = Vec::with_capacity(C);
for _ in 0 .. C {
C_vec.push(self.read_point::<C>()?);
}
let mut V_vec = Vec::with_capacity(V);
for _ in 0 .. V {
V_vec.push(self.read_point::<C>()?);
}
Ok(Commitments { C: PointVector(C_vec), V: PointVector(V_vec) })
}
/// Sample a challenge.
pub fn challenge<F: PrimeField>(&mut self) -> F {
challenge(&mut self.digest)
}
/// Complete the transcript, returning the advanced slice.
pub fn complete(self) -> &'a [u8] {
self.transcript
}
}

39
crypto/evrf/secq256k1/Cargo.toml Normal file
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[package]
name = "secq256k1"
version = "0.1.0"
description = "An implementation of the curve secp256k1 cycles with"
license = "MIT"
repository = "https://github.com/serai-dex/serai/tree/develop/crypto/evrf/secq256k1"
authors = ["Luke Parker <lukeparker5132@gmail.com>"]
keywords = ["secp256k1", "secq256k1", "group"]
edition = "2021"
[package.metadata.docs.rs]
all-features = true
rustdoc-args = ["--cfg", "docsrs"]
[dependencies]
rustversion = "1"
hex-literal = { version = "0.4", default-features = false }
rand_core = { version = "0.6", default-features = false, features = ["std"] }
zeroize = { version = "^1.5", default-features = false, features = ["std", "zeroize_derive"] }
subtle = { version = "^2.4", default-features = false, features = ["std"] }
generic-array = { version = "0.14", default-features = false }
crypto-bigint = { version = "0.5", default-features = false, features = ["zeroize"] }
k256 = { version = "0.13", default-features = false, features = ["arithmetic"] }
blake2 = { version = "0.10", default-features = false, features = ["std"] }
ciphersuite = { path = "../../ciphersuite", version = "0.4", default-features = false, features = ["std"] }
ec-divisors = { path = "../divisors" }
generalized-bulletproofs-ec-gadgets = { path = "../ec-gadgets" }
[dev-dependencies]
hex = "0.4"
rand_core = { version = "0.6", features = ["std"] }
ff-group-tests = { path = "../../ff-group-tests" }

21
crypto/evrf/secq256k1/LICENSE Normal file
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@@ -0,0 +1,21 @@
MIT License
Copyright (c) 2022-2024 Luke Parker
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.

5
crypto/evrf/secq256k1/README.md Normal file
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# secq256k1
An implementation of the curve secp256k1 cycles with.
Scalars and field elements are encoded in their big-endian formats.

295
crypto/evrf/secq256k1/src/backend.rs Normal file
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use zeroize::Zeroize;
// Use black_box when possible
#[rustversion::since(1.66)]
use core::hint::black_box;
#[rustversion::before(1.66)]
fn black_box<T>(val: T) -> T {
val
}
pub(crate) fn u8_from_bool(bit_ref: &mut bool) -> u8 {
let bit_ref = black_box(bit_ref);
