Merge branch 'develop' into firo

crypto/dalek-ff-group/Cargo.toml

@@ -1,9 +1,11 @@
 [package]
 name = "dalek-ff-group"
-version = "0.1.0"
+version = "0.1.1"
 description = "ff/group bindings around curve25519-dalek"
 license = "MIT"
+repository = "https://github.com/serai-dex/serai"
 authors = ["Luke Parker <lukeparker5132@gmail.com>"]
+keywords = ["curve25519", "ed25519", "ristretto", "dalek", "group"]
 edition = "2021"
 
 [dependencies]
@@ -12,7 +14,8 @@ digest = "0.10"
 
 subtle = "2.4"
 
-ff = "0.11"
-group = "0.11"
+ff = "0.12"
+group = "0.12"
 
+crypto-bigint = "0.4"
 curve25519-dalek =  "3.2"

crypto/dalek-ff-group/README.md

@@ -1,3 +1,6 @@
 # Dalek FF/Group
 
-ff/group bindings around curve25519-dalek with a random function based around a more modern rand_core.
+ff/group bindings around curve25519-dalek with a from_hash/random function based
+around modern dependencies.
+
+Some functions currently remain unimplemented.

crypto/dalek-ff-group/src/field.rs

@@ -0,0 +1,142 @@
+use core::ops::{Add, AddAssign, Sub, SubAssign, Neg, Mul, MulAssign};
+
+use rand_core::RngCore;
+
+use subtle::{Choice, CtOption, ConstantTimeEq, ConditionallySelectable};
+use crypto_bigint::{Encoding, U256, U512};
+
+use ff::{Field, PrimeField, FieldBits, PrimeFieldBits};
+
+use crate::{choice, constant_time, math_op, math, from_wrapper, from_uint};
+
+const FIELD_MODULUS: U256 = U256::from_be_hex(
+  "7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffed"
+);
+
+#[derive(Clone, Copy, PartialEq, Eq, Debug, Default)]
+pub struct FieldElement(U256);
+
+pub const SQRT_M1: FieldElement = FieldElement(
+  U256::from_be_hex("2b8324804fc1df0b2b4d00993dfbd7a72f431806ad2fe478c4ee1b274a0ea0b0")
+);
+
+constant_time!(FieldElement, U256);
+math!(
+  FieldElement,
+  FieldElement,
+  |x, y| U256::add_mod(&x, &y, &FIELD_MODULUS),
+  |x, y| U256::sub_mod(&x, &y, &FIELD_MODULUS),
+  |x, y| {
+    #[allow(non_snake_case)]
+    let WIDE_MODULUS: U512 = U512::from((U256::ZERO, FIELD_MODULUS));
+    debug_assert_eq!(FIELD_MODULUS.to_le_bytes()[..], WIDE_MODULUS.to_le_bytes()[.. 32]);
+
+    let wide = U256::mul_wide(&x, &y);
+    U256::from_le_slice(
+      &U512::from((wide.1, wide.0)).reduce(&WIDE_MODULUS).unwrap().to_le_bytes()[.. 32]
+    )
+  }
+);
+from_uint!(FieldElement, U256);
+
+impl Neg for FieldElement {
+  type Output = Self;
+  fn neg(self) -> Self::Output { Self(self.0.neg_mod(&FIELD_MODULUS)) }
+}
+
+impl Field for FieldElement {
+  fn random(mut rng: impl RngCore) -> Self {
+    let mut bytes = [0; 64];
+    rng.fill_bytes(&mut bytes);
+
+    #[allow(non_snake_case)]
+    let WIDE_MODULUS: U512 = U512::from((U256::ZERO, FIELD_MODULUS));
+    debug_assert_eq!(FIELD_MODULUS.to_le_bytes()[..], WIDE_MODULUS.to_le_bytes()[.. 32]);
+
+    FieldElement(
+      U256::from_le_slice(
+        &U512::from_be_bytes(bytes).reduce(&WIDE_MODULUS).unwrap().to_le_bytes()[.. 32]
+      )
+    )
+  }
+
+  fn zero() -> Self { Self(U256::ZERO) }
+  fn one() -> Self { Self(U256::ONE) }
+  fn square(&self) -> Self { *self * self }
+  fn double(&self) -> Self { *self + self }
+
+  fn invert(&self) -> CtOption<Self> {
+    CtOption::new(self.pow(-FieldElement(U256::from(2u64))), !self.is_zero())
+  }
+
+  fn sqrt(&self) -> CtOption<Self> {
+    let c1 = SQRT_M1;
+    let c2 = FIELD_MODULUS.saturating_add(&U256::from(3u8)).checked_div(&U256::from(8u8)).unwrap();
+
+    let tv1 = self.pow(FieldElement(c2));
+    let tv2 = tv1 * c1;
+    let res = Self::conditional_select(&tv2, &tv1, tv1.square().ct_eq(self));
+    debug_assert_eq!(res * res, *self);
+    CtOption::new(Self::conditional_select(&tv2, &tv1, tv1.square().ct_eq(self)), 1.into())
+  }
+
+  fn is_zero(&self) -> Choice { self.0.ct_eq(&U256::ZERO) }
+  fn cube(&self) -> Self { *self * self * self }
+  fn pow_vartime<S: AsRef<[u64]>>(&self, _exp: S) -> Self { unimplemented!() }
+}
+
+impl PrimeField for FieldElement {
+  type Repr = [u8; 32];
+  const NUM_BITS: u32 = 255;
+  const CAPACITY: u32 = 254;
+  fn from_repr(bytes: [u8; 32]) -> CtOption<Self> {
+    let res = Self(U256::from_le_bytes(bytes));
+    CtOption::new(res, res.0.add_mod(&U256::ZERO, &FIELD_MODULUS).ct_eq(&res.0))
+  }
+  fn to_repr(&self) -> [u8; 32] { self.0.to_le_bytes() }
+
+  const S: u32 = 2;
+  fn is_odd(&self) -> Choice { unimplemented!() }
+  fn multiplicative_generator() -> Self { 2u64.into() }
+  fn root_of_unity() -> Self {
+    FieldElement(
+      U256::from_be_hex("2b8324804fc1df0b2b4d00993dfbd7a72f431806ad2fe478c4ee1b274a0ea0b0")
+    )
+  }
+}
+
+impl PrimeFieldBits for FieldElement {
+  type ReprBits = [u8; 32];
+
+  fn to_le_bits(&self) -> FieldBits<Self::ReprBits> {
+    self.to_repr().into()
+  }
+
+  fn char_le_bits() -> FieldBits<Self::ReprBits> {
+    FIELD_MODULUS.to_le_bytes().into()
+  }
+}
+
+impl FieldElement {
+  pub fn from_square(value: [u8; 32]) -> FieldElement {
+    let value = U256::from_le_bytes(value);
+    FieldElement(value) * FieldElement(value)
+  }
+
+  pub fn pow(&self, other: FieldElement) -> FieldElement {
+    let mut res = FieldElement(U256::ONE);
+    let mut m = *self;
+    for bit in other.to_le_bits() {
+      res *= FieldElement::conditional_select(&FieldElement(U256::ONE), &m, choice(bit));
+      m *= m;
+    }
+    res
+  }
+}
+
+#[test]
+fn test_mul() {
+  assert_eq!(FieldElement(FIELD_MODULUS) * FieldElement::one(), FieldElement::zero());
+  assert_eq!(FieldElement(FIELD_MODULUS) * FieldElement::one().double(), FieldElement::zero());
+  assert_eq!(SQRT_M1.square(), -FieldElement::one());
+}

crypto/dalek-ff-group/src/lib.rs

@@ -1,114 +1,189 @@
+#![no_std]
+
 use core::{
   ops::{Deref, Add, AddAssign, Sub, SubAssign, Neg, Mul, MulAssign},
   borrow::Borrow,
   iter::{Iterator, Sum}
 };
 
+use subtle::{ConstantTimeEq, ConditionallySelectable};
+
 use rand_core::RngCore;
 use digest::{consts::U64, Digest};
 
-use subtle::{Choice, CtOption, ConstantTimeEq, ConditionallySelectable};
+use subtle::{Choice, CtOption};
 
 pub use curve25519_dalek as dalek;
 
 use dalek::{
   constants,
-  traits::{Identity, IsIdentity},
+  traits::Identity,
   scalar::Scalar as DScalar,
   edwards::{
-    EdwardsPoint as DPoint,
-    EdwardsBasepointTable as DTable,
-    CompressedEdwardsY as DCompressed
+    EdwardsPoint as DEdwardsPoint,
+    EdwardsBasepointTable as DEdwardsBasepointTable,
+    CompressedEdwardsY as DCompressedEdwards
+  },
+  ristretto::{
+    RistrettoPoint as DRistrettoPoint,
+    RistrettoBasepointTable as DRistrettoBasepointTable,
+    CompressedRistretto as DCompressedRistretto
   }
 };
 
-use ff::{Field, PrimeField};
-use group::Group;
+use ff::{Field, PrimeField, FieldBits, PrimeFieldBits};
+use group::{Group, GroupEncoding, prime::PrimeGroup};
 
+pub mod field;
+
+// Convert a boolean to a Choice in a *presumably* constant time manner
+fn choice(value: bool) -> Choice {
+  let bit = value as u8;
+  debug_assert_eq!(bit | 1, 1);
+  Choice::from(bit)
+}
+
+macro_rules! deref_borrow {
+  ($Source: ident, $Target: ident) => {
+    impl Deref for $Source {
+      type Target = $Target;
+
+      fn deref(&self) -> &Self::Target {
+        &self.0
+      }
+    }
+
+    impl Borrow<$Target> for $Source {
+      fn borrow(&self) -> &$Target {
+        &self.0
+      }
+    }
+
+    impl Borrow<$Target> for &$Source {
+      fn borrow(&self) -> &$Target {
+        &self.0
+      }
+    }
+  }
+}
+
+#[doc(hidden)]
+#[macro_export]
+macro_rules! constant_time {
+  ($Value: ident, $Inner: ident) => {
+    impl ConstantTimeEq for $Value {
+      fn ct_eq(&self, other: &Self) -> Choice { self.0.ct_eq(&other.0) }
+    }
+
+    impl ConditionallySelectable for $Value {
+      fn conditional_select(a: &Self, b: &Self, choice: Choice) -> Self {
+        $Value($Inner::conditional_select(&a.0, &b.0, choice))
+      }
+    }
+  }
+}
+
+#[doc(hidden)]
+#[macro_export]
+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 = $function(self.0, other.0);
+      }
+    }
+  }
+}
+
+#[doc(hidden)]
+#[macro_export]
+macro_rules! math {
+  ($Value: ident, $Factor: ident, $add: expr, $sub: expr, $mul: expr) => {
+    math_op!($Value, $Value, Add, add, AddAssign, add_assign, $add);
+    math_op!($Value, $Value, Sub, sub, SubAssign, sub_assign, $sub);
+    math_op!($Value, $Factor, Mul, mul, MulAssign, mul_assign, $mul);
+  }
+}
+
+macro_rules! math_neg {
+  ($Value: ident, $Factor: ident, $add: expr, $sub: expr, $mul: expr) => {
+    math!($Value, $Factor, $add, $sub, $mul);
+
+    impl Neg for $Value {
+      type Output = Self;
+      fn neg(self) -> Self::Output { Self(-self.0) }
+    }
+  }
+}
+
+#[doc(hidden)]
+#[macro_export]
+macro_rules! from_wrapper {
+  ($wrapper: ident, $inner: ident, $uint: ident) => {
+    impl From<$uint> for $wrapper {
+      fn from(a: $uint) -> $wrapper { Self($inner::from(a)) }
+    }
+  }
+}
+
+#[doc(hidden)]
+#[macro_export]
+macro_rules! from_uint {
+  ($wrapper: ident, $inner: ident) => {
+    from_wrapper!($wrapper, $inner, u8);
+    from_wrapper!($wrapper, $inner, u16);
+    from_wrapper!($wrapper, $inner, u32);
+    from_wrapper!($wrapper, $inner, u64);
+  }
+}
+
+/// Wrapper around the dalek Scalar type
 #[derive(Clone, Copy, PartialEq, Eq, Debug, Default)]
 pub struct Scalar(pub DScalar);
+deref_borrow!(Scalar, DScalar);
+constant_time!(Scalar, DScalar);
+math_neg!(Scalar, Scalar, DScalar::add, DScalar::sub, DScalar::mul);
+from_uint!(Scalar, DScalar);
 
-impl Deref for Scalar {
-  type Target = DScalar;
-
-  fn deref(&self) -> &Self::Target {
-    &self.0
+impl Scalar {
+  /// Perform wide reduction on a 64-byte array to create a Scalar without bias
+  pub fn from_bytes_mod_order_wide(bytes: &[u8; 64]) -> Scalar {
+    Self(DScalar::from_bytes_mod_order_wide(bytes))
   }
-}
 
-impl Borrow<DScalar> for Scalar {
-  fn borrow(&self) -> &DScalar {
-    &self.0
+  /// Derive a Scalar without bias from a digest via wide reduction
+  pub fn from_hash<D: Digest<OutputSize = U64>>(hash: D) -> Scalar {
+    let mut output = [0u8; 64];
+    output.copy_from_slice(&hash.finalize());
+    Scalar(DScalar::from_bytes_mod_order_wide(&output))
   }
 }
 
-impl Borrow<DScalar> for &Scalar {
-  fn borrow(&self) -> &DScalar {
-    &self.0
-  }
-}
-
-impl Add<Scalar> for Scalar {
-  type Output = Self;
-  fn add(self, other: Scalar) -> Scalar { Self(self.0 + other.0) }
-}
-impl AddAssign for Scalar {
-  fn add_assign(&mut self, other: Scalar) { self.0 += other.0 }
-}
-
-impl<'a> Add<&'a Scalar> for Scalar {
-  type Output = Self;
-  fn add(self, other: &'a Scalar) -> Scalar { Self(self.0 + other.0) }
-}
-impl<'a> AddAssign<&'a Scalar> for Scalar {
-  fn add_assign(&mut self, other: &'a Scalar) { self.0 += other.0 }
-}
-
-impl Sub<Scalar> for Scalar {
-  type Output = Self;
-  fn sub(self, other: Scalar) -> Scalar { Self(self.0 - other.0) }
-}
-impl SubAssign for Scalar {
-  fn sub_assign(&mut self, other: Scalar) { self.0 -= other.0 }
-}
-
-impl<'a> Sub<&'a Scalar> for Scalar {
-  type Output = Self;
-  fn sub(self, other: &'a Scalar) -> Scalar { Self(self.0 - other.0) }
-}
-impl<'a> SubAssign<&'a Scalar> for Scalar {
-  fn sub_assign(&mut self, other: &'a Scalar) { self.0 -= other.0 }
-}
-
-impl Neg for Scalar {
-  type Output = Self;
-  fn neg(self) -> Scalar { Self(-self.0) }
-}
-
-impl Mul<Scalar> for Scalar {
-  type Output = Self;
-  fn mul(self, other: Scalar) -> Scalar { Self(self.0 * other.0) }
-}
-impl MulAssign for Scalar {
-  fn mul_assign(&mut self, other: Scalar) { self.0 *= other.0 }
-}
-
-impl<'a> Mul<&'a Scalar> for Scalar {
-  type Output = Self;
-  fn mul(self, other: &'a Scalar) -> Scalar { Self(self.0 * other.0) }
-}
-impl<'a> MulAssign<&'a Scalar> for Scalar {
-  fn mul_assign(&mut self, other: &'a Scalar) { self.0 *= other.0 }
-}
-
-impl ConstantTimeEq for Scalar {
-  fn ct_eq(&self, _: &Self) -> Choice { unimplemented!() }
-}
-
-impl ConditionallySelectable for Scalar {
-  fn conditional_select(_: &Self, _: &Self, _: Choice) -> Self { unimplemented!() }
-}
-
 impl Field for Scalar {
   fn random(mut rng: impl RngCore) -> Self {
     let mut r = [0; 64];
@@ -121,194 +196,145 @@ impl Field for Scalar {
   fn square(&self) -> Self { *self * self }
   fn double(&self) -> Self { *self + self }
   fn invert(&self) -> CtOption<Self> {
-    CtOption::new(Self(self.0.invert()), Choice::from(1 as u8))
+    CtOption::new(Self(self.0.invert()), !self.is_zero())
   }
   fn sqrt(&self) -> CtOption<Self> { unimplemented!() }
-  fn is_zero(&self) -> Choice { Choice::from(if self.0 == DScalar::zero() { 1 } else { 0 }) }
+  fn is_zero(&self) -> Choice { self.0.ct_eq(&DScalar::zero()) }
   fn cube(&self) -> Self { *self * self * self }
   fn pow_vartime<S: AsRef<[u64]>>(&self, _exp: S) -> Self { unimplemented!() }
 }
 
