Initial commit

Combines the existing frost-rs, dalek-ff-group, and monero-rs repos into 
a monorepo. Makes tweaks necessary as needed. Replaces RedDSA (which was 
going to be stubbed out into a new folder for now) with an offset system 
that voids its need and allows stealth addresses with CLSAG.

sign/monero/.gitignore

@@ -0,0 +1,3 @@
+Cargo.lock
+
+.build

sign/monero/Cargo.toml

@@ -0,0 +1,34 @@
+[package]
+name = "monero-sign"
+version = "0.1.0"
+description = "Implementation of Monero transaction signing in Rust"
+license = "MIT"
+authors = ["Luke Parker <lukeparker5132@gmail.com>"]
+edition = "2021"
+
+[dependencies]
+lazy_static = "1"
+thiserror = "1"
+
+rand_core = "0.6"
+
+hex = "0.4"
+
+digest = "0.9"
+tiny-keccak = { version = "2.0", features = ["keccak"] }
+blake2 = "0.9"
+
+curve25519-dalek = { version = "3.2", features = ["std", "simd_backend"] }
+
+ff = { version = "0.10", optional = true }
+group = { version = "0.10", optional = true }
+dalek-ff-group = { path = "../dalek-ff-group", optional = true }
+frost = { path = "../frost", optional = true }
+
+monero = "0.16.0" # Locked to this specific patch version due to a bug we compensate for
+
+[features]
+multisig = ["ff", "group", "dalek-ff-group", "frost"]
+
+[dev-dependencies]
+rand = "0.8"

sign/monero/LICENSE

@@ -0,0 +1,21 @@
+MIT License
+
+Copyright (c) 2022 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.

sign/monero/build.rs

@@ -0,0 +1,104 @@
+use std::process::Command;
+use std::env;
+use std::path::Path;
+
+fn main() {
+  if !Command::new("git").args(&["submodule", "update", "--init", "--recursive"]).status().unwrap().success() {
+    panic!("git failed to init submodules");
+  }
+
+  if !Command ::new("mkdir").args(&["-p", ".build"])
+    .current_dir(&Path::new("c")).status().unwrap().success() {
+      panic!("failed to create a directory to track build progress");
+  }
+
+  let out_dir = &env::var("OUT_DIR").unwrap();
+
+  // Use a file to signal if Monero was already built, as that should never be rebuilt
+  // If the signaling file was deleted, run this script again to rebuild Monero though
+  // TODO: Move this signaling file into OUT_DIR once Monero is built statically successfully
+  println!("cargo:rerun-if-changed=c/.build/monero");
+  if !Path::new("c/.build/monero").exists() {
+    if !Command::new("cmake").args(&["cmake", "-DCMAKE_BUILD_TYPE=Release", "-DBUILD_SHARED_LIBS=1", "."])
+      .current_dir(&Path::new("c/monero")).status().unwrap().success() {
+        panic!("cmake failed to generate Monero's build scripts");
+    }
+
+    if !Command::new("make").arg(format!("-j{}", &env::var("THREADS").unwrap_or("2".to_string())))
+      .current_dir(&Path::new("c/monero")).status().unwrap().success() {
+        panic!("make failed to build Monero. Please check your dependencies");
+    }
+
+    if !Command::new("cp").args(&[
+      &format!(
+        "c/monero/src/crypto/{}cncrypto.{}",
+        &env::consts::DLL_PREFIX,
+        &env::consts::DLL_EXTENSION
+      ),
+      out_dir
+    ]).status().unwrap().success() {
+      panic!("Failed to cp cncrypto");
+    }
+
+    if !Command::new("cp").args(&[
+      &format!(
+        "c/monero/src/device/{}device.{}",
+        &env::consts::DLL_PREFIX,
+        &env::consts::DLL_EXTENSION
+      ),
+      out_dir
+    ]).status().unwrap().success() {
+      panic!("Failed to cp device");
+    }
+
+    if !Command::new("cp").args(&[
+      &format!(
+        "c/monero/src/ringct/{}ringct_basic.{}",
+        &env::consts::DLL_PREFIX,
+        &env::consts::DLL_EXTENSION
+      ),
+      out_dir
+    ]).status().unwrap().success() {
+      panic!("Failed to cp ringct_basic");
+    }
+
+    if !Command::new("cp").args(&[
+      &format!(
+        "c/monero/src/ringct/{}ringct.{}",
+        &env::consts::DLL_PREFIX,
+        &env::consts::DLL_EXTENSION
+      ),
+      out_dir
+    ]).status().unwrap().success() {
+      panic!("Failed to cp ringct");
+    }
+
+    if !Command::new("touch").arg("monero")
+      .current_dir(&Path::new("c/.build")).status().unwrap().success() {
+        panic!("failed to create a file to label Monero as built");
+    }
+  }
+
+  println!("cargo:rerun-if-changed=c/wrapper.c");
+  if !Command::new("g++").args(&[
+    "-O3", "-Wall", "-shared", "-std=c++14", "-fPIC",
+    "-Imonero/contrib/epee/include", "-Imonero/src",
+    "wrapper.c", "-o", &format!(
+      "{}/{}wrapper.{}",
+      out_dir,
+      &env::consts::DLL_PREFIX,
+      &env::consts::DLL_EXTENSION
+    ),
+    &format!("-L{}", out_dir),
+    "-ldevice", "-lringct_basic", "-lringct"
+  ]).current_dir(&Path::new("c")).status().unwrap().success() {
+    panic!("g++ failed to build the wrapper");
+  }
+
+  println!("cargo:rustc-link-search={}", out_dir);
+  println!("cargo:rustc-link-lib=cncrypto");
+  println!("cargo:rustc-link-lib=device");
+  println!("cargo:rustc-link-lib=ringct_basic");
+  println!("cargo:rustc-link-lib=ringct");
+  println!("cargo:rustc-link-lib=wrapper");
+}