let mut bit = black_box(*bit_ref);
let res = black_box(bit as u8);
bit.zeroize();
debug_assert!((res | 1) == 1);
bit_ref.zeroize();
res
}
macro_rules! math_op {
(
$Value: ident,
$Other: ident,
$Op: ident,
$op_fn: ident,
$Assign: ident,
$assign_fn: ident,
$function: expr
) => {
impl $Op<$Other> for $Value {
type Output = $Value;
fn $op_fn(self, other: $Other) -> Self::Output {
Self($function(self.0, other.0))
}
}
impl $Assign<$Other> for $Value {
fn $assign_fn(&mut self, other: $Other) {
self.0 = $function(self.0, other.0);
}
}
impl<'a> $Op<&'a $Other> for $Value {
type Output = $Value;
fn $op_fn(self, other: &'a $Other) -> Self::Output {
Self($function(self.0, other.0))
}
}
impl<'a> $Assign<&'a $Other> for $Value {
fn $assign_fn(&mut self, other: &'a $Other) {
self.0 = $function(self.0, other.0);
}
}
};
}
macro_rules! from_wrapper {
($wrapper: ident, $inner: ident, $uint: ident) => {
impl From<$uint> for $wrapper {
fn from(a: $uint) -> $wrapper {
Self(Residue::new(&$inner::from(a)))
}
}
};
}
macro_rules! field {
(
$FieldName: ident,
$ResidueType: ident,
$MODULUS_STR: ident,
$MODULUS: ident,
$WIDE_MODULUS: ident,
$NUM_BITS: literal,
$MULTIPLICATIVE_GENERATOR: literal,
$S: literal,
$ROOT_OF_UNITY: literal,
$DELTA: literal,
) => {
use core::{
ops::{DerefMut, Add, AddAssign, Neg, Sub, SubAssign, Mul, MulAssign},
iter::{Sum, Product},
};
use subtle::{Choice, CtOption, ConstantTimeEq, ConstantTimeLess, ConditionallySelectable};
use rand_core::RngCore;
use crypto_bigint::{Integer, NonZero, Encoding, impl_modulus};
use ciphersuite::group::ff::{
Field, PrimeField, FieldBits, PrimeFieldBits, helpers::sqrt_ratio_generic,
};
use $crate::backend::u8_from_bool;
fn reduce(x: U512) -> U256 {
U256::from_le_slice(&x.rem(&NonZero::new($WIDE_MODULUS).unwrap()).to_le_bytes()[.. 32])
}
impl ConstantTimeEq for $FieldName {
fn ct_eq(&self, other: &Self) -> Choice {
self.0.ct_eq(&other.0)
}
}
impl ConditionallySelectable for $FieldName {
fn conditional_select(a: &Self, b: &Self, choice: Choice) -> Self {
$FieldName(Residue::conditional_select(&a.0, &b.0, choice))
}
}
math_op!($FieldName, $FieldName, Add, add, AddAssign, add_assign, |x: $ResidueType, y| x
.add(&y));
math_op!($FieldName, $FieldName, Sub, sub, SubAssign, sub_assign, |x: $ResidueType, y| x
.sub(&y));
math_op!($FieldName, $FieldName, Mul, mul, MulAssign, mul_assign, |x: $ResidueType, y| x
.mul(&y));
from_wrapper!($FieldName, U256, u8);
from_wrapper!($FieldName, U256, u16);
from_wrapper!($FieldName, U256, u32);
from_wrapper!($FieldName, U256, u64);
from_wrapper!($FieldName, U256, u128);
impl Neg for $FieldName {
type Output = $FieldName;
fn neg(self) -> $FieldName {
Self(self.0.neg())
}
}
impl<'a> Neg for &'a $FieldName {
type Output = $FieldName;
fn neg(self) -> Self::Output {
(*self).neg()
}
}
impl $FieldName {
/// Perform an exponentation.