-impl From<u64> for Scalar {
-  fn from(a: u64) -> Scalar { Self(DScalar::from(a)) }
-}
-
 impl PrimeField for Scalar {
   type Repr = [u8; 32];
   const NUM_BITS: u32 = 253;
   const CAPACITY: u32 = 252;
   fn from_repr(bytes: [u8; 32]) -> CtOption<Self> {
-    let scalar = DScalar::from_canonical_bytes(bytes).map(|x| Scalar(x));
-    CtOption::new(
-      scalar.unwrap_or(Scalar::zero()),
-      Choice::from(if scalar.is_some() { 1 } else { 0 })
-    )
+    let scalar = DScalar::from_canonical_bytes(bytes);
+    // TODO: This unwrap_or isn't constant time, yet do we have an alternative?
+    CtOption::new(Scalar(scalar.unwrap_or(DScalar::zero())), choice(scalar.is_some()))
   }
   fn to_repr(&self) -> [u8; 32] { self.0.to_bytes() }
 
-  const S: u32 = 0;
+  const S: u32 = 2;
   fn is_odd(&self) -> Choice { unimplemented!() }
-  fn multiplicative_generator() -> Self { unimplemented!() }
+  fn multiplicative_generator() -> Self { 2u64.into() }
   fn root_of_unity() -> Self { unimplemented!() }
 }
 
-impl Scalar {
-  pub fn from_hash<D: Digest<OutputSize = U64>>(hash: D) -> Scalar {
-    let mut output = [0u8; 64];
-    output.copy_from_slice(&hash.finalize());
-    Scalar(DScalar::from_bytes_mod_order_wide(&output))
+impl PrimeFieldBits for Scalar {
+  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 bytes = (Scalar::zero() - Scalar::one()).to_repr();
+    bytes[0] += 1;
+    debug_assert_eq!(DScalar::from_bytes_mod_order(bytes), DScalar::zero());
+    bytes.into()
   }
 }
 
-#[derive(Clone, Copy, PartialEq, Eq, Debug)]
-pub struct EdwardsPoint(pub DPoint);
-pub const ED25519_BASEPOINT_POINT: EdwardsPoint = EdwardsPoint(constants::ED25519_BASEPOINT_POINT);
+macro_rules! dalek_group {
+  (
+    $Point: ident,
+    $DPoint: ident,
+    $torsion_free: expr,
 
-impl Deref for EdwardsPoint {
-    type Target = DPoint;
+    $Table: ident,
+    $DTable: ident,
 
-    fn deref(&self) -> &Self::Target {
-        &self.0
+    $DCompressed: ident,
+
+    $BASEPOINT_POINT: ident,
+    $BASEPOINT_TABLE: ident
+  ) => {
+    /// Wrapper around the dalek Point type. For Ed25519, this is restricted to the prime subgroup
+    #[derive(Clone, Copy, PartialEq, Eq, Debug)]
+    pub struct $Point(pub $DPoint);
+    deref_borrow!($Point, $DPoint);
+    constant_time!($Point, $DPoint);
+    math_neg!($Point, Scalar, $DPoint::add, $DPoint::sub, $DPoint::mul);
+
+    pub const $BASEPOINT_POINT: $Point = $Point(constants::$BASEPOINT_POINT);
+
+    impl Sum<$Point> for $Point {
+      fn sum<I: Iterator<Item = $Point>>(iter: I) -> $Point { Self($DPoint::sum(iter)) }
     }
+    impl<'a> Sum<&'a $Point> for $Point {
+      fn sum<I: Iterator<Item = &'a $Point>>(iter: I) -> $Point { Self($DPoint::sum(iter)) }
+    }
+
+    impl Group for $Point {
+      type Scalar = Scalar;
+      // Ideally, this would be cryptographically secure, yet that's not a bound on the trait
+      // k256 also does this
+      fn random(rng: impl RngCore) -> Self { &$BASEPOINT_TABLE * Scalar::random(rng) }
+      fn identity() -> Self { Self($DPoint::identity()) }
+      fn generator() -> Self { $BASEPOINT_POINT }
+      fn is_identity(&self) -> Choice { self.0.ct_eq(&$DPoint::identity()) }
+      fn double(&self) -> Self { *self + self }
+    }
+
+    impl GroupEncoding for $Point {
+      type Repr = [u8; 32];
+
+      fn from_bytes(bytes: &Self::Repr) -> CtOption<Self> {
+        let decompressed = $DCompressed(*bytes).decompress();
+        // TODO: Same note on unwrap_or as above
+        let point = decompressed.unwrap_or($DPoint::identity());
+        CtOption::new($Point(point), choice(decompressed.is_some()) & choice($torsion_free(point)))
+      }
+
+      fn from_bytes_unchecked(bytes: &Self::Repr) -> CtOption<Self> {
+        $Point::from_bytes(bytes)
+      }
+
+      fn to_bytes(&self) -> Self::Repr {
+        self.0.compress().to_bytes()
+      }
+    }
+
+    impl PrimeGroup for $Point {}
+
+    /// Wrapper around the dalek Table type, offering efficient multiplication against the
+    /// basepoint
+    pub struct $Table(pub $DTable);
+    deref_borrow!($Table, $DTable);
+    pub const $BASEPOINT_TABLE: $Table = $Table(constants::$BASEPOINT_TABLE);
+
+    impl Mul<Scalar> for &$Table {
+      type Output = $Point;
+      fn mul(self, b: Scalar) -> $Point { $Point(&b.0 * &self.0) }
+    }
+  };
 }
 
-impl Borrow<DPoint> for EdwardsPoint {
-  fn borrow(&self) -> &DPoint {
-    &self.0
-  }
-}
+dalek_group!(
+  EdwardsPoint,
+  DEdwardsPoint,
+  |point: DEdwardsPoint| point.is_torsion_free(),
 
-impl Borrow<DPoint> for &EdwardsPoint {
-  fn borrow(&self) -> &DPoint {
-    &self.0
-  }
-}
+  EdwardsBasepointTable,
+  DEdwardsBasepointTable,
 
-impl Add<EdwardsPoint> for EdwardsPoint {
-  type Output = Self;
-  fn add(self, b: EdwardsPoint) -> EdwardsPoint { Self(self.0 + b.0) }
-}
-impl AddAssign<EdwardsPoint> for EdwardsPoint {
-  fn add_assign(&mut self, other: EdwardsPoint) { self.0 += other.0 }
-}
-impl Sum<EdwardsPoint> for EdwardsPoint {
-  fn sum<I: Iterator<Item = EdwardsPoint>>(iter: I) -> EdwardsPoint { Self(DPoint::sum(iter)) }
-}
+  DCompressedEdwards,
 
-impl<'a> Add<&'a EdwardsPoint> for EdwardsPoint {
-  type Output = Self;
-  fn add(self, b: &'a EdwardsPoint) -> EdwardsPoint { Self(self.0 + b.0) }
-}
-impl<'a> AddAssign<&'a EdwardsPoint> for EdwardsPoint {
-  fn add_assign(&mut self, other: &'a EdwardsPoint) { self.0 += other.0 }
-}
-impl<'a> Sum<&'a EdwardsPoint> for EdwardsPoint {
-  fn sum<I: Iterator<Item = &'a EdwardsPoint>>(iter: I) -> EdwardsPoint { Self(DPoint::sum(iter)) }
-}
-
-impl Sub<EdwardsPoint> for EdwardsPoint {
-  type Output = Self;
-  fn sub(self, b: EdwardsPoint) -> EdwardsPoint { Self(self.0 - b.0) }
-}
-impl SubAssign<EdwardsPoint> for EdwardsPoint {
-  fn sub_assign(&mut self, other: EdwardsPoint) { self.0 -= other.0 }
-}
-
-impl<'a> Sub<&'a EdwardsPoint> for EdwardsPoint {
-  type Output = Self;
-  fn sub(self, b: &'a EdwardsPoint) -> EdwardsPoint { Self(self.0 - b.0) }
-}
-impl<'a> SubAssign<&'a EdwardsPoint> for EdwardsPoint {
-  fn sub_assign(&mut self, other: &'a EdwardsPoint) { self.0 -= other.0 }
-}
-
-impl Neg for EdwardsPoint {
-  type Output = Self;
-  fn neg(self) -> EdwardsPoint { Self(-self.0) }
-}
-
-impl Mul<Scalar> for EdwardsPoint {
-  type Output = Self;
-  fn mul(self, b: Scalar) -> EdwardsPoint { Self(b.0 * self.0) }
-}
-impl MulAssign<Scalar> for EdwardsPoint {
-  fn mul_assign(&mut self, other: Scalar) { self.0 *= other.0 }
-}
-
-impl<'a> Mul<&'a Scalar> for EdwardsPoint {
-  type Output = Self;
-  fn mul(self, b: &'a Scalar) -> EdwardsPoint { Self(b.0 * self.0) }
-}
-impl<'a> MulAssign<&'a Scalar> for EdwardsPoint {
-  fn mul_assign(&mut self, other: &'a Scalar) { self.0 *= other.0 }
-}
-
-impl Group for EdwardsPoint {
-  type Scalar = Scalar;
-  fn random(mut _rng: impl RngCore) -> Self { unimplemented!() }
-  fn identity() -> Self { Self(DPoint::identity()) }
-  fn generator() -> Self { ED25519_BASEPOINT_POINT }
-  fn is_identity(&self) -> Choice { (self.0.is_identity() as u8).into() }
-  fn double(&self) -> Self { *self + self }
-}
-
-impl Scalar {
-  pub fn from_canonical_bytes(bytes: [u8; 32]) -> Option<Scalar> {
-    DScalar::from_canonical_bytes(bytes).map(|x| Self(x))
-  }
-  pub fn from_bytes_mod_order(bytes: [u8; 32]) -> Scalar {
-    Self(DScalar::from_bytes_mod_order(bytes))
-  }
-  pub fn from_bytes_mod_order_wide(bytes: &[u8; 64]) -> Scalar {
-    Self(DScalar::from_bytes_mod_order_wide(bytes))
-  }
-}
-
-pub struct CompressedEdwardsY(pub DCompressed);
-impl CompressedEdwardsY {
-  pub fn new(y: [u8; 32]) -> CompressedEdwardsY {
-    Self(DCompressed(y))
-  }
-
-  pub fn decompress(&self) -> Option<EdwardsPoint> {
-    self.0.decompress().map(|x| EdwardsPoint(x))
-  }
-
-  pub fn to_bytes(&self) -> [u8; 32] {
-    self.0.to_bytes()
-  }
-}
-
-impl EdwardsPoint {
-  pub fn is_torsion_free(&self) -> bool {
-    self.0.is_torsion_free()
-  }
-
-  pub fn compress(&self) -> CompressedEdwardsY {
-    CompressedEdwardsY(self.0.compress())
-  }
-}
-
-pub struct EdwardsBasepointTable(pub DTable);
-pub const ED25519_BASEPOINT_TABLE: EdwardsBasepointTable = EdwardsBasepointTable(
-  constants::ED25519_BASEPOINT_TABLE
+  ED25519_BASEPOINT_POINT,
+  ED25519_BASEPOINT_TABLE
 );
 
-impl Deref for EdwardsBasepointTable {
-    type Target = DTable;
+dalek_group!(
+  RistrettoPoint,
+  DRistrettoPoint,
+  |_| true,
 
-    fn deref(&self) -> &Self::Target {
-        &self.0
-    }
-}
+  RistrettoBasepointTable,
+  DRistrettoBasepointTable,
 
-impl Borrow<DTable> for &EdwardsBasepointTable {
-  fn borrow(&self) -> &DTable {
-    &self.0
-  }
-}
+  DCompressedRistretto,
 
-impl Mul<Scalar> for &EdwardsBasepointTable {
-  type Output = EdwardsPoint;
-  fn mul(self, b: Scalar) -> EdwardsPoint { EdwardsPoint(&b.0 * &self.0) }
-}
+  RISTRETTO_BASEPOINT_POINT,
+  RISTRETTO_BASEPOINT_TABLE
+);

crypto/dleq/Cargo.toml

@@ -0,0 +1,38 @@
+[package]
+name = "dleq"
+version = "0.1.0"
+description = "Implementation of single and cross-curve Discrete Log Equality proofs"
+license = "MIT"
+authors = ["Luke Parker <lukeparker5132@gmail.com>"]
+edition = "2021"
+
+[dependencies]
+thiserror = "1"
+rand_core = "0.6"
+
+digest = "0.10"
+
+transcript = { package = "flexible-transcript", path = "../transcript", version = "0.1" }
+
+ff = "0.12"
+group = "0.12"
+
+multiexp = { path = "../multiexp", features = ["batch"], optional = true }
+
+[dev-dependencies]
+hex-literal = "0.3"
+
+blake2 = "0.10"
+
+k256 = { version = "0.11", features = ["arithmetic", "bits"] }
+dalek-ff-group = { path = "../dalek-ff-group" }
+
+transcript = { package = "flexible-transcript", path = "../transcript", features = ["recommended"] }
+
+[features]
+serialize = []
+experimental = ["multiexp"]
+secure_capacity_difference = []
+
+# Only applies to cross_group, yet is default to ensure security
+default = ["secure_capacity_difference"]

crypto/dleq/LICENSE

@@ -0,0 +1,21 @@
+MIT License
+
+Copyright (c) 2020-2022 Luke Parker, Lee Bousfield
+
+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.