sign/monero/c/wrapper.c

@@ -0,0 +1,42 @@
+#include "device/device_default.hpp"
+
+#include "ringct/rctSigs.h"
+
+extern "C" {
+  void c_hash_to_point(uint8_t* point) {
+    rct::key key_point;
+    ge_p3 e_p3;
+    memcpy(key_point.bytes, point, 32);
+    rct::hash_to_p3(e_p3, key_point);
+    ge_p3_tobytes(point, &e_p3);
+  }
+
+  bool c_verify_clsag(uint s_len, uint8_t* s, uint8_t* I, uint8_t* m, uint8_t k_len, uint8_t* k, uint8_t* p) {
+    rct::clsag clsag;
+    std::stringstream ss;
+    std::string str;
+    str.assign((char*) s, (size_t) s_len);
+    ss << str;
+    binary_archive<false> ba(ss);
+    ::serialization::serialize(ba, clsag);
+    if (!ss.good()) {
+      return false;
+    }
+    memcpy(clsag.I.bytes, I, 32);
+
+    rct::key msg;
+    memcpy(msg.bytes, m, 32);
+
+    rct::ctkeyV keys;
+    keys.resize(k_len);
+    for (uint8_t i = 0; i < k_len; i++) {
+      memcpy(keys[i].dest.bytes, &k[(i * 2) * 32], 32);
+      memcpy(keys[i].mask.bytes, &k[((i * 2) + 1) * 32], 32);
+    }
+
+    rct::key pseudo_out;
+    memcpy(pseudo_out.bytes, p, 32);
+
+    return verRctCLSAGSimple(msg, clsag, keys, pseudo_out);
+  }
+}

