One Round DKG (#589)

* 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.

spec/cryptography/Distributed Key Generation.md

@@ -1,35 +1,7 @@
 # Distributed Key Generation
 
-Serai uses a modification of Pedersen's Distributed Key Generation, which is
-actually Feldman's Verifiable Secret Sharing Scheme run by every participant, as
-described in the FROST paper. The modification included in FROST was to include
-a Schnorr Proof of Knowledge for coefficient zero, preventing rogue key attacks.
-This results in a two-round protocol.
-
-### Encryption
-
-In order to protect the secret shares during communication, the `dkg` library
-establishes a public key for encryption at the start of a given protocol.
-Every encrypted message (such as the secret shares) then includes a per-message
-encryption key. These two keys are used in an Elliptic-curve Diffie-Hellman
-handshake to derive a shared key. This shared key is then hashed to obtain a key
-and IV for use in a ChaCha20 stream cipher instance, which is xor'd against a
-message to encrypt it.
-
-### Blame
-
-Since each message has a distinct key attached, and accordingly a distinct
-shared key, it's possible to reveal the shared key for a specific message
-without revealing any other message's decryption keys. This is utilized when a
-participant misbehaves. A participant who receives an invalid encrypted message
-publishes its key, able to without concern for side effects, With the key
-published, all participants can decrypt the message in order to decide blame.
-
-While key reuse by a participant is considered as them revealing the messages
-themselves, and therefore out of scope, there is an attack where a malicious
-adversary claims another participant's encryption key. They'll fail to encrypt
-their message, and the recipient will issue a blame statement. This blame
-statement, intended to reveal the malicious adversary, also reveals the message
-by the participant whose keys were co-opted. To resolve this, a
-proof-of-possession is also included with encrypted messages, ensuring only
-those actually with per-message keys can claim to use them.
+Serai uses a modification of the one-round Distributed Key Generation described
+in the [eVRF](https://eprint.iacr.org/2024/397) paper. We only require a
+threshold to participate, sacrificing unbiased for robustness, and implement a
+verifiable encryption scheme such that anyone can can verify a ciphertext
+encrypts the expected secret share.