crypto/dleq/README.md

@@ -0,0 +1,63 @@
+# Discrete Log Equality
+
+Implementation of discrete log equality proofs for curves implementing
+`ff`/`group`. There is also a highly experimental cross-group DLEq proof, under
+the `experimental` feature, which has no formal proofs available yet is
+available here regardless. This library has NOT undergone auditing.
+
+### Cross-Group DLEq
+
+The present cross-group DLEq is based off
+[MRL-0010](https://web.getmonero.org/resources/research-lab/pubs/MRL-0010.pdf),
+which isn't computationally correct as while it proves both keys have the same
+discrete logarithm for their `G'`/`H'` component, it doesn't prove a lack of a
+`G`/`H` component. Accordingly, it was augmented with a pair of Schnorr Proof of
+Knowledges, proving a known `G'`/`H'` component, guaranteeing a lack of a
+`G`/`H` component (assuming an unknown relation between `G`/`H` and `G'`/`H'`).
+
+The challenges for the ring signatures were also merged, removing one-element
+from each bit's proof with only a slight reduction to challenge security (as
+instead of being uniform over each scalar field, they're uniform over the
+mutual bit capacity of each scalar field). This reduction is identical to the
+one applied to the proved-for scalar, and accordingly should not reduce overall
+security. It does create a lack of domain separation, yet that shouldn't be an
+issue.
+
+The following variants are available:
+
+- `ClassicLinear`. This is only for reference purposes, being the above
+  described proof, with no further optimizations.
+
+- `ConciseLinear`. This proves for 2 bits at a time, not increasing the
+  signature size for both bits yet decreasing the amount of
+  commitments/challenges in total.
+
+- `EfficientLinear`. This provides ring signatures in the form
+  `((R_G, R_H), s)`, instead of `(e, s)`, and accordingly enables a batch
+  verification of their final step. It is the most performant, and also the
+  largest, option.
+
+- `CompromiseLinear`. This provides signatures in the form `((R_G, R_H), s)` AND
+  proves for 2-bits at a time. While this increases the amount of steps in
+  verifying the ring signatures, which aren't batch verified, and decreases the
+  amount of items batched (an operation which grows in efficiency with
+  quantity), it strikes a balance between speed and size.
+
+The following numbers are from benchmarks performed with k256/curve25519_dalek
+on a Intel i7-118567:
+
+| Algorithm          | Size                    | Verification Time |
+|--------------------|-------------------------|-------------------|
+| `ClassicLinear`    | 56829 bytes (+27%)      | 157ms (0%)        |
+| `ConciseLinear`    | 44607 bytes (Reference) | 156ms (Reference) |
+| `EfficientLinear`  | 65145 bytes (+46%)      | 122ms (-22%)      |
+| `CompromiseLinear` | 48765 bytes  (+9%)      | 137ms (-12%)      |
+
+`CompromiseLinear` is the best choice by only being marginally sub-optimal
+regarding size, yet still achieving most of the desired performance
+improvements. That said, neither the original postulation (which had flaws) nor
+any construction here has been proven nor audited. Accordingly, they are solely
+experimental, and none are recommended.
+
+All proofs are suffixed "Linear" in the hope a logarithmic proof makes itself
+available, which would likely immediately become the most efficient option.

crypto/dleq/src/cross_group/aos.rs

@@ -0,0 +1,230 @@
+use rand_core::{RngCore, CryptoRng};
+
+use transcript::Transcript;
+
+use group::{ff::{Field, PrimeFieldBits}, prime::PrimeGroup};
+
+use multiexp::BatchVerifier;
+
+use crate::{
+  Generators,
+  cross_group::{DLEqError, scalar::{scalar_convert, mutual_scalar_from_bytes}}
+};
+
+#[cfg(feature = "serialize")]
+use std::io::{Read, Write};
+#[cfg(feature = "serialize")]
+use ff::PrimeField;
+#[cfg(feature = "serialize")]
+use crate::{read_scalar, cross_group::read_point};
+
+#[allow(non_camel_case_types)]
+#[derive(Clone, PartialEq, Eq, Debug)]
+pub(crate) enum Re<G0: PrimeGroup, G1: PrimeGroup> {
+  R(G0, G1),
+  // Merged challenges have a slight security reduction, yet one already applied to the scalar
+  // being proven for, and this saves ~8kb. Alternatively, challenges could be redefined as a seed,
+  // present here, which is then hashed for each of the two challenges, remaining unbiased/unique
+  // while maintaining the bandwidth savings, yet also while adding 252 hashes for
+  // Secp256k1/Ed25519
+  e(G0::Scalar)
+}
+
+impl<G0: PrimeGroup, G1: PrimeGroup> Re<G0, G1> {
+  #[allow(non_snake_case)]
+  pub(crate) fn R_default() -> Re<G0, G1> {
+    Re::R(G0::identity(), G1::identity())
+  }
+
+  pub(crate) fn e_default() -> Re<G0, G1> {
+    Re::e(G0::Scalar::zero())
+  }
+}
+
+#[allow(non_snake_case)]
+#[derive(Clone, PartialEq, Eq, Debug)]
+pub(crate) struct Aos<G0: PrimeGroup, G1: PrimeGroup, const RING_LEN: usize> {
+  Re_0: Re<G0, G1>,
+  s: [(G0::Scalar, G1::Scalar); RING_LEN]
+}
+
+impl<
+  G0: PrimeGroup,
+  G1: PrimeGroup,
+  const RING_LEN: usize
+> Aos<G0, G1, RING_LEN> where G0::Scalar: PrimeFieldBits, G1::Scalar: PrimeFieldBits {
+  #[allow(non_snake_case)]
+  fn nonces<T: Transcript>(mut transcript: T, nonces: (G0, G1)) -> (G0::Scalar, G1::Scalar) {
+    transcript.domain_separate(b"aos_membership_proof");
+    transcript.append_message(b"ring_len", &u8::try_from(RING_LEN).unwrap().to_le_bytes());
+    transcript.append_message(b"nonce_0", nonces.0.to_bytes().as_ref());
+    transcript.append_message(b"nonce_1", nonces.1.to_bytes().as_ref());
+    mutual_scalar_from_bytes(transcript.challenge(b"challenge").as_ref())
+  }
+
+  #[allow(non_snake_case)]
+  fn R(
+    generators: (Generators<G0>, Generators<G1>),
+    s: (G0::Scalar, G1::Scalar),
+    A: (G0, G1),
+    e: (G0::Scalar, G1::Scalar)
+  ) -> (G0, G1) {
+    (((generators.0.alt * s.0) - (A.0 * e.0)), ((generators.1.alt * s.1) - (A.1 * e.1)))
+  }
+
+  #[allow(non_snake_case)]
+  fn R_batch(
+    generators: (Generators<G0>, Generators<G1>),
+    s: (G0::Scalar, G1::Scalar),
+    A: (G0, G1),
+    e: (G0::Scalar, G1::Scalar)
+  ) -> (Vec<(G0::Scalar, G0)>, Vec<(G1::Scalar, G1)>) {
+    (vec![(-s.0, generators.0.alt), (e.0, A.0)], vec![(-s.1, generators.1.alt), (e.1, A.1)])
+  }
+
+  #[allow(non_snake_case)]
+  fn R_nonces<T: Transcript>(
+    transcript: T,
+    generators: (Generators<G0>, Generators<G1>),
+    s: (G0::Scalar, G1::Scalar),
+    A: (G0, G1),
+    e: (G0::Scalar, G1::Scalar)
+  ) -> (G0::Scalar, G1::Scalar) {
+    Self::nonces(transcript, Self::R(generators, s, A, e))
+  }
+
+  #[allow(non_snake_case)]
+  pub(crate) fn prove<R: RngCore + CryptoRng, T: Clone + Transcript>(
+    rng: &mut R,
+    transcript: T,
+    generators: (Generators<G0>, Generators<G1>),
+    ring: &[(G0, G1)],
+    actual: usize,
+    blinding_key: (G0::Scalar, G1::Scalar),
+    mut Re_0: Re<G0, G1>
+  ) -> Self {
+    // While it is possible to use larger values, it's not efficient to do so
+    // 2 + 2 == 2^2, yet 2 + 2 + 2 < 2^3
+    debug_assert!((RING_LEN == 2) || (RING_LEN == 4));
+    debug_assert_eq!(RING_LEN, ring.len());
+
+    let mut s = [(G0::Scalar::zero(), G1::Scalar::zero()); RING_LEN];
+
+    let r = (G0::Scalar::random(&mut *rng), G1::Scalar::random(&mut *rng));
+    #[allow(non_snake_case)]
+    let original_R = (generators.0.alt * r.0, generators.1.alt * r.1);
+    #[allow(non_snake_case)]
+    let mut R = original_R;
+
+    for i in ((actual + 1) .. (actual + RING_LEN + 1)).map(|i| i % RING_LEN) {
+      let e = Self::nonces(transcript.clone(), R);
+      if i == 0 {
+        match Re_0 {
+          Re::R(ref mut R0_0, ref mut R1_0) => { *R0_0 = R.0; *R1_0 = R.1 },
+          Re::e(ref mut e_0) => *e_0 = e.0
+        }
+      }
+
+      // Solve for the real index
+      if i == actual {
+        s[i] = (r.0 + (e.0 * blinding_key.0), r.1 + (e.1 * blinding_key.1));
+        debug_assert_eq!(Self::R(generators, s[i], ring[actual], e), original_R);
+        break;
+      // Generate a decoy response
+      } else {
+        s[i] = (G0::Scalar::random(&mut *rng), G1::Scalar::random(&mut *rng));
+      }
+
+      R = Self::R(generators, s[i], ring[i], e);
+    }
+
+    Aos { Re_0, s }
+  }
+
+  // Assumes the ring has already been transcripted in some form. Critically insecure if it hasn't
+  pub(crate) fn verify<R: RngCore + CryptoRng, T: Clone + Transcript>(
+    &self,
+    rng: &mut R,
+    transcript: T,
+    generators: (Generators<G0>, Generators<G1>),
+    batch: &mut (BatchVerifier<(), G0>, BatchVerifier<(), G1>),
+    ring: &[(G0, G1)]
+  ) -> Result<(), DLEqError> {
+    debug_assert!((RING_LEN == 2) || (RING_LEN == 4));
+    debug_assert_eq!(RING_LEN, ring.len());
+
+    #[allow(non_snake_case)]
+    match self.Re_0 {
+      Re::R(R0_0, R1_0) => {
+        let mut e = Self::nonces(transcript.clone(), (R0_0, R1_0));
+        for i in 0 .. (RING_LEN - 1) {
+          e = Self::R_nonces(transcript.clone(), generators, self.s[i], ring[i], e);
+        }
+
+        let mut statements = Self::R_batch(
+          generators,
+          *self.s.last().unwrap(),
+          *ring.last().unwrap(),
+          e
+        );
+        statements.0.push((G0::Scalar::one(), R0_0));
+        statements.1.push((G1::Scalar::one(), R1_0));
+        batch.0.queue(&mut *rng, (), statements.0);
+        batch.1.queue(&mut *rng, (), statements.1);
+      },
+
+      Re::e(e_0) => {
+        let e_0 = (e_0, scalar_convert(e_0).ok_or(DLEqError::InvalidChallenge)?);
+        let mut e = None;
+        for i in 0 .. RING_LEN {
+          e = Some(
+            Self::R_nonces(transcript.clone(), generators, self.s[i], ring[i], e.unwrap_or(e_0))
+          );
+        }
+
+        // Will panic if the above loop is never run somehow
+        // If e wasn't an Option, and instead initially set to e_0, it'd always pass
+        if e_0 != e.unwrap() {
+          Err(DLEqError::InvalidProof)?;
+        }
+      }
+    }
+
+    Ok(())
+  }
+
+  #[cfg(feature = "serialize")]
+  pub(crate) fn serialize<W: Write>(&self, w: &mut W) -> std::io::Result<()> {
+    #[allow(non_snake_case)]
+    match self.Re_0 {
+      Re::R(R0, R1) => {
+        w.write_all(R0.to_bytes().as_ref())?;
+        w.write_all(R1.to_bytes().as_ref())?;
+      },
+      Re::e(e) => w.write_all(e.to_repr().as_ref())?
+    }
+
+    for i in 0 .. RING_LEN {
+      w.write_all(self.s[i].0.to_repr().as_ref())?;
+      w.write_all(self.s[i].1.to_repr().as_ref())?;
+    }
+
+    Ok(())
+  }
+
+  #[allow(non_snake_case)]
+  #[cfg(feature = "serialize")]
+  pub(crate) fn deserialize<R: Read>(r: &mut R, mut Re_0: Re<G0, G1>) -> std::io::Result<Self> {
+    match Re_0 {
+      Re::R(ref mut R0, ref mut R1) => { *R0 = read_point(r)?; *R1 = read_point(r)? },
+      Re::e(ref mut e) => *e = read_scalar(r)?
+    }
+
+    let mut s = [(G0::Scalar::zero(), G1::Scalar::zero()); RING_LEN];
+    for i in 0 .. RING_LEN {
+      s[i] = (read_scalar(r)?, read_scalar(r)?);
+    }
+
+    Ok(Aos { Re_0, s })
+  }
+}