sign/monero/src/clsag/mod.rs

@@ -0,0 +1,241 @@
+use rand_core::{RngCore, CryptoRng};
+
+use digest::Digest;
+use blake2::Blake2b;
+
+use curve25519_dalek::{
+  constants::ED25519_BASEPOINT_TABLE,
+  scalar::Scalar,
+  traits::VartimePrecomputedMultiscalarMul,
+  edwards::{EdwardsPoint, VartimeEdwardsPrecomputation}
+};
+
+use monero::{
+  consensus::Encodable,
+  util::ringct::{Key, Clsag}
+};
+
+use crate::{SignError, c_verify_clsag, random_scalar, commitment, hash_to_scalar, hash_to_point};
+
+#[cfg(feature = "multisig")]
+mod multisig;
+#[cfg(feature = "multisig")]
+pub use multisig::Multisig;
+
+// Ring with both the index we're signing for and the data needed to rebuild its commitment
+#[derive(Clone, PartialEq, Eq, Debug)]
+pub(crate) struct SemiSignableRing {
+  ring: Vec<[EdwardsPoint; 2]>,
+  i: usize,
+  randomness: Scalar,
+  amount: u64
+}
+
+pub(crate) fn validate_sign_args(
+  ring: Vec<[EdwardsPoint; 2]>,
+  i: u8,
+  private_key: Option<&Scalar>, // Option as multisig won't have access to this
+  randomness: &Scalar,
+  amount: u64
+) -> Result<SemiSignableRing, SignError> {
+  let n = ring.len();
+  if n > u8::MAX.into() {
+    Err(SignError::InternalError("max ring size in this library is u8 max".to_string()))?;
+  }
+  if i >= (n as u8) {
+    Err(SignError::InvalidRingMember(i, n as u8))?;
+  }
+  let i: usize = i.into();
+
+  // Validate the secrets match these ring members
+  if private_key.is_some() && (ring[i][0] != (private_key.unwrap() * &ED25519_BASEPOINT_TABLE)) {
+    Err(SignError::InvalidSecret(0))?;
+  }
+  if ring[i][1] != commitment(&randomness, amount) {
+    Err(SignError::InvalidSecret(1))?;
+  }
+
+  Ok(SemiSignableRing { ring, i, randomness: *randomness, amount })
+}
+
+#[allow(non_snake_case)]
+pub(crate) fn sign_core(
+  rand_source: [u8; 64],
+  image: EdwardsPoint,
+  msg: &[u8; 32],
+  ssr: &SemiSignableRing,
+  A: EdwardsPoint,
+  AH: EdwardsPoint
+) -> (Clsag, Scalar, Scalar, Scalar, Scalar, EdwardsPoint) {
+  let n = ssr.ring.len();
+  let i: usize = ssr.i.into();
+
+  let C_out;
+
+  let mut P = vec![];
+  P.reserve_exact(n);
+  let mut C = vec![];
+  C.reserve_exact(n);
+  let mut C_non_zero = vec![];
+  C_non_zero.reserve_exact(n);
+
+  let z;
+
+  let mut next_rand = rand_source;
+  next_rand = Blake2b::digest(&next_rand).as_slice().try_into().unwrap();
+  {
+    let a = Scalar::from_bytes_mod_order_wide(&next_rand);
+    next_rand = Blake2b::digest(&next_rand).as_slice().try_into().unwrap();
+    C_out = commitment(&a, ssr.amount);
+
+    for member in &ssr.ring {
+      P.push(member[0]);
+      C_non_zero.push(member[1]);
+      C.push(C_non_zero[C_non_zero.len() - 1] - C_out);
+    }
+
+    z = ssr.randomness - a;
+  }
+
+  let H = hash_to_point(&P[i]);
+  let mut D = H * z;
+
+  // Doesn't use a constant time table as dalek takes longer to generate those then they save
+  let images_precomp = VartimeEdwardsPrecomputation::new(&[image, D]);
+  D = Scalar::from(8 as u8).invert() * D;
+
+  let mut to_hash = vec![];
+  to_hash.reserve_exact(((2 * n) + 4) * 32);
+  const PREFIX: &str = "CLSAG_";
+  const AGG_0: &str =  "CLSAG_agg_0";
+  const ROUND: &str =        "round";
+  to_hash.extend(AGG_0.bytes());
+  to_hash.extend([0; 32 - AGG_0.len()]);
+
+  for j in 0 .. n {
+    to_hash.extend(P[j].compress().to_bytes());
+  }
+
+  for j in 0 .. n {
+    to_hash.extend(C_non_zero[j].compress().to_bytes());
+  }
+
+  to_hash.extend(image.compress().to_bytes());
+  let D_bytes = D.compress().to_bytes();
+  to_hash.extend(D_bytes);
+  to_hash.extend(C_out.compress().to_bytes());
+  let mu_P = hash_to_scalar(&to_hash);
+  to_hash[AGG_0.len() - 1] = '1' as u8;
+  let mu_C = hash_to_scalar(&to_hash);
+
+  to_hash.truncate(((2 * n) + 1) * 32);
+  to_hash.reserve_exact(((2 * n) + 5) * 32);
+  for j in 0 .. ROUND.len() {
+    to_hash[PREFIX.len() + j] = ROUND.as_bytes()[j] as u8;
+  }
+  to_hash.extend(C_out.compress().to_bytes());
+  to_hash.extend(msg);
+  to_hash.extend(A.compress().to_bytes());
+  to_hash.extend(AH.compress().to_bytes());
+  let mut c = hash_to_scalar(&to_hash);
+
+  let mut c1 = Scalar::zero();
+  let mut j = (i + 1) % n;
+  if j == 0 {
+    c1 = c;
+  }
+
+  let mut s = vec![];
+  s.resize(n, Scalar::zero());
+  while j != i {
+    s[j] = Scalar::from_bytes_mod_order_wide(&next_rand);
+    next_rand = Blake2b::digest(&next_rand).as_slice().try_into().unwrap();
+    let c_p = mu_P * c;
+    let c_c = mu_C * c;
+
+    let L = (&s[j] * &ED25519_BASEPOINT_TABLE) + (c_p * P[j]) + (c_c * C[j]);
+    let PH = hash_to_point(&P[j]);
+    // Shouldn't be an issue as all of the variables in this vartime statement are public
+    let R = (s[j] * PH) + images_precomp.vartime_multiscalar_mul(&[c_p, c_c]);
+
+    to_hash.truncate(((2 * n) + 3) * 32);
+    to_hash.extend(L.compress().to_bytes());
+    to_hash.extend(R.compress().to_bytes());
+    c = hash_to_scalar(&to_hash);
+
+    j = (j + 1) % n;
+    if j == 0 {
+      c1 = c;
+    }
+  }
+
+  (
+    Clsag {
+      s: s.iter().map(|s| Key { key: s.to_bytes() }).collect(),
+      c1: Key { key: c1.to_bytes() },
+      D: Key { key: D_bytes }
+    },
+    c, mu_C, z, mu_P,
+    C_out
+  )
+}
+
+#[allow(non_snake_case)]
+pub fn sign<R: RngCore + CryptoRng>(
+  rng: &mut R,
+  image: EdwardsPoint,
+  msg: [u8; 32],
+  ring: Vec<[EdwardsPoint; 2]>,
+  i: u8,
+  private_key: &Scalar,
+  randomness: &Scalar,
+  amount: u64
+) -> Result<(Clsag, EdwardsPoint), SignError> {
+  let ssr = validate_sign_args(ring, i, Some(private_key), randomness, amount)?;
+  let a = random_scalar(rng);
+  let mut rand_source = [0; 64];
+  rng.fill_bytes(&mut rand_source);
+  let (mut clsag, c, mu_C, z, mu_P, C_out) = sign_core(
+    rand_source,
+    image,
+    &msg, &ssr,
+    &a * &ED25519_BASEPOINT_TABLE, a * hash_to_point(&ssr.ring[ssr.i][0])
+  );
+  clsag.s[i as usize] = Key { key: (a - (c * ((mu_C * z) + (mu_P * private_key)))).to_bytes() };
+
+  Ok((clsag, C_out))
+}
+
+// Uses Monero's C verification function to ensure compatibility with Monero
+pub fn verify(
+  clsag: &Clsag,
+  image: EdwardsPoint,
+  msg: &[u8; 32],
+  ring: &[[EdwardsPoint; 2]],
+  pseudo_out: EdwardsPoint
+) -> Result<(), SignError> {
+  // Workaround for the fact monero-rs doesn't include the length of clsag.s in clsag encoding
+  // despite it being part of clsag encoding. Reason for the patch version pin
+  let mut serialized = vec![clsag.s.len() as u8];
+  clsag.consensus_encode(&mut serialized).unwrap();
+
+  let image_bytes = image.compress().to_bytes();
+
+  let mut ring_bytes = vec![];
+  for member in ring {
+    ring_bytes.extend(&member[0].compress().to_bytes());
+    ring_bytes.extend(&member[1].compress().to_bytes());
+  }
+
+  let pseudo_out_bytes = pseudo_out.compress().to_bytes();
+
+  let success;
+  unsafe {
+    success = c_verify_clsag(
+      serialized.len(), serialized.as_ptr(), image_bytes.as_ptr(),
+      msg.as_ptr(), ring.len() as u8, ring_bytes.as_ptr(), pseudo_out_bytes.as_ptr()
+    );
+  }
+
+  if success { Ok(()) } else { Err(SignError::InvalidSignature) }
+}