pub fn pow(&self, other: $FieldName) -> $FieldName {
let mut table = [Self(Residue::ONE); 16];
table[1] = *self;
for i in 2 .. 16 {
table[i] = table[i - 1] * self;
}
let mut res = Self(Residue::ONE);
let mut bits = 0;
for (i, mut bit) in other.to_le_bits().iter_mut().rev().enumerate() {
bits <<= 1;
let mut bit = u8_from_bool(bit.deref_mut());
bits |= bit;
bit.zeroize();
if ((i + 1) % 4) == 0 {
if i != 3 {
for _ in 0 .. 4 {
res *= res;
}
}
let mut factor = table[0];
for (j, candidate) in table[1 ..].iter().enumerate() {
let j = j + 1;
factor = Self::conditional_select(&factor, &candidate, usize::from(bits).ct_eq(&j));
}
res *= factor;
bits = 0;
}
}
res
}
}
impl Field for $FieldName {
const ZERO: Self = Self(Residue::ZERO);
const ONE: Self = Self(Residue::ONE);
fn random(mut rng: impl RngCore) -> Self {
let mut bytes = [0; 64];
rng.fill_bytes(&mut bytes);
$FieldName(Residue::new(&reduce(U512::from_be_slice(bytes.as_ref()))))
}
fn square(&self) -> Self {
Self(self.0.square())
}
fn double(&self) -> Self {
*self + self
}
fn invert(&self) -> CtOption<Self> {
let res = self.0.invert();
CtOption::new(Self(res.0), res.1.into())
}
fn sqrt(&self) -> CtOption<Self> {
// (p + 1) // 4, as valid since p % 4 == 3
let mod_plus_one_div_four = $MODULUS.saturating_add(&U256::ONE).wrapping_div(&(4u8.into()));
let res = self.pow(Self($ResidueType::new_checked(&mod_plus_one_div_four).unwrap()));
CtOption::new(res, res.square().ct_eq(self))
}
fn sqrt_ratio(num: &Self, div: &Self) -> (Choice, Self) {
sqrt_ratio_generic(num, div)
}
}
impl PrimeField for $FieldName {
type Repr = [u8; 32];
const MODULUS: &'static str = $MODULUS_STR;
const NUM_BITS: u32 = $NUM_BITS;
const CAPACITY: u32 = $NUM_BITS - 1;
const TWO_INV: Self = $FieldName($ResidueType::new(&U256::from_u8(2)).invert().0);
const MULTIPLICATIVE_GENERATOR: Self =
Self(Residue::new(&U256::from_u8($MULTIPLICATIVE_GENERATOR)));
const S: u32 = $S;
const ROOT_OF_UNITY: Self = $FieldName(Residue::new(&U256::from_be_hex($ROOT_OF_UNITY)));
const ROOT_OF_UNITY_INV: Self = Self(Self::ROOT_OF_UNITY.0.invert().0);
const DELTA: Self = $FieldName(Residue::new(&U256::from_be_hex($DELTA)));
fn from_repr(bytes: Self::Repr) -> CtOption<Self> {
let res = U256::from_be_slice(&bytes);
CtOption::new($FieldName(Residue::new(&res)), res.ct_lt(&$MODULUS))
}
fn to_repr(&self) -> Self::Repr {
let mut repr = [0; 32];
repr.copy_from_slice(&self.0.retrieve().to_be_bytes());
repr
}
fn is_odd(&self) -> Choice {
self.0.retrieve().is_odd()
}
}
impl PrimeFieldBits for $FieldName {
type ReprBits = [u8; 32];
fn to_le_bits(&self) -> FieldBits<Self::ReprBits> {
let mut repr = [0; 32];
repr.copy_from_slice(&self.0.retrieve().to_le_bytes());
repr.into()
}
fn char_le_bits() -> FieldBits<Self::ReprBits> {
let mut repr = [0; 32];
repr.copy_from_slice(&MODULUS.to_le_bytes());
repr.into()
}
}
impl Sum<$FieldName> for $FieldName {
fn sum<I: Iterator<Item = $FieldName>>(iter: I) -> $FieldName {
let mut res = $FieldName::ZERO;
for item in iter {
res += item;
}
res
}
}
impl<'a> Sum<&'a $FieldName> for $FieldName {
fn sum<I: Iterator<Item = &'a $FieldName>>(iter: I) -> $FieldName {
iter.cloned().sum()
}
}
impl Product<$FieldName> for $FieldName {
fn product<I: Iterator<Item = $FieldName>>(iter: I) -> $FieldName {
let mut res = $FieldName::ONE;
for item in iter {
res *= item;
}
res
}
}
impl<'a> Product<&'a $FieldName> for $FieldName {
fn product<I: Iterator<Item = &'a $FieldName>>(iter: I) -> $FieldName {
iter.cloned().product()
}
}
};
}

47
crypto/evrf/secq256k1/src/lib.rs Normal file
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@@ -0,0 +1,47 @@
#![cfg_attr(docsrs, feature(doc_auto_cfg))]
#![doc = include_str!("../README.md")]
use generic_array::typenum::{Sum, Diff, Quot, U, U1, U2};
use ciphersuite::group::{ff::PrimeField, Group};
#[macro_use]
mod backend;
mod scalar;
pub use scalar::Scalar;
pub use k256::Scalar as FieldElement;
mod point;
pub use point::Point;
/// Ciphersuite for Secq256k1.