crypto/dleq/src/cross_group/bits.rs

@@ -0,0 +1,175 @@
+use rand_core::{RngCore, CryptoRng};
+
+use transcript::Transcript;
+
+use group::{ff::PrimeFieldBits, prime::PrimeGroup};
+use multiexp::BatchVerifier;
+
+use crate::{Generators, cross_group::{DLEqError, aos::{Re, Aos}}};
+
+#[cfg(feature = "serialize")]
+use std::io::{Read, Write};
+#[cfg(feature = "serialize")]
+use crate::cross_group::read_point;
+
+pub(crate) enum BitSignature {
+  ClassicLinear,
+  ConciseLinear,
+  EfficientLinear,
+  CompromiseLinear
+}
+
+impl BitSignature {
+  pub(crate) const fn to_u8(&self) -> u8 {
+    match self {
+      BitSignature::ClassicLinear => 0,
+      BitSignature::ConciseLinear => 1,
+      BitSignature::EfficientLinear => 2,
+      BitSignature::CompromiseLinear => 3
+    }
+  }
+
+  pub(crate) const fn from(algorithm: u8) -> BitSignature {
+    match algorithm {
+      0 => BitSignature::ClassicLinear,
+      1 => BitSignature::ConciseLinear,
+      2 => BitSignature::EfficientLinear,
+      3 => BitSignature::CompromiseLinear,
+      _ => panic!("Unknown algorithm")
+    }
+  }
+
+  pub(crate) const fn bits(&self) -> usize {
+    match self {
+      BitSignature::ClassicLinear => 1,
+      BitSignature::ConciseLinear => 2,
+      BitSignature::EfficientLinear => 1,
+      BitSignature::CompromiseLinear => 2
+    }
+  }
+
+  pub(crate) const fn ring_len(&self) -> usize {
+    2_usize.pow(self.bits() as u32)
+  }
+
+  fn aos_form<G0: PrimeGroup, G1: PrimeGroup>(&self) -> Re<G0, G1> {
+    match self {
+      BitSignature::ClassicLinear => Re::e_default(),
+      BitSignature::ConciseLinear => Re::e_default(),
+      BitSignature::EfficientLinear => Re::R_default(),
+      BitSignature::CompromiseLinear => Re::R_default()
+    }
+  }
+}
+
+#[derive(Clone, PartialEq, Eq, Debug)]
+pub(crate) struct Bits<
+  G0: PrimeGroup,
+  G1: PrimeGroup,
+  const SIGNATURE: u8,
+  const RING_LEN: usize
+> {
+  pub(crate) commitments: (G0, G1),
+  signature: Aos<G0, G1, RING_LEN>
+}
+
+impl<
+  G0: PrimeGroup,
+  G1: PrimeGroup,
+  const SIGNATURE: u8,
+  const RING_LEN: usize
+> Bits<G0, G1, SIGNATURE, RING_LEN> where G0::Scalar: PrimeFieldBits, G1::Scalar: PrimeFieldBits {
+  fn transcript<T: Transcript>(transcript: &mut T, i: usize, commitments: (G0, G1)) {
+    transcript.domain_separate(b"bits");
+    transcript.append_message(b"group", &u16::try_from(i).unwrap().to_le_bytes());
+    transcript.append_message(b"commitment_0", commitments.0.to_bytes().as_ref());
+    transcript.append_message(b"commitment_1", commitments.1.to_bytes().as_ref());
+  }
+
+  fn ring(pow_2: (G0, G1), commitments: (G0, G1)) -> Vec<(G0, G1)> {
+    let mut res = vec![commitments; RING_LEN];
+    for i in 1 .. RING_LEN  {
+      res[i] = (res[i - 1].0 - pow_2.0, res[i - 1].1 - pow_2.1);
+    }
+    res
+  }
+
+  fn shift(pow_2: &mut (G0, G1)) {
+    for _ in 0 .. BitSignature::from(SIGNATURE).bits() {
+      pow_2.0 = pow_2.0.double();
+      pow_2.1 = pow_2.1.double();
+    }
+  }
+
+  pub(crate) fn prove<R: RngCore + CryptoRng, T: Clone + Transcript>(
+    rng: &mut R,
+    transcript: &mut T,
+    generators: (Generators<G0>, Generators<G1>),
+    i: usize,
+    pow_2: &mut (G0, G1),
+    bits: u8,
+    blinding_key: (G0::Scalar, G1::Scalar)
+  ) -> Self {
+    let mut commitments = (
+      (generators.0.alt * blinding_key.0),
+      (generators.1.alt * blinding_key.1)
+    );
+    commitments.0 += pow_2.0 * G0::Scalar::from(bits.into());
+    commitments.1 += pow_2.1 * G1::Scalar::from(bits.into());
+
+    Self::transcript(transcript, i, commitments);
+
+    let signature = Aos::prove(
+      rng,
+      transcript.clone(),
+      generators,
+      &Self::ring(*pow_2, commitments),
+      usize::from(bits),
+      blinding_key,
+      BitSignature::from(SIGNATURE).aos_form()
+    );
+
+    Self::shift(pow_2);
+    Bits { commitments, signature }
+  }
+
+  pub(crate) fn verify<R: RngCore + CryptoRng, T: Clone + Transcript>(
+    &self,
+    rng: &mut R,
+    transcript: &mut T,
+    generators: (Generators<G0>, Generators<G1>),
+    batch: &mut (BatchVerifier<(), G0>, BatchVerifier<(), G1>),
+    i: usize,
+    pow_2: &mut (G0, G1)
+  ) -> Result<(), DLEqError> {
+    Self::transcript(transcript, i, self.commitments);
+
+    self.signature.verify(
+      rng,
+      transcript.clone(),
+      generators,
+      batch,
+      &Self::ring(*pow_2, self.commitments)
+    )?;
+
+    Self::shift(pow_2);
+    Ok(())
+  }
+
+  #[cfg(feature = "serialize")]
+  pub(crate) fn serialize<W: Write>(&self, w: &mut W) -> std::io::Result<()> {
+    w.write_all(self.commitments.0.to_bytes().as_ref())?;
+    w.write_all(self.commitments.1.to_bytes().as_ref())?;
+    self.signature.serialize(w)
+  }
+
+  #[cfg(feature = "serialize")]
+  pub(crate) fn deserialize<R: Read>(r: &mut R) -> std::io::Result<Self> {
+    Ok(
+      Bits {
+        commitments: (read_point(r)?, read_point(r)?),
+        signature: Aos::deserialize(r, BitSignature::from(SIGNATURE).aos_form())?
+      }
+    )
+  }
+}

crypto/dleq/src/cross_group/mod.rs

@@ -0,0 +1,366 @@
+use thiserror::Error;
+
+use rand_core::{RngCore, CryptoRng};
+use digest::Digest;
+
+use transcript::Transcript;
+
+use group::{ff::{Field, PrimeField, PrimeFieldBits}, prime::PrimeGroup};
+use multiexp::BatchVerifier;
+
+use crate::Generators;
+
+pub mod scalar;
+use scalar::{scalar_convert, mutual_scalar_from_bytes};
+
+pub(crate) mod schnorr;
+use schnorr::SchnorrPoK;
+
+pub(crate) mod aos;
+
+mod bits;
+use bits::{BitSignature, Bits};
+
+#[cfg(feature = "serialize")]
+use std::io::{Read, Write};
+
+#[cfg(feature = "serialize")]
+pub(crate) fn read_point<R: Read, G: PrimeGroup>(r: &mut R) -> std::io::Result<G> {
+  let mut repr = G::Repr::default();
+  r.read_exact(repr.as_mut())?;
+  let point = G::from_bytes(&repr);
+  if point.is_none().into() {
+    Err(std::io::Error::new(std::io::ErrorKind::Other, "invalid point"))?;
+  }
+  Ok(point.unwrap())
+}
+
+#[derive(Error, PartialEq, Eq, Debug)]
+pub enum DLEqError {
+  #[error("invalid proof of knowledge")]
+  InvalidProofOfKnowledge,
+  #[error("invalid proof length")]
+  InvalidProofLength,
+  #[error("invalid challenge")]
+  InvalidChallenge,
+  #[error("invalid proof")]
+  InvalidProof
+}
+
+// This should never be directly instantiated and uses a u8 to represent internal values
+// Any external usage is likely invalid
+#[doc(hidden)]
+// Debug would be such a dump of data this likely isn't helpful, but at least it's available to
+// anyone who wants it
+#[derive(Clone, PartialEq, Eq, Debug)]
+pub struct __DLEqProof<
+  G0: PrimeGroup,
+  G1: PrimeGroup,
+  const SIGNATURE: u8,
+  const RING_LEN: usize,
+  const REMAINDER_RING_LEN: usize
+> where G0::Scalar: PrimeFieldBits, G1::Scalar: PrimeFieldBits {
+  bits: Vec<Bits<G0, G1, SIGNATURE, RING_LEN>>,
+  remainder: Option<Bits<G0, G1, SIGNATURE, REMAINDER_RING_LEN>>,
+  poks: (SchnorrPoK<G0>, SchnorrPoK<G1>)
+}
+
+macro_rules! dleq {
+  ($name: ident, $signature: expr, $remainder: literal) => {
+    pub type $name<G0, G1> = __DLEqProof<
+      G0,
+      G1,
+      { $signature.to_u8() },
+      { $signature.ring_len() },
+      // There may not be a remainder, yet if there is one, it'll be just one bit
+      // A ring for one bit has a RING_LEN of 2
+      { if $remainder { 2 } else { 0 } }
+    >;
+  }
+}
+
+// Proves for 1-bit at a time with the signature form (e, s), as originally described in MRL-0010.
+// Uses a merged challenge, unlike MRL-0010, for the ring signature, saving an element from each
+// bit and removing a hash while slightly reducing challenge security. This security reduction is
+// already applied to the scalar being proven for, a result of the requirement it's mutually valid
+// over both scalar fields, hence its application here as well. This is mainly here as a point of
+// reference for the following DLEq proofs, all which use merged challenges, and isn't performant
+// in comparison to the others
+dleq!(ClassicLinearDLEq, BitSignature::ClassicLinear, false);
+
+// Proves for 2-bits at a time to save 3/7 elements of every other bit
+// <9% smaller than CompromiseLinear, yet ~12% slower
+dleq!(ConciseLinearDLEq, BitSignature::ConciseLinear, true);
+
+// Uses AOS signatures of the form R, s, to enable the final step of the ring signature to be
+// batch verified, at the cost of adding an additional element per bit
+dleq!(EfficientLinearDLEq, BitSignature::EfficientLinear, false);
+
+// Proves for 2-bits at a time while using the R, s form. This saves 3/7 elements of every other
+// bit, while adding 1 element to every bit, and is more efficient than ConciseLinear yet less
+// efficient than EfficientLinear due to having more ring signature steps which aren't batched
+// >25% smaller than EfficientLinear and just 11% slower, making it the recommended option
+dleq!(CompromiseLinearDLEq, BitSignature::CompromiseLinear, true);
+
+impl<
+  G0: PrimeGroup,
+  G1: PrimeGroup,
+  const SIGNATURE: u8,
+  const RING_LEN: usize,
+  const REMAINDER_RING_LEN: usize
+> __DLEqProof<G0, G1, SIGNATURE, RING_LEN, REMAINDER_RING_LEN> where
+  G0::Scalar: PrimeFieldBits, G1::Scalar: PrimeFieldBits {
+
+  pub(crate) fn transcript<T: Transcript>(
+    transcript: &mut T,
+    generators: (Generators<G0>, Generators<G1>),
+    keys: (G0, G1)
+  ) {
+    transcript.domain_separate(b"cross_group_dleq");
+    generators.0.transcript(transcript);
+    generators.1.transcript(transcript);
+    transcript.domain_separate(b"points");
+    transcript.append_message(b"point_0", keys.0.to_bytes().as_ref());
+    transcript.append_message(b"point_1", keys.1.to_bytes().as_ref());
+  }
+
+  pub(crate) fn blinding_key<R: RngCore + CryptoRng, F: PrimeField>(
+    rng: &mut R,
+    total: &mut F,
+    last: bool
+  ) -> F {
+    let blinding_key = if last {
+      -*total
+    } else {
+      F::random(&mut *rng)
+    };
+    *total += blinding_key;
+    blinding_key
+  }
+
+  fn reconstruct_keys(&self) -> (G0, G1) {
+    let mut res = (
+      self.bits.iter().map(|bit| bit.commitments.0).sum::<G0>(),
+      self.bits.iter().map(|bit| bit.commitments.1).sum::<G1>()
+    );
+
+    if let Some(bit) = &self.remainder {
+      res.0 += bit.commitments.0;
+      res.1 += bit.commitments.1;
+    }
+
+    res
+  }
+
+  fn prove_internal<R: RngCore + CryptoRng, T: Clone + Transcript>(
+    rng: &mut R,
+    transcript: &mut T,
+    generators: (Generators<G0>, Generators<G1>),
+    f: (G0::Scalar, G1::Scalar)
+  ) -> (Self, (G0::Scalar, G1::Scalar)) {
+    Self::transcript(
+      transcript,
+      generators,
+      ((generators.0.primary * f.0), (generators.1.primary * f.1))
+    );
+
+    let poks = (
+      SchnorrPoK::<G0>::prove(rng, transcript, generators.0.primary, f.0),
+      SchnorrPoK::<G1>::prove(rng, transcript, generators.1.primary, f.1)
+    );
+
+    let mut blinding_key_total = (G0::Scalar::zero(), G1::Scalar::zero());
+    let mut blinding_key = |rng: &mut R, last| {
+      let blinding_key = (
+        Self::blinding_key(&mut *rng, &mut blinding_key_total.0, last),
+        Self::blinding_key(&mut *rng, &mut blinding_key_total.1, last)
+      );
+      if last {
+        debug_assert_eq!(blinding_key_total.0, G0::Scalar::zero());
+        debug_assert_eq!(blinding_key_total.1, G1::Scalar::zero());
+      }
+      blinding_key
+    };
+
+    let capacity = usize::try_from(G0::Scalar::CAPACITY.min(G1::Scalar::CAPACITY)).unwrap();
+    let bits_per_group = BitSignature::from(SIGNATURE).bits();
+
+    let mut pow_2 = (generators.0.primary, generators.1.primary);
+
+    let raw_bits = f.0.to_le_bits();
+    let mut bits = Vec::with_capacity(capacity);
+    let mut these_bits: u8 = 0;
+    for (i, bit) in raw_bits.iter().enumerate() {
+      if i == capacity {
+        break;
+      }
+
+      let bit = *bit as u8;
+      debug_assert_eq!(bit | 1, 1);
+
+      // Accumulate this bit
+      these_bits |= bit << (i % bits_per_group);
+      if (i % bits_per_group) == (bits_per_group - 1) {
+        let last = i == (capacity - 1);
+        let blinding_key = blinding_key(&mut *rng, last);
+        bits.push(
+          Bits::prove(
+            &mut *rng,
+            transcript,
+            generators,
+            i / bits_per_group,
+            &mut pow_2,
+            these_bits,
+            blinding_key
+          )
+        );
+        these_bits = 0;
+      }
+    }
+    debug_assert_eq!(bits.len(), capacity / bits_per_group);
+
+    let mut remainder = None;
+    if capacity != ((capacity / bits_per_group) * bits_per_group) {
+      let blinding_key = blinding_key(&mut *rng, true);
+      remainder = Some(
+        Bits::prove(
+          &mut *rng,
+          transcript,
+          generators,
+          capacity / bits_per_group,
+          &mut pow_2,
+          these_bits,
+          blinding_key
+        )
+      );
+    }
+
+    let proof = __DLEqProof { bits, remainder, poks };
+    debug_assert_eq!(
+      proof.reconstruct_keys(),
+      (generators.0.primary * f.0, generators.1.primary * f.1)
+    );
+    (proof, f)
+  }
+
+  /// Prove the cross-Group Discrete Log Equality for the points derived from the scalar created as
+  /// the output of the passed in Digest. Given the non-standard requirements to achieve
+  /// uniformity, needing to be < 2^x instead of less than a prime moduli, this is the simplest way
+  /// to safely and securely generate a Scalar, without risk of failure, nor bias
+  /// It also ensures a lack of determinable relation between keys, guaranteeing security in the
+  /// currently expected use case for this, atomic swaps, where each swap leaks the key. Knowing
+  /// the relationship between keys would allow breaking all swaps after just one
+  pub fn prove<R: RngCore + CryptoRng, T: Clone + Transcript, D: Digest>(
+    rng: &mut R,
+    transcript: &mut T,
+    generators: (Generators<G0>, Generators<G1>),
+    digest: D
+  ) -> (Self, (G0::Scalar, G1::Scalar)) {
+    Self::prove_internal(
+      rng,
+      transcript,
+      generators,
+      mutual_scalar_from_bytes(digest.finalize().as_ref())
+    )
+  }
+
+  /// Prove the cross-Group Discrete Log Equality for the points derived from the scalar passed in,
+  /// failing if it's not mutually valid. This allows for rejection sampling externally derived
+  /// scalars until they're safely usable, as needed
+  pub fn prove_without_bias<R: RngCore + CryptoRng, T: Clone + Transcript>(
+    rng: &mut R,
+    transcript: &mut T,
+    generators: (Generators<G0>, Generators<G1>),
+    f0: G0::Scalar
+  ) -> Option<(Self, (G0::Scalar, G1::Scalar))> {
+    scalar_convert(f0).map(|f1| Self::prove_internal(rng, transcript, generators, (f0, f1)))
+  }
+
+  /// Verify a cross-Group Discrete Log Equality statement, returning the points proven for
+  pub fn verify<R: RngCore + CryptoRng, T: Clone + Transcript>(
+    &self,
+    rng: &mut R,
+    transcript: &mut T,
+    generators: (Generators<G0>, Generators<G1>)
+  ) -> Result<(G0, G1), DLEqError> {
+    let capacity = usize::try_from(
+      G0::Scalar::CAPACITY.min(G1::Scalar::CAPACITY)
+    ).unwrap();
+    let bits_per_group = BitSignature::from(SIGNATURE).bits();
+    let has_remainder = (capacity % bits_per_group) != 0;
+
+    // These shouldn't be possible, as locally created and deserialized proofs should be properly
+    // formed in these regards, yet it doesn't hurt to check and would be problematic if true
+    if (self.bits.len() != (capacity / bits_per_group)) || (
+      (self.remainder.is_none() && has_remainder) || (self.remainder.is_some() && !has_remainder)
+    ) {
+      return Err(DLEqError::InvalidProofLength);
+    }
+
+    let keys = self.reconstruct_keys();
+    Self::transcript(transcript, generators, keys);
+
+    let batch_capacity = match BitSignature::from(SIGNATURE) {
+      BitSignature::ClassicLinear => 3,
+      BitSignature::ConciseLinear => 3,
+      BitSignature::EfficientLinear => (self.bits.len() + 1) * 3,
+      BitSignature::CompromiseLinear => (self.bits.len() + 1) * 3
+    };
+    let mut batch = (BatchVerifier::new(batch_capacity), BatchVerifier::new(batch_capacity));
+
+    self.poks.0.verify(&mut *rng, transcript, generators.0.primary, keys.0, &mut batch.0);
+    self.poks.1.verify(&mut *rng, transcript, generators.1.primary, keys.1, &mut batch.1);
+
+    let mut pow_2 = (generators.0.primary, generators.1.primary);
+    for (i, bits) in self.bits.iter().enumerate() {
+      bits.verify(&mut *rng, transcript, generators, &mut batch, i, &mut pow_2)?;
+    }
+    if let Some(bit) = &self.remainder {
+      bit.verify(&mut *rng, transcript, generators, &mut batch, self.bits.len(), &mut pow_2)?;
+    }
+
+    if (!batch.0.verify_vartime()) || (!batch.1.verify_vartime()) {
+      Err(DLEqError::InvalidProof)?;
+    }
+
+    Ok(keys)
+  }
+
+  #[cfg(feature = "serialize")]
+  pub fn serialize<W: Write>(&self, w: &mut W) -> std::io::Result<()> {
+    for bit in &self.bits {
+      bit.serialize(w)?;
+    }
+    if let Some(bit) = &self.remainder {
+      bit.serialize(w)?;
+    }
+    self.poks.0.serialize(w)?;
+    self.poks.1.serialize(w)
+  }
+
+  #[cfg(feature = "serialize")]
+  pub fn deserialize<R: Read>(r: &mut R) -> std::io::Result<Self> {
+    let capacity = usize::try_from(
+      G0::Scalar::CAPACITY.min(G1::Scalar::CAPACITY)
+    ).unwrap();
+    let bits_per_group = BitSignature::from(SIGNATURE).bits();
+
+    let mut bits = Vec::with_capacity(capacity / bits_per_group);
+    for _ in 0 .. (capacity / bits_per_group) {
+      bits.push(Bits::deserialize(r)?);
+    }
+
+    let mut remainder = None;
+    if (capacity % bits_per_group) != 0 {
+      remainder = Some(Bits::deserialize(r)?);
+    }
+
+    Ok(
+      __DLEqProof {
+        bits,
+        remainder,
+        poks: (SchnorrPoK::deserialize(r)?, SchnorrPoK::deserialize(r)?)
+      }
+    )
+  }
+}