sign/monero/src/clsag/multisig.rs

@@ -0,0 +1,198 @@
+use rand_core::{RngCore, CryptoRng};
+
+use digest::Digest;
+use blake2::Blake2b;
+
+use curve25519_dalek::{
+  constants::ED25519_BASEPOINT_TABLE,
+  scalar::Scalar,
+  edwards::EdwardsPoint
+};
+
+use dalek_ff_group as dfg;
+use group::Group;
+use frost::{Curve, FrostError, algorithm::Algorithm};
+
+use monero::util::ringct::{Key, Clsag};
+
+use crate::{
+  SignError,
+  hash_to_point,
+  frost::{Ed25519, DLEqProof},
+  clsag::{SemiSignableRing, validate_sign_args, sign_core, verify}
+};
+
+#[allow(non_snake_case)]
+#[derive(Clone, Debug)]
+struct ClsagSignInterim {
+  c: Scalar,
+  mu_C: Scalar,
+  z: Scalar,
+  mu_P: Scalar,
+
+  clsag: Clsag,
+  C_out: EdwardsPoint
+}
+
+#[allow(non_snake_case)]
+#[derive(Clone, Debug)]
+pub struct Multisig {
+  b: Vec<u8>,
+  AH: dfg::EdwardsPoint,
+
+  image: EdwardsPoint,
+  msg: [u8; 32],
+  ssr: SemiSignableRing,
+
+  interim: Option<ClsagSignInterim>
+}
+
+impl Multisig {
+  pub fn new(
+    image: EdwardsPoint,
+    msg: [u8; 32],
+    ring: Vec<[EdwardsPoint; 2]>,
+    i: u8,
+    randomness: &Scalar,
+    amount: u64
+  ) -> Result<Multisig, SignError> {
+    let ssr = validate_sign_args(ring, i, None, randomness, amount)?;
+    Ok(
+      Multisig {
+        b: vec![],
+        AH: dfg::EdwardsPoint::identity(),
+
+        image,
+        msg,
+        ssr,
+
+        interim: None
+      }
+    )
+  }
+}
+
+impl Algorithm<Ed25519> for Multisig {
+  type Signature = (Clsag, EdwardsPoint);
+
+  fn context(&self) -> Vec<u8> {
+    let mut context = self.image.compress().to_bytes().to_vec();
+    for pair in &self.ssr.ring {
+      context.extend(&pair[0].compress().to_bytes());
+    }
+    context.extend(&u8::try_from(self.ssr.i).unwrap().to_le_bytes());
+    context.extend(&self.ssr.randomness.to_bytes());
+    context.extend(&self.ssr.amount.to_le_bytes());
+    context
+  }
+
+  // We arguably don't have to commit to at all thanks to xG and yG being committed to, both of
+  // those being proven to have the same scalar as xH and yH, yet it doesn't hurt
+  fn addendum_commit_len() -> usize {
+    64
+  }
+
+  fn preprocess_addendum<R: RngCore + CryptoRng>(
+    rng: &mut R,
+    group_key: &dfg::EdwardsPoint,
+    nonces: &[dfg::Scalar; 2]
+  ) -> Vec<u8> {
+    #[allow(non_snake_case)]
+    let H = hash_to_point(&group_key.0);
+    let h0 = nonces[0].0 * H;
+    let h1 = nonces[1].0 * H;
+    // 32 + 32 + 64 + 64
+    let mut serialized = Vec::with_capacity(192);
+    serialized.extend(h0.compress().to_bytes());
+    serialized.extend(h1.compress().to_bytes());
+    serialized.extend(&DLEqProof::prove(rng, &nonces[0].0, &H, &h0).serialize());
+    serialized.extend(&DLEqProof::prove(rng, &nonces[1].0, &H, &h1).serialize());
+    serialized
+  }
+
+  fn process_addendum(
+    &mut self,
+    l: usize,
+    commitments: &[dfg::EdwardsPoint; 2],
+    p: &dfg::Scalar,
+    serialized: &[u8]
+  ) -> Result<(), FrostError> {
+    if serialized.len() != 192 {
+      // Not an optimal error but...
+      Err(FrostError::InvalidCommitmentQuantity(l, 6, serialized.len() / 32))?;
+    }
+
+    let alt = &hash_to_point(&self.ssr.ring[self.ssr.i][0]);
+
+    let h0 = <Ed25519 as Curve>::G_from_slice(&serialized[0 .. 32]).map_err(|_| FrostError::InvalidCommitment(l))?;
+    DLEqProof::deserialize(&serialized[64 .. 128]).ok_or(FrostError::InvalidCommitment(l))?.verify(
+      &alt,
+      &commitments[0],
+      &h0
+    ).map_err(|_| FrostError::InvalidCommitment(l))?;
+
+    let h1 = <Ed25519 as Curve>::G_from_slice(&serialized[32 .. 64]).map_err(|_| FrostError::InvalidCommitment(l))?;
+    DLEqProof::deserialize(&serialized[128 .. 192]).ok_or(FrostError::InvalidCommitment(l))?.verify(
+      &alt,
+      &commitments[1],
+      &h1
+    ).map_err(|_| FrostError::InvalidCommitment(l))?;
+
+    self.b.extend(&l.to_le_bytes());
+    self.b.extend(&serialized[0 .. 64]);
+    self.AH += h0 + (h1 * p);
+
+    Ok(())
+  }
+
+  fn sign_share(
+    &mut self,
+    _: dfg::EdwardsPoint,
+    secret: dfg::Scalar,
+    nonce: dfg::Scalar,
+    nonce_sum: dfg::EdwardsPoint,
+    _: &[u8],
+  ) -> dfg::Scalar {
+    // Use everyone's commitments to derive a random source all signers can agree upon
+    // Cannot be manipulated to effect and all signers must, and will, know this
+    let rand_source = Blake2b::new().chain("Clsag_randomness").chain(&self.b).finalize().as_slice().try_into().unwrap();
+    #[allow(non_snake_case)]
+    let (clsag, c, mu_C, z, mu_P, C_out) = sign_core(rand_source, self.image, &self.msg, &self.ssr, nonce_sum.0, self.AH.0);
+
+    let share = dfg::Scalar(nonce.0 - (c * (mu_P * secret.0)));
+
+    self.interim = Some(ClsagSignInterim { c, mu_C, z, mu_P, clsag, C_out });
+    share
+  }
+
+  fn verify(
+    &self,
+    _: dfg::EdwardsPoint,
+    _: dfg::EdwardsPoint,
+    sum: dfg::Scalar
+  ) -> Option<Self::Signature> {
+    let interim = self.interim.as_ref().unwrap();
+
+    // Subtract the randomness's presence, which is done once and not fractionalized among shares
+    let s = sum.0 - (interim.c * (interim.mu_C * interim.z));
+
+    let mut clsag = interim.clsag.clone();
+    clsag.s[self.ssr.i] = Key { key: s.to_bytes() };
+    if verify(&clsag, self.image, &self.msg, &self.ssr.ring, interim.C_out).is_ok() {
+      return Some((clsag, interim.C_out));
+    }
+    return None;
+  }
+
+  fn verify_share(
+    &self,
+    verification_share: dfg::EdwardsPoint,
+    nonce: dfg::EdwardsPoint,
+    share: dfg::Scalar,
+  ) -> bool {
+    let interim = self.interim.as_ref().unwrap();
+    return (&share.0 * &ED25519_BASEPOINT_TABLE) == (
+      nonce.0 - (interim.c * (interim.mu_P * verification_share.0))
+    );
+  }
+}