///
/// hash_to_F is implemented with a naive concatenation of the dst and data, allowing transposition
/// between the two. This means `dst: b"abc", data: b"def"`, will produce the same scalar as
/// `dst: "abcdef", data: b""`. Please use carefully, not letting dsts be substrings of each other.
#[derive(Clone, Copy, PartialEq, Eq, Debug, zeroize::Zeroize)]
pub struct Secq256k1;
impl ciphersuite::Ciphersuite for Secq256k1 {
type F = Scalar;
type G = Point;
type H = blake2::Blake2b512;
const ID: &'static [u8] = b"secq256k1";
fn generator() -> Self::G {
Point::generator()
}
fn hash_to_F(dst: &[u8], data: &[u8]) -> Self::F {
use blake2::Digest;
Scalar::wide_reduce(Self::H::digest([dst, data].concat()).as_slice().try_into().unwrap())
}
}
impl generalized_bulletproofs_ec_gadgets::DiscreteLogParameters for Secq256k1 {
type ScalarBits = U<{ Scalar::NUM_BITS as usize }>;
type XCoefficients = Quot<Sum<Self::ScalarBits, U1>, U2>;
type XCoefficientsMinusOne = Diff<Self::XCoefficients, U1>;
type YxCoefficients = Diff<Quot<Sum<Sum<Self::ScalarBits, U1>, U1>, U2>, U2>;
}

414
crypto/evrf/secq256k1/src/point.rs Normal file
View File

@@ -0,0 +1,414 @@
use core::{
ops::{DerefMut, Add, AddAssign, Neg, Sub, SubAssign, Mul, MulAssign},
iter::Sum,
};
use rand_core::RngCore;
use zeroize::Zeroize;
use subtle::{Choice, CtOption, ConstantTimeEq, ConditionallySelectable, ConditionallyNegatable};
use generic_array::{typenum::U33, GenericArray};
use ciphersuite::group::{
ff::{Field, PrimeField, PrimeFieldBits},
Group, GroupEncoding,
prime::PrimeGroup,
};
use crate::{backend::u8_from_bool, Scalar, FieldElement};
fn recover_y(x: FieldElement) -> CtOption<FieldElement> {
// x**3 + B since a = 0
((x.square() * x) + FieldElement::from(7u64)).sqrt()
}
/// Point.