crypto/dleq/src/cross_group/scalar.rs

@@ -0,0 +1,49 @@
+use ff::PrimeFieldBits;
+
+/// Convert a uniform scalar into one usable on both fields, clearing the top bits as needed
+pub fn scalar_normalize<F0: PrimeFieldBits, F1: PrimeFieldBits>(scalar: F0) -> (F0, F1) {
+  let mutual_capacity = F0::CAPACITY.min(F1::CAPACITY);
+
+  // The security of a mutual key is the security of the lower field. Accordingly, this bans a
+  // difference of more than 4 bits
+  #[cfg(feature = "secure_capacity_difference")]
+  assert!((F0::CAPACITY.max(F1::CAPACITY) - mutual_capacity) < 4);
+
+  let mut res1 = F0::zero();
+  let mut res2 = F1::zero();
+  // Uses the bit view API to ensure a consistent endianess
+  let mut bits = scalar.to_le_bits();
+  // Convert it to big endian
+  bits.reverse();
+  for bit in bits.iter().skip(bits.len() - usize::try_from(mutual_capacity).unwrap()) {
+    res1 = res1.double();
+    res2 = res2.double();
+
+    let bit = *bit as u8;
+    debug_assert_eq!(bit | 1, 1);
+
+    res1 += F0::from(bit.into());
+    res2 += F1::from(bit.into());
+  }
+
+  (res1, res2)
+}
+
+/// Helper to convert a scalar between fields. Returns None if the scalar isn't mutually valid
+pub fn scalar_convert<F0: PrimeFieldBits, F1: PrimeFieldBits>(scalar: F0) -> Option<F1> {
+  let (valid, converted) = scalar_normalize(scalar);
+  Some(converted).filter(|_| scalar == valid)
+}
+
+/// Create a mutually valid scalar from bytes via bit truncation to not introduce bias
+pub fn mutual_scalar_from_bytes<F0: PrimeFieldBits, F1: PrimeFieldBits>(bytes: &[u8]) -> (F0, F1) {
+  let capacity = usize::try_from(F0::CAPACITY.min(F1::CAPACITY)).unwrap();
+  debug_assert!((bytes.len() * 8) >= capacity);
+
+  let mut accum = F0::zero();
+  for b in 0 .. capacity {
+    accum = accum.double();
+    accum += F0::from(((bytes[b / 8] >> (b % 8)) & 1).into());
+  }
+  (accum, scalar_convert(accum).unwrap())
+}

crypto/dleq/src/cross_group/schnorr.rs

@@ -0,0 +1,79 @@
+use rand_core::{RngCore, CryptoRng};
+
+use transcript::Transcript;
+
+use group::{ff::{Field, PrimeFieldBits}, prime::PrimeGroup};
+use multiexp::BatchVerifier;
+
+use crate::challenge;
+
+#[cfg(feature = "serialize")]
+use std::io::{Read, Write};
+#[cfg(feature = "serialize")]
+use ff::PrimeField;
+#[cfg(feature = "serialize")]
+use crate::{read_scalar, cross_group::read_point};
+
+#[allow(non_snake_case)]
+#[derive(Clone, PartialEq, Eq, Debug)]
+pub(crate) struct SchnorrPoK<G: PrimeGroup> {
+  R: G,
+  s: G::Scalar
+}
+
+impl<G: PrimeGroup> SchnorrPoK<G> where G::Scalar: PrimeFieldBits {
+  // Not hram due to the lack of m
+  #[allow(non_snake_case)]
+  fn hra<T: Transcript>(transcript: &mut T, generator: G, R: G, A: G) -> G::Scalar {
+    transcript.domain_separate(b"schnorr_proof_of_knowledge");
+    transcript.append_message(b"generator", generator.to_bytes().as_ref());
+    transcript.append_message(b"nonce", R.to_bytes().as_ref());
+    transcript.append_message(b"public_key", A.to_bytes().as_ref());
+    challenge(transcript)
+  }
+
+  pub(crate) fn prove<R: RngCore + CryptoRng, T: Transcript>(
+    rng: &mut R,
+    transcript: &mut T,
+    generator: G,
+    private_key: G::Scalar
+  ) -> SchnorrPoK<G> {
+    let nonce = G::Scalar::random(rng);
+    #[allow(non_snake_case)]
+    let R = generator * nonce;
+    SchnorrPoK {
+      R,
+      s: nonce + (private_key * SchnorrPoK::hra(transcript, generator, R, generator * private_key))
+    }
+  }
+
+  pub(crate) fn verify<R: RngCore + CryptoRng, T: Transcript>(
+    &self,
+    rng: &mut R,
+    transcript: &mut T,
+    generator: G,
+    public_key: G,
+    batch: &mut BatchVerifier<(), G>
+  ) {
+    batch.queue(
+      rng,
+      (),
+      [
+        (-self.s, generator),
+        (G::Scalar::one(), self.R),
+        (Self::hra(transcript, generator, self.R, public_key), public_key)
+      ]
+    );
+  }
+
+  #[cfg(feature = "serialize")]
+  pub fn serialize<W: Write>(&self, w: &mut W) -> std::io::Result<()> {
+    w.write_all(self.R.to_bytes().as_ref())?;
+    w.write_all(self.s.to_repr().as_ref())
+  }
+
+  #[cfg(feature = "serialize")]
+  pub fn deserialize<R: Read>(r: &mut R) -> std::io::Result<SchnorrPoK<G>> {
+    Ok(SchnorrPoK { R: read_point(r)?, s: read_scalar(r)? })
+  }
+}

crypto/dleq/src/lib.rs

@@ -0,0 +1,151 @@
+use thiserror::Error;
+use rand_core::{RngCore, CryptoRng};
+
+use transcript::Transcript;
+
+use ff::{Field, PrimeField};
+use group::prime::PrimeGroup;
+
+#[cfg(feature = "serialize")]
+use std::io::{self, ErrorKind, Error, Read, Write};
+
+#[cfg(feature = "experimental")]
+pub mod cross_group;
+
+#[cfg(test)]
+mod tests;
+
+#[derive(Clone, Copy, PartialEq, Eq)]
+pub struct Generators<G: PrimeGroup> {
+  primary: G,
+  alt: G
+}
+
+impl<G: PrimeGroup> Generators<G> {
+  pub fn new(primary: G, alt: G) -> Generators<G> {
+    Generators { primary, alt }
+  }
+
+  fn transcript<T: Transcript>(&self, transcript: &mut T) {
+    transcript.domain_separate(b"generators");
+    transcript.append_message(b"primary", self.primary.to_bytes().as_ref());
+    transcript.append_message(b"alternate", self.alt.to_bytes().as_ref());
+  }
+}
+
+pub(crate) fn challenge<T: Transcript, F: PrimeField>(transcript: &mut T) -> F {
+  // From here, there are three ways to get a scalar under the ff/group API
+  // 1: Scalar::random(ChaCha12Rng::from_seed(self.transcript.rng_seed(b"challenge")))
+  // 2: Grabbing a UInt library to perform reduction by the modulus, then determining endianess
+  //    and loading it in
+  // 3: Iterating over each byte and manually doubling/adding. This is simplest
+
+  // Get a wide amount of bytes to safely reduce without bias
+  let target = ((usize::try_from(F::NUM_BITS).unwrap() + 7) / 8) * 2;
+  let mut challenge_bytes = transcript.challenge(b"challenge").as_ref().to_vec();
+  while challenge_bytes.len() < target {
+    // Secure given transcripts updating on challenge
+    challenge_bytes.extend(transcript.challenge(b"challenge_extension").as_ref());
+  }
+  challenge_bytes.truncate(target);
+
+  let mut challenge = F::zero();
+  for b in challenge_bytes {
+    for _ in 0 .. 8 {
+      challenge = challenge.double();
+    }
+    challenge += F::from(u64::from(b));
+  }
+  challenge
+}
+
+#[cfg(feature = "serialize")]
+fn read_scalar<R: Read, F: PrimeField>(r: &mut R) -> io::Result<F> {
+  let mut repr = F::Repr::default();
+  r.read_exact(repr.as_mut())?;
+  let scalar = F::from_repr(repr);
+  if scalar.is_none().into() {
+    Err(Error::new(ErrorKind::Other, "invalid scalar"))?;
+  }
+  Ok(scalar.unwrap())
+}
+
+#[derive(Error, Debug)]
+pub enum DLEqError {
+  #[error("invalid proof")]
+  InvalidProof
+}
+
+#[derive(Clone, PartialEq, Eq, Debug)]
+pub struct DLEqProof<G: PrimeGroup> {
+  c: G::Scalar,
+  s: G::Scalar
+}
+
+#[allow(non_snake_case)]
+impl<G: PrimeGroup> DLEqProof<G> {
+  fn challenge<T: Transcript>(
+    transcript: &mut T,
+    generators: Generators<G>,
+    nonces: (G, G),
+    points: (G, G)
+  ) -> G::Scalar {
+    generators.transcript(transcript);
+    transcript.domain_separate(b"dleq");
+    transcript.append_message(b"nonce_primary", nonces.0.to_bytes().as_ref());
+    transcript.append_message(b"nonce_alternate", nonces.1.to_bytes().as_ref());
+    transcript.append_message(b"point_primary", points.0.to_bytes().as_ref());
+    transcript.append_message(b"point_alternate", points.1.to_bytes().as_ref());
+    challenge(transcript)
+  }
+
+  pub fn prove<R: RngCore + CryptoRng, T: Transcript>(
+    rng: &mut R,
+    transcript: &mut T,
+    generators: Generators<G>,
+    scalar: G::Scalar
+  ) -> DLEqProof<G> {
+    let r = G::Scalar::random(rng);
+    let c = Self::challenge(
+      transcript,
+      generators,
+      (generators.primary * r, generators.alt * r),
+      (generators.primary * scalar, generators.alt * scalar)
+    );
+    let s = r + (c * scalar);
+
+    DLEqProof { c, s }
+  }
+
+  pub fn verify<T: Transcript>(
+    &self,
+    transcript: &mut T,
+    generators: Generators<G>,
+    points: (G, G)
+  ) -> Result<(), DLEqError> {
+    if self.c != Self::challenge(
+      transcript,
+      generators,
+      (
+        (generators.primary * self.s) - (points.0 * self.c),
+        (generators.alt * self.s) -  (points.1 * self.c)
+      ),
+      points
+    ) {
+      Err(DLEqError::InvalidProof)?;
+    }
+
+    Ok(())
+  }
+
+  #[cfg(feature = "serialize")]
+  pub fn serialize<W: Write>(&self, w: &mut W) -> io::Result<()> {
+    w.write_all(self.c.to_repr().as_ref())?;
+    w.write_all(self.s.to_repr().as_ref())
+  }
+
+  #[cfg(feature = "serialize")]
+  pub fn deserialize<R: Read>(r: &mut R) -> io::Result<DLEqProof<G>> {
+    Ok(DLEqProof { c: read_scalar(r)?, s: read_scalar(r)? })
+  }
+}