sign/monero/src/frost.rs

@@ -0,0 +1,189 @@
+use core::convert::TryInto;
+
+use rand_core::{RngCore, CryptoRng};
+
+use digest::Digest;
+use blake2::Blake2b;
+
+use curve25519_dalek::{
+  constants::ED25519_BASEPOINT_TABLE as DTable,
+  traits::VartimeMultiscalarMul,
+  scalar::Scalar as DScalar,
+  edwards::EdwardsPoint as DPoint
+};
+
+use dalek_ff_group::EdwardsPoint;
+
+use ff::PrimeField;
+use group::Group;
+
+use dalek_ff_group as dfg;
+use frost::{CurveError, Curve};
+
+use crate::{SignError, random_scalar};
+
+#[derive(Clone, Copy, PartialEq, Eq, Debug)]
+pub struct Ed25519;
+impl Curve for Ed25519 {
+  type F = dfg::Scalar;
+  type G = dfg::EdwardsPoint;
+  type T = &'static dfg::EdwardsBasepointTable;
+
+  fn id() -> String {
+    "Ed25519".to_string()
+  }
+
+  fn id_len() -> u8 {
+    Self::id().len() as u8
+  }
+
+  fn generator() -> Self::G {
+    Self::G::generator()
+  }
+
+  fn generator_table() -> Self::T {
+    &dfg::ED25519_BASEPOINT_TABLE
+  }
+
+  fn multiexp_vartime(scalars: &[Self::F], points: &[Self::G]) -> Self::G {
+    EdwardsPoint(DPoint::vartime_multiscalar_mul(scalars, points))
+  }
+
+  fn F_len() -> usize {
+    32
+  }
+
+  fn G_len() -> usize {
+    32
+  }
+
+  fn F_from_le_slice(slice: &[u8]) -> Result<Self::F, CurveError> {
+    let scalar = Self::F::from_repr(
+      slice.try_into().map_err(|_| CurveError::InvalidLength(32, slice.len()))?
+    );
+    if scalar.is_some() {
+      Ok(scalar.unwrap())
+    } else {
+      Err(CurveError::InvalidScalar(hex::encode(slice)))
+    }
+  }
+
+  fn F_from_le_slice_unreduced(slice: &[u8]) -> Self::F {
+    let mut wide: [u8; 64] = [0; 64];
+    wide[..slice.len()].copy_from_slice(slice);
+    dfg::Scalar::from_bytes_mod_order_wide(&wide)
+  }
+
+  fn G_from_slice(slice: &[u8]) -> Result<Self::G, CurveError> {
+    let point = dfg::CompressedEdwardsY::new(
+      slice.try_into().map_err(|_| CurveError::InvalidLength(32, slice.len()))?
+    ).decompress();
+
+    if point.is_some() {
+      let point = point.unwrap();
+      // Ban torsioned points
+      if !point.is_torsion_free() {
+        Err(CurveError::InvalidPoint(hex::encode(slice)))?
+      }
+      Ok(point)
+    } else {
+      Err(CurveError::InvalidPoint(hex::encode(slice)))?
+    }
+  }
+
+  fn F_to_le_bytes(f: &Self::F) -> Vec<u8> {
+    f.to_repr().to_vec()
+  }
+
+  fn G_to_bytes(g: &Self::G) -> Vec<u8> {
+    g.compress().to_bytes().to_vec()
+  }
+
+  fn F_from_bytes_wide(bytes: [u8; 64]) -> Self::F {
+    dfg::Scalar::from_bytes_mod_order_wide(&bytes)
+  }
+}
+
+// Used to prove legitimacy in several locations
+#[derive(Clone)]
+pub struct DLEqProof {
+  s: DScalar,
+  c: DScalar
+}
+
+#[allow(non_snake_case)]
+impl DLEqProof {
+  pub fn prove<R: RngCore + CryptoRng>(
+    rng: &mut R,
+    secret: &DScalar,
+    H: &DPoint,
+    alt: &DPoint
+  ) -> DLEqProof {
+    let r = random_scalar(rng);
+    let R1 =  &DTable * &r;
+    let R2 = r * H;
+
+    let c = DScalar::from_hash(
+      Blake2b::new()
+        .chain(R1.compress().to_bytes())
+        .chain(R2.compress().to_bytes())
+        .chain((secret * &DTable).compress().to_bytes())
+        .chain(alt.compress().to_bytes())
+    );
+    let s = r + (c * secret);
+
+    DLEqProof { s, c }
+  }
+
+  pub fn verify(
+    &self,
+    H: &DPoint,
+    primary: &DPoint,
+    alt: &DPoint
+  ) -> Result<(), SignError> {
+    let s = self.s;
+    let c = self.c;
+
+    let R1 = (&s * &DTable) - (c * primary);
+    let R2 = (s * H) - (c * alt);
+
+    let expected_c = DScalar::from_hash(
+      Blake2b::new()
+        .chain(R1.compress().to_bytes())
+        .chain(R2.compress().to_bytes())
+        .chain(primary.compress().to_bytes())
+        .chain(alt.compress().to_bytes())
+    );
+
+    // Take the opportunity to ensure a lack of torsion in key images/randomness commitments
+    if (!primary.is_torsion_free()) || (!alt.is_torsion_free()) || (c != expected_c) {
+      Err(SignError::InvalidDLEqProof)?;
+    }
+
+    Ok(())
+  }
+
+  pub fn serialize(
+    &self
+  ) -> Vec<u8> {
+    let mut res = Vec::with_capacity(64);
+    res.extend(self.s.to_bytes());
+    res.extend(self.c.to_bytes());
+    res
+  }
+
+  pub fn deserialize(
+    serialized: &[u8]
+  ) -> Option<DLEqProof> {
+    if serialized.len() != 64 {
+      return None;
+    }
+
+    Some(
+      DLEqProof {
+        s: DScalar::from_bytes_mod_order(serialized[0 .. 32].try_into().unwrap()),
+        c: DScalar::from_bytes_mod_order(serialized[32 .. 64].try_into().unwrap())
+      }
+    )
+  }
+}