#[derive(Clone, Copy, Debug, Zeroize)]
#[repr(C)]
pub struct Point {
x: FieldElement, // / Z
y: FieldElement, // / Z
z: FieldElement,
}
impl ConstantTimeEq for Point {
fn ct_eq(&self, other: &Self) -> Choice {
let x1 = self.x * other.z;
let x2 = other.x * self.z;
let y1 = self.y * other.z;
let y2 = other.y * self.z;
(self.x.is_zero() & other.x.is_zero()) | (x1.ct_eq(&x2) & y1.ct_eq(&y2))
}
}
impl PartialEq for Point {
fn eq(&self, other: &Point) -> bool {
self.ct_eq(other).into()
}
}
impl Eq for Point {}
impl ConditionallySelectable for Point {
fn conditional_select(a: &Self, b: &Self, choice: Choice) -> Self {
Point {
x: FieldElement::conditional_select(&a.x, &b.x, choice),
y: FieldElement::conditional_select(&a.y, &b.y, choice),
z: FieldElement::conditional_select(&a.z, &b.z, choice),
}
}
}
impl Add for Point {
type Output = Point;
#[allow(non_snake_case)]
fn add(self, other: Self) -> Self {
// add-2015-rcb
let a = FieldElement::ZERO;
let B = FieldElement::from(7u64);
let b3 = B + B + B;
let X1 = self.x;
let Y1 = self.y;
let Z1 = self.z;
let X2 = other.x;
let Y2 = other.y;
let Z2 = other.z;
let t0 = X1 * X2;
let t1 = Y1 * Y2;
let t2 = Z1 * Z2;
let t3 = X1 + Y1;
let t4 = X2 + Y2;
let t3 = t3 * t4;
let t4 = t0 + t1;
let t3 = t3 - t4;
let t4 = X1 + Z1;
let t5 = X2 + Z2;
let t4 = t4 * t5;
let t5 = t0 + t2;
let t4 = t4 - t5;
let t5 = Y1 + Z1;
let X3 = Y2 + Z2;
let t5 = t5 * X3;
let X3 = t1 + t2;
let t5 = t5 - X3;
let Z3 = a * t4;
let X3 = b3 * t2;
let Z3 = X3 + Z3;
let X3 = t1 - Z3;
let Z3 = t1 + Z3;
let Y3 = X3 * Z3;
let t1 = t0 + t0;
let t1 = t1 + t0;
let t2 = a * t2;
let t4 = b3 * t4;
let t1 = t1 + t2;
let t2 = t0 - t2;
let t2 = a * t2;
let t4 = t4 + t2;
let t0 = t1 * t4;
let Y3 = Y3 + t0;
let t0 = t5 * t4;
let X3 = t3 * X3;
let X3 = X3 - t0;
let t0 = t3 * t1;
let Z3 = t5 * Z3;
let Z3 = Z3 + t0;
Point { x: X3, y: Y3, z: Z3 }
}
}
impl AddAssign for Point {
fn add_assign(&mut self, other: Point) {
*self = *self + other;
}
}
impl Add<&Point> for Point {
type Output = Point;
fn add(self, other: &Point) -> Point {
self + *other
}
}
impl AddAssign<&Point> for Point {
fn add_assign(&mut self, other: &Point) {
*self += *other;
}
}
impl Neg for Point {
type Output = Point;
fn neg(self) -> Self {
Point { x: self.x, y: -self.y, z: self.z }
}
}
impl Sub for Point {
type Output = Point;
#[allow(clippy::suspicious_arithmetic_impl)]
fn sub(self, other: Self) -> Self {
self + other.neg()
}
}
impl SubAssign for Point {
fn sub_assign(&mut self, other: Point) {
*self = *self - other;
}
}
impl Sub<&Point> for Point {
type Output = Point;
fn sub(self, other: &Point) -> Point {
self - *other
}
}
impl SubAssign<&Point> for Point {
fn sub_assign(&mut self, other: &Point) {
*self -= *other;
}
}
impl Group for Point {
type Scalar = Scalar;
fn random(mut rng: impl RngCore) -> Self {
loop {
let mut bytes = GenericArray::default();
rng.fill_bytes(bytes.as_mut());
let opt = Self::from_bytes(&bytes);
if opt.is_some().into() {
return opt.unwrap();
}
}
}
fn identity() -> Self {
Point { x: FieldElement::ZERO, y: FieldElement::ONE, z: FieldElement::ZERO }
}
fn generator() -> Self {
Point {
x: FieldElement::from_repr(
hex_literal::hex!("0000000000000000000000000000000000000000000000000000000000000001")
.into(),
)
.unwrap(),
y: FieldElement::from_repr(