crypto/dleq/src/tests/cross_group/aos.rs

@@ -0,0 +1,69 @@
+use rand_core::OsRng;
+
+use group::{ff::Field, Group};
+
+use multiexp::BatchVerifier;
+
+use crate::{
+  cross_group::aos::{Re, Aos},
+  tests::cross_group::{G0, G1, transcript, generators}
+};
+
+#[allow(non_snake_case)]
+#[cfg(feature = "serialize")]
+fn test_aos_serialization<const RING_LEN: usize>(proof: Aos<G0, G1, RING_LEN>, Re_0: Re<G0, G1>) {
+  let mut buf = vec![];
+  proof.serialize(&mut buf).unwrap();
+  let deserialized = Aos::deserialize(&mut std::io::Cursor::new(buf), Re_0).unwrap();
+  assert_eq!(proof, deserialized);
+}
+
+fn test_aos<const RING_LEN: usize>(default: Re<G0, G1>) {
+  let generators = generators();
+
+  let mut ring_keys = [(<G0 as Group>::Scalar::zero(), <G1 as Group>::Scalar::zero()); RING_LEN];
+  // Side-effect of G0 being a type-alias with identity() deprecated
+  #[allow(deprecated)]
+  let mut ring = [(G0::identity(), G1::identity()); RING_LEN];
+  for i in 0 .. RING_LEN {
+    ring_keys[i] = (
+      <G0 as Group>::Scalar::random(&mut OsRng),
+      <G1 as Group>::Scalar::random(&mut OsRng)
+    );
+    ring[i] = (generators.0.alt * ring_keys[i].0, generators.1.alt * ring_keys[i].1);
+  }
+
+  for actual in 0 .. RING_LEN {
+    let proof = Aos::<_, _, RING_LEN>::prove(
+      &mut OsRng,
+      transcript(),
+      generators,
+      &ring,
+      actual,
+      ring_keys[actual],
+      default.clone()
+    );
+
+    let mut batch = (BatchVerifier::new(0), BatchVerifier::new(0));
+    proof.verify(&mut OsRng, transcript(), generators, &mut batch, &ring).unwrap();
+    // For e, these should have nothing. For R, these should have 6 elements each which sum to 0
+    assert!(batch.0.verify_vartime());
+    assert!(batch.1.verify_vartime());
+
+    #[cfg(feature = "serialize")]
+    test_aos_serialization(proof, default.clone());
+  }
+}
+
+#[test]
+fn test_aos_e() {
+  test_aos::<2>(Re::e_default());
+  test_aos::<4>(Re::e_default());
+}
+
+#[allow(non_snake_case)]
+#[test]
+fn test_aos_R() {
+  // Batch verification appreciates the longer vectors, which means not batching bits
+  test_aos::<2>(Re::R_default());
+}

crypto/dleq/src/tests/cross_group/mod.rs

@@ -0,0 +1,192 @@
+use hex_literal::hex;
+use rand_core::{RngCore, OsRng};
+
+use ff::{Field, PrimeField};
+use group::{Group, GroupEncoding};
+
+use blake2::{Digest, Blake2b512};
+
+use k256::{Scalar, ProjectivePoint};
+use dalek_ff_group::{self as dfg, EdwardsPoint, CompressedEdwardsY};
+
+use transcript::RecommendedTranscript;
+
+use crate::{
+  Generators,
+  cross_group::{
+    scalar::mutual_scalar_from_bytes,
+    ClassicLinearDLEq, EfficientLinearDLEq, ConciseLinearDLEq, CompromiseLinearDLEq
+  }
+};
+
+mod scalar;
+mod schnorr;
+mod aos;
+
+type G0 = ProjectivePoint;
+type G1 = EdwardsPoint;
+
+pub(crate) fn transcript() -> RecommendedTranscript {
+  RecommendedTranscript::new(b"Cross-Group DLEq Proof Test")
+}
+
+pub(crate) fn generators() -> (Generators<G0>, Generators<G1>) {
+  (
+    Generators::new(
+      ProjectivePoint::GENERATOR,
+      ProjectivePoint::from_bytes(
+        &(hex!("0250929b74c1a04954b78b4b6035e97a5e078a5a0f28ec96d547bfee9ace803ac0").into())
+      ).unwrap()
+    ),
+
+    Generators::new(
+      EdwardsPoint::generator(),
+      CompressedEdwardsY::new(
+        hex!("8b655970153799af2aeadc9ff1add0ea6c7251d54154cfa92c173a0dd39c1f94")
+      ).decompress().unwrap()
+    )
+  )
+}
+
+macro_rules! verify_and_deserialize {
+  ($type: ty, $proof: ident, $generators: ident, $keys: ident) => {
+    let public_keys = $proof.verify(&mut OsRng, &mut transcript(), $generators).unwrap();
+    assert_eq!($generators.0.primary * $keys.0, public_keys.0);
+    assert_eq!($generators.1.primary * $keys.1, public_keys.1);
+
+    #[cfg(feature = "serialize")]
+    {
+      let mut buf = vec![];
+      $proof.serialize(&mut buf).unwrap();
+      let deserialized = <$type>::deserialize(&mut std::io::Cursor::new(&buf)).unwrap();
+      assert_eq!($proof, deserialized);
+    }
+  }
+}
+
+macro_rules! test_dleq {
+  ($str: literal, $benchmark: ident, $name: ident, $type: ident) => {
+    #[ignore]
+    #[test]
+    fn $benchmark() {
+      println!("Benchmarking with Secp256k1/Ed25519");
+      let generators = generators();
+
+      let mut seed = [0; 32];
+      OsRng.fill_bytes(&mut seed);
+      let key = Blake2b512::new().chain_update(seed);
+
+      let runs = 200;
+      let mut proofs = Vec::with_capacity(usize::try_from(runs).unwrap());
+      let time = std::time::Instant::now();
+      for _ in 0 .. runs {
+        proofs.push($type::prove(&mut OsRng, &mut transcript(), generators, key.clone()).0);
+      }
+      println!("{} had a average prove time of {}ms", $str, time.elapsed().as_millis() / runs);
+
+      let time = std::time::Instant::now();
+      for proof in &proofs {
+        proof.verify(&mut OsRng, &mut transcript(), generators).unwrap();
+      }
+      println!("{} had a average verify time of {}ms", $str, time.elapsed().as_millis() / runs);
+
+      #[cfg(feature = "serialize")]
+      {
+        let mut buf = vec![];
+        proofs[0].serialize(&mut buf).unwrap();
+        println!("{} had a proof size of {} bytes", $str, buf.len());
+      }
+    }
+
+    #[test]
+    fn $name() {
+      let generators = generators();
+
+      for i in 0 .. 1 {
+        let (proof, keys) = if i == 0 {
+          let mut seed = [0; 32];
+          OsRng.fill_bytes(&mut seed);
+
+          $type::prove(
+            &mut OsRng,
+            &mut transcript(),
+            generators,
+            Blake2b512::new().chain_update(seed)
+          )
+        } else {
+          let mut key;
+          let mut res;
+          while {
+            key = Scalar::random(&mut OsRng);
+            res = $type::prove_without_bias(&mut OsRng, &mut transcript(), generators, key);
+            res.is_none()
+          } {}
+          let res = res.unwrap();
+          assert_eq!(key, res.1.0);
+          res
+        };
+
+        verify_and_deserialize!($type::<G0, G1>, proof, generators, keys);
+      }
+    }
+  }
+}
+
+test_dleq!("ClassicLinear", benchmark_classic_linear, test_classic_linear, ClassicLinearDLEq);
+test_dleq!("ConciseLinear", benchmark_concise_linear, test_concise_linear, ConciseLinearDLEq);
+test_dleq!(
+  "EfficientLinear",
+  benchmark_efficient_linear,
+  test_efficient_linear,
+  EfficientLinearDLEq
+);
+test_dleq!(
+  "CompromiseLinear",
+  benchmark_compromise_linear,
+  test_compromise_linear,
+  CompromiseLinearDLEq
+);
+
+#[test]
+fn test_rejection_sampling() {
+  let mut pow_2 = Scalar::one();
+  for _ in 0 .. dfg::Scalar::CAPACITY {
+    pow_2 = pow_2.double();
+  }
+
+  assert!(
+    // Either would work
+    EfficientLinearDLEq::prove_without_bias(
+      &mut OsRng,
+      &mut transcript(),
+      generators(),
+      pow_2
+    ).is_none()
+  );
+}
+
+#[test]
+fn test_remainder() {
+  // Uses Secp256k1 for both to achieve an odd capacity of 255
+  assert_eq!(Scalar::CAPACITY, 255);
+  let generators = (generators().0, generators().0);
+  // This will ignore any unused bits, ensuring every remaining one is set
+  let keys = mutual_scalar_from_bytes(&[0xFF; 32]);
+  assert_eq!(keys.0 + Scalar::one(), Scalar::from(2u64).pow_vartime(&[255]));
+  assert_eq!(keys.0, keys.1);
+
+  let (proof, res) = ConciseLinearDLEq::prove_without_bias(
+    &mut OsRng,
+    &mut transcript(),
+    generators,
+    keys.0
+  ).unwrap();
+  assert_eq!(keys, res);
+
+  verify_and_deserialize!(
+    ConciseLinearDLEq::<ProjectivePoint, ProjectivePoint>,
+    proof,
+    generators,
+    keys
+  );
+}

crypto/dleq/src/tests/cross_group/scalar.rs

@@ -0,0 +1,47 @@
+use rand_core::OsRng;
+
+use ff::{Field, PrimeField};
+
+use k256::Scalar as K256Scalar;
+use dalek_ff_group::Scalar as DalekScalar;
+
+use crate::cross_group::scalar::{scalar_normalize, scalar_convert};
+
+#[test]
+fn test_scalar() {
+  assert_eq!(
+    scalar_normalize::<_, DalekScalar>(K256Scalar::zero()),
+    (K256Scalar::zero(), DalekScalar::zero())
+  );
+
+  assert_eq!(
+    scalar_normalize::<_, DalekScalar>(K256Scalar::one()),
+    (K256Scalar::one(), DalekScalar::one())
+  );
+
+  let mut initial;
+  while {
+    initial = K256Scalar::random(&mut OsRng);
+    let (k, ed) = scalar_normalize::<_, DalekScalar>(initial);
+
+    // The initial scalar should equal the new scalar with Ed25519's capacity
+    let mut initial_bytes = (&initial.to_repr()).to_vec();
+    // Drop the first 4 bits to hit 252
+    initial_bytes[0] = initial_bytes[0] & 0b00001111;
+    let k_bytes = (&k.to_repr()).to_vec();
+    assert_eq!(initial_bytes, k_bytes);
+
+    let mut ed_bytes = ed.to_repr().as_ref().to_vec();
+    // Reverse to big endian
+    ed_bytes.reverse();
+    assert_eq!(k_bytes, ed_bytes);
+
+    // Verify conversion works as expected
+    assert_eq!(scalar_convert::<_, DalekScalar>(k), Some(ed));
+
+    // Run this test again if this secp256k1 scalar didn't have any bits cleared
+    initial == k
+  } {}
+  // Verify conversion returns None when the scalar isn't mutually valid
+  assert!(scalar_convert::<_, DalekScalar>(initial).is_none());
+}

crypto/dleq/src/tests/cross_group/schnorr.rs

@@ -0,0 +1,38 @@
+use rand_core::OsRng;
+
+use group::{ff::{Field, PrimeFieldBits}, prime::PrimeGroup};
+use multiexp::BatchVerifier;
+
+use transcript::RecommendedTranscript;
+
+use crate::cross_group::schnorr::SchnorrPoK;
+
+fn test_schnorr<G: PrimeGroup>() where G::Scalar: PrimeFieldBits {
+  let private = G::Scalar::random(&mut OsRng);
+
+  let transcript = RecommendedTranscript::new(b"Schnorr Test");
+  let mut batch = BatchVerifier::new(3);
+  SchnorrPoK::prove(
+    &mut OsRng,
+    &mut transcript.clone(),
+    G::generator(),
+    private
+  ).verify(
+    &mut OsRng,
+    &mut transcript.clone(),
+    G::generator(),
+    G::generator() * private,
+    &mut batch
+  );
+  assert!(batch.verify_vartime());
+}
+
+#[test]
+fn test_secp256k1() {
+  test_schnorr::<k256::ProjectivePoint>();
+}
+
+#[test]
+fn test_ed25519() {
+  test_schnorr::<dalek_ff_group::EdwardsPoint>();
+}

crypto/dleq/src/tests/mod.rs

@@ -0,0 +1,43 @@
+#[cfg(feature = "experimental")]
+mod cross_group;
+
+use hex_literal::hex;
+use rand_core::OsRng;
+
+use ff::Field;
+use group::GroupEncoding;
+
+use k256::{Scalar, ProjectivePoint};
+
+use transcript::RecommendedTranscript;
+
+use crate::{Generators, DLEqProof};
+
+#[test]
+fn test_dleq() {
+  let transcript = || RecommendedTranscript::new(b"DLEq Proof Test");
+
+  let generators = Generators::new(
+    ProjectivePoint::GENERATOR,
+    ProjectivePoint::from_bytes(
+      &(hex!("0250929b74c1a04954b78b4b6035e97a5e078a5a0f28ec96d547bfee9ace803ac0").into())
+    ).unwrap()
+  );
+
+  let key = Scalar::random(&mut OsRng);
+  let proof = DLEqProof::prove(&mut OsRng, &mut transcript(), generators, key);
+
+  let keys = (generators.primary * key, generators.alt * key);
+  proof.verify(&mut transcript(), generators, keys).unwrap();
+
+  #[cfg(feature = "serialize")]
+  {
+    let mut buf = vec![];
+    proof.serialize(&mut buf).unwrap();
+    let deserialized = DLEqProof::<ProjectivePoint>::deserialize(
+      &mut std::io::Cursor::new(&buf)
+    ).unwrap();
+    assert_eq!(proof, deserialized);
+    deserialized.verify(&mut transcript(), generators, keys).unwrap();
+  }
+}

crypto/frost/Cargo.toml

@@ -1,24 +1,46 @@
 [package]
-name = "frost"
+name = "modular-frost"
 version = "0.1.0"
-description = "Implementation of FROST over ff/group"
+description = "Modular implementation of FROST over ff/group"
 license = "MIT"
+repository = "https://github.com/serai-dex/serai"
 authors = ["Luke Parker <lukeparker5132@gmail.com>"]
+keywords = ["frost", "multisig", "threshold"]
 edition = "2021"
 
 [dependencies]
 thiserror = "1"
 
 rand_core = "0.6"
+hex = "0.4"
 
-ff = "0.11"
-group = "0.11"
+sha2 = { version = "0.10", optional = true }
 
-transcript = { path = "../transcript" }
+ff = "0.12"
+group = "0.12"
 
-multiexp = { path = "../multiexp", features = ["batch"] }
+elliptic-curve = { version = "0.12", features = ["hash2curve"], optional = true }
+p256 = { version = "0.11", features = ["arithmetic", "bits", "hash2curve"], optional = true }
+k256 = { version = "0.11", features = ["arithmetic", "bits", "hash2curve"], optional = true }
+dalek-ff-group = { path = "../dalek-ff-group", version = "0.1", optional = true }
+
+transcript = { package = "flexible-transcript", path = "../transcript", version = "0.1" }
+
+multiexp = { path = "../multiexp", version = "0.1", features = ["batch"] }
+
+dleq = { package = "dleq", path = "../dleq", version = "0.1", features = ["serialize"] }
 
 [dev-dependencies]
 rand = "0.8"
+
 sha2 = "0.10"
-k256 = { version = "0.10", features = ["arithmetic"] }
+dalek-ff-group = { path = "../dalek-ff-group" }
+
+[features]
+curves = ["sha2"] # All officially denoted curves use the SHA2 family of hashes
+kp256 = ["elliptic-curve", "curves"]
+p256 = ["kp256", "dep:p256"]
+secp256k1 = ["kp256", "k256"]
+dalek = ["curves", "dalek-ff-group"]
+ed25519 = ["dalek"]
+ristretto = ["dalek"]

crypto/frost/README.md

@@ -1,3 +1,6 @@
-# FROST
+# Modular FROST
 
-Implementation of FROST for any curve with a ff/group API.
+A modular implementation of FROST for any curve with a ff/group API. Notably,
+beyond curve modularity, custom algorithms may be specified, providing support
+for privacy coins. The provided Schnorr algorithm also has a modular HRAM due
+to the variety in existence, enabling integration with existing systems.