sign/monero/src/key_image/mod.rs

@@ -0,0 +1,16 @@
+use curve25519_dalek::{
+  constants::ED25519_BASEPOINT_TABLE,
+  scalar::Scalar,
+  edwards::EdwardsPoint
+};
+
+use crate::hash_to_point;
+
+#[cfg(feature = "multisig")]
+mod multisig;
+#[cfg(feature = "multisig")]
+pub use crate::key_image::multisig::{Package, multisig};
+
+pub fn single(secret: &Scalar) -> EdwardsPoint {
+  secret * hash_to_point(&(secret * &ED25519_BASEPOINT_TABLE))
+}

sign/monero/src/key_image/multisig.rs

@@ -0,0 +1,75 @@
+use rand_core::{RngCore, CryptoRng};
+
+use curve25519_dalek::edwards::EdwardsPoint;
+use dalek_ff_group::Scalar;
+use frost::{MultisigKeys, sign::lagrange};
+
+use crate::{SignError, hash_to_point, frost::{Ed25519, DLEqProof}};
+
+#[derive(Clone)]
+#[allow(non_snake_case)]
+pub struct Package {
+  // Don't serialize
+  H: EdwardsPoint,
+  i: usize,
+
+  // Serialize
+  image: EdwardsPoint,
+  proof: DLEqProof
+}
+
+#[allow(non_snake_case)]
+pub fn multisig<R: RngCore + CryptoRng>(
+  rng: &mut R,
+  keys: &MultisigKeys<Ed25519>,
+  included: &[usize]
+) -> Package {
+  let i = keys.params().i();
+  let secret = (keys.secret_share() * lagrange::<Scalar>(i, included)).0;
+
+  let H = hash_to_point(&keys.group_key().0);
+  let image = secret * H;
+  // Includes a proof. Since:
+  // sum(lagranged_secrets) = group_private
+  // group_private * G = output_key
+  // group_private * H = key_image
+  // Then sum(lagranged_secrets * H) = key_image
+  // lagranged_secret * G is known. lagranged_secret * H is being sent
+  // Any discrete log equality proof confirms the same secret was used,
+  // forming a valid key_image share
+  Package { H, i, image, proof: DLEqProof::prove(rng, &secret, &H, &image) }
+}
+
+#[allow(non_snake_case)]
+impl Package {
+  pub fn resolve(
+    self,
+    shares: Vec<Option<(EdwardsPoint, Package)>>
+  ) -> Result<EdwardsPoint, SignError> {
+    let mut included = vec![self.i];
+    for i in 1 .. shares.len() {
+      if shares[i].is_some() {
+        included.push(i);
+      }
+    }
+
+    let mut image = self.image;
+    for i in 0 .. shares.len() {
+      if shares[i].is_none() {
+        continue;
+      }
+
+      let (other, shares) = shares[i].as_ref().unwrap();
+      let other = other * lagrange::<Scalar>(i, &included).0;
+
+      // Verify their proof
+      let share = shares.image;
+      shares.proof.verify(&self.H, &other, &share).map_err(|_| SignError::InvalidKeyImage(i))?;
+
+      // Add their share to the image
+      image += share;
+    }
+
+    Ok(image)
+  }
+}