hex_literal::hex!("0C7C97045A2074634909ABDF82C9BD0248916189041F2AF0C1B800D1FFC278C0")
.into(),
)
.unwrap(),
z: FieldElement::ONE,
}
}
fn is_identity(&self) -> Choice {
self.z.ct_eq(&FieldElement::ZERO)
}
#[allow(non_snake_case)]
fn double(&self) -> Self {
// dbl-2007-bl
let a = FieldElement::ZERO;
let X1 = self.x;
let Y1 = self.y;
let Z1 = self.z;
let XX = X1 * X1;
let ZZ = Z1 * Z1;
let w = (a * ZZ) + XX.double() + XX;
let s = (Y1 * Z1).double();
let ss = s * s;
let sss = s * ss;
let R = Y1 * s;
let RR = R * R;
let B = X1 + R;
let B = (B * B) - XX - RR;
let h = (w * w) - B.double();
let X3 = h * s;
let Y3 = w * (B - h) - RR.double();
let Z3 = sss;
let res = Self { x: X3, y: Y3, z: Z3 };
// If self is identity, res will not be well-formed
// Accordingly, we return self if self was the identity
Self::conditional_select(&res, self, self.is_identity())
}
}
impl Sum<Point> for Point {
fn sum<I: Iterator<Item = Point>>(iter: I) -> Point {
let mut res = Self::identity();
for i in iter {
res += i;
}
res
}
}
impl<'a> Sum<&'a Point> for Point {
fn sum<I: Iterator<Item = &'a Point>>(iter: I) -> Point {
Point::sum(iter.cloned())
}
}
impl Mul<Scalar> for Point {
type Output = Point;
fn mul(self, mut other: Scalar) -> Point {
// Precompute the optimal amount that's a multiple of 2
let mut table = [Point::identity(); 16];
table[1] = self;
for i in 2 .. 16 {
table[i] = table[i - 1] + self;
}
let mut res = Self::identity();
let mut bits = 0;
for (i, mut bit) in other.to_le_bits().iter_mut().rev().enumerate() {
bits <<= 1;
let mut bit = u8_from_bool(bit.deref_mut());
bits |= bit;
bit.zeroize();
if ((i + 1) % 4) == 0 {
if i != 3 {
for _ in 0 .. 4 {
res = res.double();
}
}
let mut term = table[0];
for (j, candidate) in table[1 ..].iter().enumerate() {
let j = j + 1;
term = Self::conditional_select(&term, candidate, usize::from(bits).ct_eq(&j));
}
res += term;
bits = 0;
}
}
other.zeroize();
res
}
}
impl MulAssign<Scalar> for Point {
fn mul_assign(&mut self, other: Scalar) {
*self = *self * other;
}
}
impl Mul<&Scalar> for Point {
type Output = Point;
fn mul(self, other: &Scalar) -> Point {
self * *other
}
}
impl MulAssign<&Scalar> for Point {
fn mul_assign(&mut self, other: &Scalar) {
*self *= *other;
}
}
impl GroupEncoding for Point {
type Repr = GenericArray<u8, U33>;
fn from_bytes(bytes: &Self::Repr) -> CtOption<Self> {
// Extract and clear the sign bit
let sign = Choice::from(bytes[0] & 1);
// Parse x, recover y
FieldElement::from_repr(*GenericArray::from_slice(&bytes[1 ..])).and_then(|x| {
let is_identity = x.is_zero();
let y = recover_y(x).map(|mut y| {
y.conditional_negate(y.is_odd().ct_eq(&!sign));
y
});
// If this the identity, set y to 1
let y =
CtOption::conditional_select(&y, &CtOption::new(FieldElement::ONE, 1.into()), is_identity);
// Create the point if we have a y solution
let point = y.map(|y| Point { x, y, z: FieldElement::ONE });
let not_negative_zero = !(is_identity & sign);
// Only return the point if it isn't -0 and the sign byte wasn't malleated
CtOption::conditional_select(
&CtOption::new(Point::identity(), 0.into()),
&point,
not_negative_zero & ((bytes[0] & 1).ct_eq(&bytes[0])),
)
})
}
fn from_bytes_unchecked(bytes: &Self::Repr) -> CtOption<Self> {
Point::from_bytes(bytes)
}
fn to_bytes(&self) -> Self::Repr {