crypto/frost/src/algorithm.rs

@@ -4,7 +4,7 @@ use rand_core::{RngCore, CryptoRng};
 
 use transcript::Transcript;
 
-use crate::{Curve, FrostError, MultisigView, schnorr};
+use crate::{Curve, FrostError, FrostView, schnorr};
 pub use schnorr::SchnorrSignature;
 
 /// Algorithm to use FROST with
@@ -13,22 +13,25 @@ pub trait Algorithm<C: Curve>: Clone {
   /// The resulting type of the signatures this algorithm will produce
   type Signature: Clone + PartialEq + Debug;
 
+  /// Obtain a mutable borrow of the underlying transcript
   fn transcript(&mut self) -> &mut Self::Transcript;
 
+  /// Obtain the list of nonces to generate, as specified by the basepoints to create commitments
+  /// against per-nonce. These are not committed to by FROST on the underlying transcript
+  fn nonces(&self) -> Vec<Vec<C::G>>;
+
   /// Generate an addendum to FROST"s preprocessing stage
   fn preprocess_addendum<R: RngCore + CryptoRng>(
     &mut self,
     rng: &mut R,
-    params: &MultisigView<C>,
-    nonces: &[C::F; 2],
+    params: &FrostView<C>,
   ) -> Vec<u8>;
 
   /// Proccess the addendum for the specified participant. Guaranteed to be ordered
   fn process_addendum(
     &mut self,
-    params: &MultisigView<C>,
+    params: &FrostView<C>,
     l: u16,
-    commitments: &[C::G; 2],
     serialized: &[u8],
   ) -> Result<(), FrostError>;
 
@@ -38,23 +41,24 @@ pub trait Algorithm<C: Curve>: Clone {
   /// The nonce will already have been processed into the combined form d + (e * p)
   fn sign_share(
     &mut self,
-    params: &MultisigView<C>,
-    nonce_sum: C::G,
-    binding: C::F,
-    nonce: C::F,
+    params: &FrostView<C>,
+    nonce_sums: &[Vec<C::G>],
+    nonces: &[C::F],
     msg: &[u8],
   ) -> C::F;
 
   /// Verify a signature
-  fn verify(&self, group_key: C::G, nonce: C::G, sum: C::F) -> Option<Self::Signature>;
+  #[must_use]
+  fn verify(&self, group_key: C::G, nonces: &[Vec<C::G>], sum: C::F) -> Option<Self::Signature>;
 
   /// Verify a specific share given as a response. Used to determine blame if signature
   /// verification fails
+  #[must_use]
   fn verify_share(
     &self,
     l: u16,
     verification_share: C::G,
-    nonce: C::G,
+    nonces: &[Vec<C::G>],
     share: C::F,
   ) -> bool;
 }
@@ -63,6 +67,12 @@ pub trait Algorithm<C: Curve>: Clone {
 #[derive(Clone, Debug)]
 pub struct IetfTranscript(Vec<u8>);
 impl Transcript for IetfTranscript {
+  type Challenge = Vec<u8>;
+
+  fn new(_: &'static [u8]) -> IetfTranscript {
+    unimplemented!("IetfTranscript should not be used with multiple nonce protocols");
+  }
+
   fn domain_separate(&mut self, _: &[u8]) {}
 
   fn append_message(&mut self, _: &'static [u8], message: &[u8]) {
@@ -112,20 +122,22 @@ impl<C: Curve, H: Hram<C>> Algorithm<C> for Schnorr<C, H> {
     &mut self.transcript
   }
 
+  fn nonces(&self) -> Vec<Vec<C::G>> {
+    vec![vec![C::GENERATOR]]
+  }
+
   fn preprocess_addendum<R: RngCore + CryptoRng>(
     &mut self,
     _: &mut R,
-    _: &MultisigView<C>,
-    _: &[C::F; 2],
+    _: &FrostView<C>,
   ) -> Vec<u8> {
     vec![]
   }
 
   fn process_addendum(
     &mut self,
-    _: &MultisigView<C>,
+    _: &FrostView<C>,
     _: u16,
-    _: &[C::G; 2],
     _: &[u8],
   ) -> Result<(), FrostError> {
     Ok(())
@@ -133,19 +145,19 @@ impl<C: Curve, H: Hram<C>> Algorithm<C> for Schnorr<C, H> {
 
   fn sign_share(
     &mut self,
-    params: &MultisigView<C>,
-    nonce_sum: C::G,
-    _: C::F,
-    nonce: C::F,
+    params: &FrostView<C>,
+    nonce_sums: &[Vec<C::G>],
+    nonces: &[C::F],
     msg: &[u8],
   ) -> C::F {
-    let c = H::hram(&nonce_sum, &params.group_key(), msg);
+    let c = H::hram(&nonce_sums[0][0], &params.group_key(), msg);
     self.c = Some(c);
-    schnorr::sign::<C>(params.secret_share(), nonce, c).s
+    schnorr::sign::<C>(params.secret_share(), nonces[0], c).s
   }
 
-  fn verify(&self, group_key: C::G, nonce: C::G, sum: C::F) -> Option<Self::Signature> {
-    let sig = SchnorrSignature { R: nonce, s: sum };
+  #[must_use]
+  fn verify(&self, group_key: C::G, nonces: &[Vec<C::G>], sum: C::F) -> Option<Self::Signature> {
+    let sig = SchnorrSignature { R: nonces[0][0], s: sum };
     if schnorr::verify::<C>(group_key, self.c.unwrap(), &sig) {
       Some(sig)
     } else {
@@ -153,17 +165,18 @@ impl<C: Curve, H: Hram<C>> Algorithm<C> for Schnorr<C, H> {
     }
   }
 
+  #[must_use]
   fn verify_share(
     &self,
     _: u16,
     verification_share: C::G,
-    nonce: C::G,
+    nonces: &[Vec<C::G>],
     share: C::F,
   ) -> bool {
     schnorr::verify::<C>(
       verification_share,
       self.c.unwrap(),
-      &SchnorrSignature { R: nonce, s: share}
+      &SchnorrSignature { R: nonces[0][0], s: share}
     )
   }
 }

crypto/frost/src/curve/dalek.rs

@@ -0,0 +1,91 @@
+use rand_core::{RngCore, CryptoRng};
+
+use sha2::{Digest, Sha512};
+
+use dalek_ff_group::Scalar;
+
+use crate::{curve::Curve, algorithm::Hram};
+
+macro_rules! dalek_curve {
+  (
+    $Curve:      ident,
+    $Hram:       ident,
+    $Point:      ident,
+
+    $POINT: ident,
+
+    $ID:      literal,
+    $CONTEXT: literal,
+    $chal:    literal,
+    $digest:  literal,
+  ) => {
+    use dalek_ff_group::{$Point, $POINT};
+
+    #[derive(Clone, Copy, PartialEq, Eq, Debug)]
+    pub struct $Curve;
+    impl Curve for $Curve {
+      type F = Scalar;
+      type G = $Point;
+
+      const ID: &'static [u8] = $ID;
+      const GENERATOR: Self::G = $POINT;
+
+      fn random_nonce<R: RngCore + CryptoRng>(secret: Self::F, rng: &mut R) -> Self::F {
+        let mut seed = vec![0; 32];
+        rng.fill_bytes(&mut seed);
+        seed.extend(&secret.to_bytes());
+        Self::hash_to_F(b"nonce", &seed)
+      }
+
+      fn hash_msg(msg: &[u8]) -> Vec<u8> {
+        Sha512::new()
+          .chain_update($CONTEXT)
+          .chain_update($digest)
+          .chain_update(msg)
+          .finalize()
+          .to_vec()
+      }
+
+      fn hash_binding_factor(binding: &[u8]) -> Self::F {
+        Self::hash_to_F(b"rho", binding)
+      }
+
+      fn hash_to_F(dst: &[u8], msg: &[u8]) -> Self::F {
+        Scalar::from_hash(Sha512::new().chain_update($CONTEXT).chain_update(dst).chain_update(msg))
+      }
+    }
+
+    #[derive(Copy, Clone)]
+    pub struct $Hram;
+    impl Hram<$Curve> for $Hram {
+      #[allow(non_snake_case)]
+      fn hram(R: &$Point, A: &$Point, m: &[u8]) -> Scalar {
+        $Curve::hash_to_F($chal, &[&R.compress().to_bytes(), &A.compress().to_bytes(), m].concat())
+      }
+    }
+  }
+}
+
+#[cfg(any(test, feature = "ristretto"))]
+dalek_curve!(
+  Ristretto,
+  IetfRistrettoHram,
+  RistrettoPoint,
+  RISTRETTO_BASEPOINT_POINT,
+  b"ristretto",
+  b"FROST-RISTRETTO255-SHA512-v5",
+  b"chal",
+  b"digest",
+);
+
+#[cfg(feature = "ed25519")]
+dalek_curve!(
+  Ed25519,
+  IetfEd25519Hram,
+  EdwardsPoint,
+  ED25519_BASEPOINT_POINT,
+  b"edwards25519",
+  b"",
+  b"",
+  b"",
+);

crypto/frost/src/curve/kp256.rs

@@ -0,0 +1,105 @@
+use rand_core::{RngCore, CryptoRng};
+
+use sha2::{digest::Update, Digest, Sha256};
+
+use group::{ff::Field, GroupEncoding};
+
+use elliptic_curve::{bigint::{Encoding, U384}, hash2curve::{Expander, ExpandMsg, ExpandMsgXmd}};
+
+use crate::{curve::{Curve, F_from_slice}, algorithm::Hram};
+
+macro_rules! kp_curve {
+  (
+    $lib:   ident,
+    $Curve: ident,
+    $Hram:  ident,
+
+    $ID:      literal,
+    $CONTEXT: literal
+  ) => {
+    #[derive(Clone, Copy, PartialEq, Eq, Debug)]
+    pub struct $Curve;
+    impl Curve for $Curve {
+      type F = $lib::Scalar;
+      type G = $lib::ProjectivePoint;
+
+      const ID: &'static [u8] = $ID;
+      const GENERATOR: Self::G = $lib::ProjectivePoint::GENERATOR;
+
+      fn random_nonce<R: RngCore + CryptoRng>(secret: Self::F, rng: &mut R) -> Self::F {
+        let mut seed = vec![0; 32];
+        rng.fill_bytes(&mut seed);
+        seed.extend(secret.to_bytes());
+        Self::hash_to_F(&[$CONTEXT as &[u8], b"nonce"].concat(), &seed)
+      }
+
+      fn hash_msg(msg: &[u8]) -> Vec<u8> {
+        (&Sha256::new()
+          .chain($CONTEXT)
+          .chain(b"digest")
+          .chain(msg)
+          .finalize()
+        ).to_vec()
+      }
+
+      fn hash_binding_factor(binding: &[u8]) -> Self::F {
+        Self::hash_to_F(&[$CONTEXT as &[u8], b"rho"].concat(), binding)
+      }
+
+      fn hash_to_F(dst: &[u8], msg: &[u8]) -> Self::F {
+        let mut dst = dst;
+        let oversize = Sha256::digest([b"H2C-OVERSIZE-DST-", dst].concat());
+        if dst.len() > 255 {
+          dst = &oversize;
+        }
+
+        // While one of these two libraries does support directly hashing to the Scalar field, the
+        // other doesn't. While that's probably an oversight, this is a universally working method
+        let mut modulus = vec![0; 16];
+        modulus.extend((Self::F::zero() - Self::F::one()).to_bytes());
+        let modulus = U384::from_be_slice(&modulus).wrapping_add(&U384::ONE);
+        F_from_slice::<Self::F>(
+          &U384::from_be_slice(&{
+            let mut bytes = [0; 48];
+            ExpandMsgXmd::<Sha256>::expand_message(
+              &[msg],
+              dst,
+              48
+            ).unwrap().fill_bytes(&mut bytes);
+            bytes
+          }).reduce(&modulus).unwrap().to_be_bytes()[16 ..]
+        ).unwrap()
+      }
+    }
+
+    #[derive(Clone)]
+    pub struct $Hram;
+    impl Hram<$Curve> for $Hram {
+      #[allow(non_snake_case)]
+      fn hram(R: &$lib::ProjectivePoint, A: &$lib::ProjectivePoint, m: &[u8]) -> $lib::Scalar {
+        $Curve::hash_to_F(
+          &[$CONTEXT as &[u8], b"chal"].concat(),
+          &[R.to_bytes().as_ref(), A.to_bytes().as_ref(), m].concat()
+        )
+      }
+    }
+  }
+}
+
+#[cfg(feature = "p256")]
+kp_curve!(
+  p256,
+  P256,
+  IetfP256Hram,
+  b"P-256",
+  b"FROST-P256-SHA256-v5"
+);
+
+#[cfg(feature = "secp256k1")]
+kp_curve!(
+  k256,
+  Secp256k1,
+  NonIetfSecp256k1Hram,
+  b"secp256k1",
+  b"FROST-secp256k1-SHA256-v5"
+);