sign/monero/src/lib.rs

@@ -0,0 +1,82 @@
+use lazy_static::lazy_static;
+use thiserror::Error;
+
+use rand_core::{RngCore, CryptoRng};
+
+use tiny_keccak::{Hasher, Keccak};
+
+use curve25519_dalek::{
+  constants::ED25519_BASEPOINT_TABLE,
+  scalar::Scalar,
+  edwards::{EdwardsPoint, EdwardsBasepointTable, CompressedEdwardsY}
+};
+
+use monero::util::key;
+
+#[cfg(feature = "multisig")]
+pub mod frost;
+
+pub mod key_image;
+pub mod clsag;
+
+#[link(name = "wrapper")]
+extern "C" {
+  fn c_hash_to_point(point: *const u8);
+  pub(crate) fn c_verify_clsag(
+    serialized_len: usize, serialized: *const u8, I: *const u8,
+    msg: *const u8, ring_size: u8, ring: *const u8, pseudo_out: *const u8
+  ) -> bool;
+}
+
+#[derive(Error, Debug)]
+pub enum SignError {
+  #[error("internal error ({0})")]
+  InternalError(String),
+  #[error("invalid discrete log equality proof")]
+  InvalidDLEqProof,
+  #[error("invalid key image {0}")]
+  InvalidKeyImage(usize),
+  #[error("invalid ring member (member {0}, ring size {1})")]
+  InvalidRingMember(u8, u8),
+  #[error("invalid secret for ring (index {0})")]
+  InvalidSecret(u8),
+  #[error("invalid commitment {0}")]
+  InvalidCommitment(usize),
+  #[error("invalid share {0}")]
+  InvalidShare(usize),
+  #[error("invalid signature")]
+  InvalidSignature
+}
+
+// Allows using a modern rand as dalek's is notoriously dated
+pub fn random_scalar<R: RngCore + CryptoRng>(rng: &mut R) -> Scalar {
+  let mut r = [0; 64];
+  rng.fill_bytes(&mut r);
+  Scalar::from_bytes_mod_order_wide(&r)
+}
+
+lazy_static! {
+  static ref H_TABLE: EdwardsBasepointTable = EdwardsBasepointTable::create(&key::H.point.decompress().unwrap());
+}
+
+// aG + bH
+pub fn commitment(randomness: &Scalar, amount: u64) -> EdwardsPoint {
+  (randomness * &ED25519_BASEPOINT_TABLE) + (&Scalar::from(amount) * &*H_TABLE)
+}
+
+pub fn hash_to_scalar(data: &[u8]) -> Scalar {
+  let mut keccak = Keccak::v256();
+  keccak.update(data);
+
+  let mut res = [0; 32];
+  keccak.finalize(&mut res);
+  Scalar::from_bytes_mod_order(res)
+}
+
+pub fn hash_to_point(point: &EdwardsPoint) -> EdwardsPoint {
+  let mut bytes = point.compress().to_bytes();
+  unsafe {
+    c_hash_to_point(bytes.as_mut_ptr());
+  }
+  CompressedEdwardsY::from_slice(&bytes).decompress().unwrap()
+}

sign/monero/tests/clsag.rs

@@ -0,0 +1,155 @@
+use rand::{RngCore, rngs::OsRng};
+
+use curve25519_dalek::{constants::ED25519_BASEPOINT_TABLE, scalar::Scalar};
+
+use monero_sign::{SignError, random_scalar, commitment, key_image, clsag};
+
+#[cfg(feature = "multisig")]
+use ::frost::sign;
+
+#[cfg(feature = "multisig")]
+mod frost;
+#[cfg(feature = "multisig")]
+use crate::frost::generate_keys;
+
+#[cfg(feature = "multisig")]
+const THRESHOLD: usize = 5;
+#[cfg(feature = "multisig")]
+const PARTICIPANTS: usize = 8;
+
+const RING_INDEX: u8 = 3;
+const RING_LEN: u64 = 11;
+const AMOUNT: u64 = 1337;
+
+#[test]
+fn test_single() -> Result<(), SignError> {
+  let msg = [1; 32];
+
+  let mut secrets = [Scalar::zero(), Scalar::zero()];
+  let mut ring = vec![];
+  for i in 0 .. RING_LEN {
+    let dest = random_scalar(&mut OsRng);
+    let a = random_scalar(&mut OsRng);
+    let amount;
+    if i == RING_INDEX.into() {
+      secrets = [dest, a];
+      amount = AMOUNT;
+    } else {
+      amount = OsRng.next_u64();
+    }
+    let mask = commitment(&a, amount);
+    ring.push([&dest * &ED25519_BASEPOINT_TABLE, mask]);
+  }
+
+  let image = key_image::single(&secrets[0]);
+  let (clsag, pseudo_out) = clsag::sign(
+    &mut OsRng,
+    image,
+    msg,
+    ring.clone(),
+    RING_INDEX,
+    &secrets[0],
+    &secrets[1],
+    AMOUNT
+  )?;
+  clsag::verify(&clsag, image, &msg, &ring, pseudo_out)?;
+  Ok(())
+}
+
+#[cfg(feature = "multisig")]
+#[test]
+fn test_multisig() -> Result<(), SignError> {
+  let (keys, group_private) = generate_keys(THRESHOLD, PARTICIPANTS);
+  let t = keys[0].params().t();
+
+  let mut images = vec![];
+  images.resize(PARTICIPANTS + 1, None);
+  let included = (1 ..= THRESHOLD).collect::<Vec<usize>>();
+  for i in &included {
+    let i = *i;
+    images[i] = Some(
+      (
+        keys[0].verification_shares()[i].0,
+        key_image::multisig(&mut OsRng, &keys[i - 1], &included)
+      )
+    );
+  }
+
+  let msg = [1; 32];
+
+  images.push(None);
+  let ki_used = images.swap_remove(1).unwrap().1;
+  let image = ki_used.resolve(images).unwrap();
+
+  let randomness = random_scalar(&mut OsRng);
+  let mut ring = vec![];
+  for i in 0 .. RING_LEN {
+    let dest;
+    let a;
+    let amount;
+    if i != RING_INDEX.into() {
+      dest = random_scalar(&mut OsRng);
+      a = random_scalar(&mut OsRng);
+      amount = OsRng.next_u64();
+    } else {
+      dest = group_private.0;
+      a = randomness;
+      amount = AMOUNT;
+    }
+    let mask = commitment(&a, amount);
+    ring.push([&dest * &ED25519_BASEPOINT_TABLE, mask]);
+  }
+
+  let mut machines = vec![];
+  let mut commitments = Vec::with_capacity(PARTICIPANTS + 1);
+  commitments.resize(PARTICIPANTS + 1, None);
+  for i in 1 ..= t {
+    machines.push(
+      sign::StateMachine::new(
+        sign::Params::new(
+          clsag::Multisig::new(image, msg, ring.clone(), RING_INDEX, &randomness, AMOUNT).unwrap(),
+          keys[i - 1].clone(),
+          &(1 ..= t).collect::<Vec<usize>>()
+        ).unwrap()
+      )
+    );
+    commitments[i] = Some(machines[i - 1].preprocess(&mut OsRng).unwrap());
+  }
+
+  let mut shares = Vec::with_capacity(PARTICIPANTS + 1);
+  shares.resize(PARTICIPANTS + 1, None);
+  for i in 1 ..= t {
+    shares[i] = Some(
+      machines[i - 1].sign(
+        &commitments
+          .iter()
+          .enumerate()
+          .map(|(idx, value)| if idx == i { None } else { value.to_owned() })
+          .collect::<Vec<Option<Vec<u8>>>>(),
+        b"Hello World"
+      ).unwrap()
+    );
+  }
+
+  let mut signature = None;
+  for i in 1 ..= t {
+    // Multisig does call verify to ensure integrity upon complete, before checking individual key
+    // shares. For FROST Schnorr, it's cheaper. For CLSAG, it may be more expensive? Yet it ensures
+    // we have usable signatures, not just signatures we think are usable
+    let sig = machines[i - 1].complete(
+      &shares
+        .iter()
+        .enumerate()
+        .map(|(idx, value)| if idx == i { None } else { value.to_owned() })
+        .collect::<Vec<Option<Vec<u8>>>>()
+    ).unwrap();
+    if signature.is_none() {
+      signature = Some(sig.clone());
+    }
+    // Check the commitment out and the non-decoy s scalar are identical to every other signature
+    assert_eq!(sig.1, signature.as_ref().unwrap().1);
+    assert_eq!(sig.0.s[RING_INDEX as usize], signature.as_ref().unwrap().0.s[RING_INDEX as usize]);
+  }
+
+  Ok(())
+}