let Some(z) = Option::<FieldElement>::from(self.z.invert()) else {
return *GenericArray::from_slice(&[0; 33]);
};
let x = self.x * z;
let y = self.y * z;
let mut res = *GenericArray::from_slice(&[0; 33]);
res[1 ..].as_mut().copy_from_slice(&x.to_repr());
// The following conditional select normalizes the sign to 0 when x is 0
let y_sign = u8::conditional_select(&y.is_odd().unwrap_u8(), &0, x.ct_eq(&FieldElement::ZERO));
res[0] |= y_sign;
res
}
}
impl PrimeGroup for Point {}
impl ec_divisors::DivisorCurve for Point {
type FieldElement = FieldElement;
fn a() -> Self::FieldElement {
FieldElement::from(0u64)
}
fn b() -> Self::FieldElement {
FieldElement::from(7u64)
}
fn to_xy(point: Self) -> Option<(Self::FieldElement, Self::FieldElement)> {
let z: Self::FieldElement = Option::from(point.z.invert())?;
Some((point.x * z, point.y * z))
}
}
#[test]
fn test_curve() {
ff_group_tests::group::test_prime_group_bits::<_, Point>(&mut rand_core::OsRng);
}
#[test]
fn generator() {
assert_eq!(
Point::generator(),
Point::from_bytes(GenericArray::from_slice(&hex_literal::hex!(
"000000000000000000000000000000000000000000000000000000000000000001"
)))
.unwrap()
);
}
#[test]
fn zero_x_is_invalid() {
assert!(Option::<FieldElement>::from(recover_y(FieldElement::ZERO)).is_none());
}
// Checks random won't infinitely loop
#[test]
fn random() {
Point::random(&mut rand_core::OsRng);
}

52
crypto/evrf/secq256k1/src/scalar.rs Normal file
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@@ -0,0 +1,52 @@
use zeroize::{DefaultIsZeroes, Zeroize};
use crypto_bigint::{
U256, U512,
modular::constant_mod::{ResidueParams, Residue},
};
const MODULUS_STR: &str = "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F";
impl_modulus!(SecQ, U256, MODULUS_STR);
type ResidueType = Residue<SecQ, { SecQ::LIMBS }>;
/// The Scalar field of secq256k1.
///
/// This is equivalent to the field secp256k1 is defined over.
#[derive(Clone, Copy, PartialEq, Eq, Default, Debug)]
#[repr(C)]
pub struct Scalar(pub(crate) ResidueType);
impl DefaultIsZeroes for Scalar {}
pub(crate) const MODULUS: U256 = U256::from_be_hex(MODULUS_STR);
const WIDE_MODULUS: U512 = U512::from_be_hex(concat!(
"0000000000000000000000000000000000000000000000000000000000000000",
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F",
));
field!(
Scalar,
ResidueType,
MODULUS_STR,
MODULUS,
WIDE_MODULUS,
256,
3,
1,
"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2e",
"0000000000000000000000000000000000000000000000000000000000000009",
);
impl Scalar {
/// Perform a wide reduction, presumably to obtain a non-biased Scalar field element.
pub fn wide_reduce(bytes: [u8; 64]) -> Scalar {
Scalar(Residue::new(&reduce(U512::from_le_slice(bytes.as_ref()))))
}
}
#[test]
fn test_scalar_field() {
ff_group_tests::prime_field::test_prime_field_bits::<_, Scalar>(&mut rand_core::OsRng);
}

1
crypto/frost/src/tests/vectors.rs
View File

@@ -122,6 +122,7 @@ fn vectors_to_multisig_keys<C: Curve>(vectors: &Vectors) -> HashMap<Participant,
serialized.extend(vectors.threshold.to_le_bytes());
serialized.extend(u16::try_from(shares.len()).unwrap().to_le_bytes());
serialized.extend(i.to_le_bytes());
serialized.push(1);
serialized.extend(shares[usize::from(i) - 1].to_repr().as_ref());
for share in &verification_shares {
serialized.extend(share.to_bytes().as_ref());