sign/monero/tests/frost.rs

@@ -0,0 +1,65 @@
+#![cfg(feature = "multisig")]
+
+use std::rc::Rc;
+
+use rand::rngs::OsRng;
+
+use ff::Field;
+use dalek_ff_group::{ED25519_BASEPOINT_TABLE, Scalar};
+
+use frost::{
+  MultisigParams, MultisigKeys,
+  key_gen,
+  sign::lagrange
+};
+
+use monero_sign::frost::Ed25519;
+
+pub fn generate_keys(t: usize, n: usize) -> (Vec<Rc<MultisigKeys<Ed25519>>>, Scalar) {
+  let mut params = vec![];
+  let mut machines = vec![];
+  let mut commitments = vec![vec![]];
+  for i in 1 ..= n {
+    params.push(
+      MultisigParams::new(t, n, i).unwrap()
+    );
+    machines.push(
+      key_gen::StateMachine::<Ed25519>::new(
+        params[i - 1],
+        "monero-sign-rs test suite".to_string()
+      )
+    );
+    commitments.push(machines[i - 1].generate_coefficients(&mut OsRng).unwrap());
+  }
+
+  let mut secret_shares = vec![];
+  for i in 1 ..= n {
+    secret_shares.push(
+      machines[i - 1].generate_secret_shares(
+        &mut OsRng,
+        commitments
+          .iter()
+          .enumerate()
+          .map(|(idx, commitments)| if idx == i { vec![] } else { commitments.to_vec() })
+          .collect()
+      ).unwrap()
+    );
+  }
+
+  let mut keys = vec![];
+  for i in 1 ..= n {
+    let mut our_secret_shares = vec![vec![]];
+    our_secret_shares.extend(
+      secret_shares.iter().map(|shares| shares[i].clone()).collect::<Vec<Vec<u8>>>()
+    );
+    keys.push(Rc::new(machines[i - 1].complete(our_secret_shares).unwrap().clone()));
+  }
+
+  let mut group_private = Scalar::zero();
+  for i in 0 .. t {
+    group_private += keys[i].secret_share() * lagrange::<Scalar>(i + 1, &(1 ..= t).collect::<Vec<usize>>());
+  }
+  assert_eq!(&ED25519_BASEPOINT_TABLE * group_private, keys[0].group_key());
+
+  (keys, group_private)
+}

sign/monero/tests/key_image.rs

@@ -0,0 +1,36 @@
+#![cfg(feature = "multisig")]
+
+use rand::rngs::OsRng;
+
+use monero_sign::{SignError, key_image};
+
+mod frost;
+use crate::frost::generate_keys;
+
+#[test]
+fn test() -> Result<(), SignError> {
+  let (keys, group_private) = generate_keys(3, 5);
+  let image = key_image::single(&group_private);
+
+  let mut packages = vec![];
+  packages.resize(5 + 1, None);
+  let included = vec![1, 3, 4];
+  for i in &included {
+    let i = *i;
+    packages[i] = Some(
+      (
+        keys[0].verification_shares()[i].0,
+        key_image::multisig(&mut OsRng, &keys[i - 1], &included)
+      )
+    );
+  }
+
+  for i in included {
+    let mut packages = packages.clone();
+    packages.push(None);
+    let package = packages.swap_remove(i).unwrap().1;
+    assert_eq!(image, package.resolve(packages).unwrap());
+  }
+
+  Ok(())
+}