crypto/frost/src/curve/mod.rs

@@ -0,0 +1,117 @@
+use core::fmt::Debug;
+
+use thiserror::Error;
+
+use rand_core::{RngCore, CryptoRng};
+
+use ff::{PrimeField, PrimeFieldBits};
+use group::{Group, GroupOps, GroupEncoding, prime::PrimeGroup};
+
+#[cfg(any(test, feature = "dalek"))]
+mod dalek;
+#[cfg(any(test, feature = "ristretto"))]
+pub use dalek::{Ristretto, IetfRistrettoHram};
+#[cfg(feature = "ed25519")]
+pub use dalek::{Ed25519, IetfEd25519Hram};
+
+#[cfg(feature = "kp256")]
+mod kp256;
+#[cfg(feature = "secp256k1")]
+pub use kp256::{Secp256k1, NonIetfSecp256k1Hram};
+#[cfg(feature = "p256")]
+pub use kp256::{P256, IetfP256Hram};
+
+/// Set of errors for curve-related operations, namely encoding and decoding
+#[derive(Clone, Error, Debug)]
+pub enum CurveError {
+  #[error("invalid length for data (expected {0}, got {0})")]
+  InvalidLength(usize, usize),
+  #[error("invalid scalar")]
+  InvalidScalar,
+  #[error("invalid point")]
+  InvalidPoint,
+}
+
+/// Unified trait to manage a field/group
+// This should be moved into its own crate if the need for generic cryptography over ff/group
+// continues, which is the exact reason ff/group exists (to provide a generic interface)
+// elliptic-curve exists, yet it doesn't really serve the same role, nor does it use &[u8]/Vec<u8>
+// It uses GenericArray which will hopefully be deprecated as Rust evolves and doesn't offer enough
+// advantages in the modern day to be worth the hassle -- Kayaba
+pub trait Curve: Clone + Copy + PartialEq + Eq + Debug {
+  /// Scalar field element type
+  // This is available via G::Scalar yet `C::G::Scalar` is ambiguous, forcing horrific accesses
+  type F: PrimeField + PrimeFieldBits;
+  /// Group element type
+  type G: Group<Scalar = Self::F> + GroupOps + PrimeGroup;
+
+  /// ID for this curve
+  const ID: &'static [u8];
+
+  /// Generator for the group
+  // While group does provide this in its API, privacy coins may want to use a custom basepoint
+  const GENERATOR: Self::G;
+
+  /// Securely generate a random nonce. H4 from the IETF draft
+  fn random_nonce<R: RngCore + CryptoRng>(secret: Self::F, rng: &mut R) -> Self::F;
+
+  /// Hash the message for the binding factor. H3 from the IETF draft
+  // This doesn't actually need to be part of Curve as it does nothing with the curve
+  // This also solely relates to FROST and with a proper Algorithm/HRAM, all projects using
+  // aggregatable signatures over this curve will work without issue
+  // It is kept here as Curve + H{1, 2, 3} is effectively a ciphersuite according to the IETF draft
+  // and moving it to Schnorr would force all of them into being ciphersuite-specific
+  // H2 is left to the Schnorr Algorithm as H2 is the H used in HRAM, which Schnorr further
+  // modularizes
+  fn hash_msg(msg: &[u8]) -> Vec<u8>;
+
+  /// Hash the commitments and message to calculate the binding factor. H1 from the IETF draft
+  fn hash_binding_factor(binding: &[u8]) -> Self::F;
+
+  // The following methods would optimally be F:: and G:: yet developers can't control F/G
+  // They can control a trait they pass into this library
+
+  /// Field element from hash. Used during key gen and by other crates under Serai as a general
+  /// utility
+  // Not parameterized by Digest as it's fine for it to use its own hash function as relevant to
+  // hash_msg and hash_binding_factor
+  #[allow(non_snake_case)]
+  fn hash_to_F(dst: &[u8], msg: &[u8]) -> Self::F;
+}
+
+#[allow(non_snake_case)]
+pub(crate) fn F_len<C: Curve>() -> usize {
+  <C::F as PrimeField>::Repr::default().as_ref().len()
+}
+
+#[allow(non_snake_case)]
+pub(crate) fn G_len<C: Curve>() -> usize {
+  <C::G as GroupEncoding>::Repr::default().as_ref().len()
+}
+
+/// Field element from slice
+#[allow(non_snake_case)]
+pub(crate) fn F_from_slice<F: PrimeField>(slice: &[u8]) -> Result<F, CurveError> {
+  let mut encoding = F::Repr::default();
+  encoding.as_mut().copy_from_slice(slice);
+
+  let point = Option::<F>::from(F::from_repr(encoding)).ok_or(CurveError::InvalidScalar)?;
+  if point.to_repr().as_ref() != slice {
+    Err(CurveError::InvalidScalar)?;
+  }
+  Ok(point)
+}
+
+/// Group element from slice
+#[allow(non_snake_case)]
+pub(crate) fn G_from_slice<G: PrimeGroup>(slice: &[u8]) -> Result<G, CurveError> {
+  let mut encoding = G::Repr::default();
+  encoding.as_mut().copy_from_slice(slice);
+
+  let point = Option::<G>::from(G::from_bytes(&encoding)).ok_or(CurveError::InvalidPoint)?;
+  // Ban the identity, per the FROST spec, and non-canonical points
+  if (point.is_identity().into()) || (point.to_bytes().as_ref() != slice) {
+    Err(CurveError::InvalidPoint)?;
+  }
+  Ok(point)
+}

crypto/frost/src/key_gen.rs

@@ -1,14 +1,14 @@
-use core::fmt;
-use std::collections::HashMap;
+use std::{marker::PhantomData, collections::HashMap};
 
 use rand_core::{RngCore, CryptoRng};
 
-use ff::{Field, PrimeField};
+use group::{ff::{Field, PrimeField}, GroupEncoding};
 
 use multiexp::{multiexp_vartime, BatchVerifier};
 
 use crate::{
-  Curve, MultisigParams, MultisigKeys, FrostError,
+  curve::{Curve, F_len, G_len, F_from_slice, G_from_slice},
+  FrostError, FrostParams, FrostKeys,
   schnorr::{self, SchnorrSignature},
   validate_map
 };
@@ -16,29 +16,34 @@ use crate::{
 #[allow(non_snake_case)]
 fn challenge<C: Curve>(context: &str, l: u16, R: &[u8], Am: &[u8]) -> C::F {
   const DST: &'static [u8] = b"FROST Schnorr Proof of Knowledge";
+
   // Uses hash_msg to get a fixed size value out of the context string
-  C::hash_to_F(&[DST, &C::hash_msg(context.as_bytes()), &l.to_be_bytes(), R, Am].concat())
+  let mut transcript = C::hash_msg(context.as_bytes());
+  transcript.extend(l.to_be_bytes());
+  transcript.extend(R);
+  transcript.extend(Am);
+  C::hash_to_F(DST, &transcript)
 }
 
 // Implements steps 1 through 3 of round 1 of FROST DKG. Returns the coefficients, commitments, and
 // the serialized commitments to be broadcasted over an authenticated channel to all parties
 fn generate_key_r1<R: RngCore + CryptoRng, C: Curve>(
   rng: &mut R,
-  params: &MultisigParams,
+  params: &FrostParams,
   context: &str,
 ) -> (Vec<C::F>, Vec<u8>) {
   let t = usize::from(params.t);
   let mut coefficients = Vec::with_capacity(t);
   let mut commitments = Vec::with_capacity(t);
-  let mut serialized = Vec::with_capacity((C::G_len() * t) + C::G_len() + C::F_len());
+  let mut serialized = Vec::with_capacity((G_len::<C>() * t) + G_len::<C>() + F_len::<C>());
 
   for i in 0 .. t {
     // Step 1: Generate t random values to form a polynomial with
     coefficients.push(C::F::random(&mut *rng));
     // Step 3: Generate public commitments
-    commitments.push(C::generator_table() * coefficients[i]);
+    commitments.push(C::GENERATOR * coefficients[i]);
     // Serialize them for publication
-    serialized.extend(&C::G_to_bytes(&commitments[i]));
+    serialized.extend(commitments[i].to_bytes().as_ref());
   }
 
   // Step 2: Provide a proof of knowledge
@@ -54,7 +59,7 @@ fn generate_key_r1<R: RngCore + CryptoRng, C: Curve>(
       challenge::<C>(
         context,
         params.i(),
-        &C::G_to_bytes(&(C::generator_table() * r)),
+        (C::GENERATOR * r).to_bytes().as_ref(),
         &serialized
       )
     ).serialize()
@@ -67,7 +72,7 @@ fn generate_key_r1<R: RngCore + CryptoRng, C: Curve>(
 // Verify the received data from the first round of key generation
 fn verify_r1<R: RngCore + CryptoRng, C: Curve>(
   rng: &mut R,
-  params: &MultisigParams,
+  params: &FrostParams,
   context: &str,
   our_commitments: Vec<u8>,
   mut serialized: HashMap<u16, Vec<u8>>,
@@ -78,19 +83,19 @@ fn verify_r1<R: RngCore + CryptoRng, C: Curve>(
     (params.i(), our_commitments)
   )?;
 
-  let commitments_len = usize::from(params.t()) * C::G_len();
+  let commitments_len = usize::from(params.t()) * G_len::<C>();
 
   let mut commitments = HashMap::new();
 
   #[allow(non_snake_case)]
-  let R_bytes = |l| &serialized[&l][commitments_len .. commitments_len + C::G_len()];
+  let R_bytes = |l| &serialized[&l][commitments_len .. commitments_len + G_len::<C>()];
   #[allow(non_snake_case)]
-  let R = |l| C::G_from_slice(R_bytes(l)).map_err(|_| FrostError::InvalidProofOfKnowledge(l));
+  let R = |l| G_from_slice::<C::G>(R_bytes(l)).map_err(|_| FrostError::InvalidProofOfKnowledge(l));
   #[allow(non_snake_case)]
   let Am = |l| &serialized[&l][0 .. commitments_len];
 
-  let s = |l| C::F_from_slice(
-    &serialized[&l][commitments_len + C::G_len() ..]
+  let s = |l| F_from_slice::<C::F>(
+    &serialized[&l][commitments_len + G_len::<C>() ..]
   ).map_err(|_| FrostError::InvalidProofOfKnowledge(l));
 
   let mut signatures = Vec::with_capacity(usize::from(params.n() - 1));
@@ -98,8 +103,8 @@ fn verify_r1<R: RngCore + CryptoRng, C: Curve>(
     let mut these_commitments = vec![];
     for c in 0 .. usize::from(params.t()) {
       these_commitments.push(
-        C::G_from_slice(
-          &serialized[&l][(c * C::G_len()) .. ((c + 1) * C::G_len())]
+        G_from_slice::<C::G>(
+          &serialized[&l][(c * G_len::<C>()) .. ((c + 1) * G_len::<C>())]
         ).map_err(|_| FrostError::InvalidCommitment(l.try_into().unwrap()))?
       );
     }
@@ -144,7 +149,7 @@ fn polynomial<F: PrimeField>(
 // counterparty to receive
 fn generate_key_r2<R: RngCore + CryptoRng, C: Curve>(
   rng: &mut R,
-  params: &MultisigParams,
+  params: &FrostParams,
   context: &str,
   coefficients: Vec<C::F>,
   our_commitments: Vec<u8>,
@@ -161,7 +166,7 @@ fn generate_key_r2<R: RngCore + CryptoRng, C: Curve>(
       continue;
     }
 
-    res.insert(l, C::F_to_bytes(&polynomial(&coefficients, l)));
+    res.insert(l, polynomial(&coefficients, l).to_repr().as_ref().to_vec());
   }
 
   // Calculate our own share
@@ -185,22 +190,22 @@ fn generate_key_r2<R: RngCore + CryptoRng, C: Curve>(
 /// broadcasted initially
 fn complete_r2<R: RngCore + CryptoRng, C: Curve>(
   rng: &mut R,
-  params: MultisigParams,
+  params: FrostParams,
   mut secret_share: C::F,
   commitments: HashMap<u16, Vec<C::G>>,
   // Vec to preserve ownership
   mut serialized: HashMap<u16, Vec<u8>>,
-) -> Result<MultisigKeys<C>, FrostError> {
+) -> Result<FrostKeys<C>, FrostError> {
   validate_map(
     &mut serialized,
     &(1 ..= params.n()).into_iter().collect::<Vec<_>>(),
-    (params.i(), C::F_to_bytes(&secret_share))
+    (params.i(), secret_share.to_repr().as_ref().to_vec())
   )?;
 
   // Step 2. Verify each share
   let mut shares = HashMap::new();
   for (l, share) in serialized {
-    shares.insert(l, C::F_from_slice(&share).map_err(|_| FrostError::InvalidShare(l))?);
+    shares.insert(l, F_from_slice::<C::F>(&share).map_err(|_| FrostError::InvalidShare(l))?);
   }
 
   // Calculate the exponent for a given participant and apply it to a series of commitments
@@ -219,7 +224,7 @@ fn complete_r2<R: RngCore + CryptoRng, C: Curve>(
     res
   };
 
-  let mut batch = BatchVerifier::new(shares.len(), C::little_endian());
+  let mut batch = BatchVerifier::new(shares.len());
   for (l, share) in &shares {
     if *l == params.i() {
       continue;
@@ -232,7 +237,7 @@ fn complete_r2<R: RngCore + CryptoRng, C: Curve>(
     // ensure that malleability isn't present is to use this n * t algorithm, which runs
     // per sender and not as an aggregate of all senders, which also enables blame
     let mut values = exponential(params.i, &commitments[l]);
-    values.push((-*share, C::generator()));
+    values.push((-*share, C::GENERATOR));
     batch.queue(rng, *l, values);
   }
   batch.verify_with_vartime_blame().map_err(|l| FrostError::InvalidCommitment(l))?;
@@ -249,14 +254,15 @@ fn complete_r2<R: RngCore + CryptoRng, C: Curve>(
   // Calculate each user's verification share
   let mut verification_shares = HashMap::new();
   for i in 1 ..= params.n() {
-    verification_shares.insert(i, multiexp_vartime(exponential(i, &stripes), C::little_endian()));
+    verification_shares.insert(i, multiexp_vartime(&exponential(i, &stripes)));
   }
-  debug_assert_eq!(C::generator_table() * secret_share, verification_shares[&params.i()]);
+  // Removing this check would enable optimizing the above from t + (n * t) to t + ((n - 1) * t)
+  debug_assert_eq!(C::GENERATOR * secret_share, verification_shares[&params.i()]);
 
   // TODO: Clear serialized and shares
 
   Ok(
-    MultisigKeys {
+    FrostKeys {
       params,
       secret_share,
       group_key: stripes[0],
@@ -266,100 +272,76 @@ fn complete_r2<R: RngCore + CryptoRng, C: Curve>(
   )
 }
 
-/// State of a Key Generation machine
-#[derive(Clone, Copy, PartialEq, Eq, Debug)]
-pub enum State {
-  Fresh,
-  GeneratedCoefficients,
-  GeneratedSecretShares,
-  Complete,
-}
-
-impl fmt::Display for State {
-  fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
-    write!(f, "{:?}", self)
-  }
-}
-
-/// State machine which manages key generation
-#[allow(non_snake_case)]
-pub struct StateMachine<C: Curve> {
-  params: MultisigParams,
+pub struct KeyGenMachine<C: Curve> {
+  params: FrostParams,
   context: String,
-  state: State,
-  coefficients: Option<Vec<C::F>>,
-  our_commitments: Option<Vec<u8>>,
-  secret: Option<C::F>,
-  commitments: Option<HashMap<u16, Vec<C::G>>>
+  _curve: PhantomData<C>,
 }
 
-impl<C: Curve> StateMachine<C> {
+pub struct SecretShareMachine<C: Curve> {
+  params: FrostParams,
+  context: String,
+  coefficients: Vec<C::F>,
+  our_commitments: Vec<u8>,
+}
+
+pub struct KeyMachine<C: Curve> {
+  params: FrostParams,
+  secret: C::F,
+  commitments: HashMap<u16, Vec<C::G>>,
+}
+
+impl<C: Curve> KeyGenMachine<C> {
   /// Creates a new machine to generate a key for the specified curve in the specified multisig
   // The context string must be unique among multisigs
-  pub fn new(params: MultisigParams, context: String) -> StateMachine<C> {
-    StateMachine {
-      params,
-      context,
-      state: State::Fresh,
-      coefficients: None,
-      our_commitments: None,
-      secret: None,
-      commitments: None
-    }
+  pub fn new(params: FrostParams, context: String) -> KeyGenMachine<C> {
+    KeyGenMachine { params, context, _curve: PhantomData }
   }
 
   /// Start generating a key according to the FROST DKG spec
   /// Returns a serialized list of commitments to be sent to all parties over an authenticated
   /// channel. If any party submits multiple sets of commitments, they MUST be treated as malicious
   pub fn generate_coefficients<R: RngCore + CryptoRng>(
-    &mut self,
+    self,
     rng: &mut R
-  ) -> Result<Vec<u8>, FrostError> {
-    if self.state != State::Fresh {
-      Err(FrostError::InvalidKeyGenTransition(State::Fresh, self.state))?;
-    }
-
-    let (coefficients, serialized) = generate_key_r1::<R, C>(
-      rng,
-      &self.params,
-      &self.context,
-    );
-
-    self.coefficients = Some(coefficients);
-    self.our_commitments = Some(serialized.clone());
-    self.state = State::GeneratedCoefficients;
-    Ok(serialized)
+  ) -> (SecretShareMachine<C>, Vec<u8>) {
+    let (coefficients, serialized) = generate_key_r1::<R, C>(rng, &self.params, &self.context);
+    (
+      SecretShareMachine {
+        params: self.params,
+        context: self.context,
+        coefficients,
+        our_commitments: serialized.clone()
+      },
+      serialized,
+    )
   }
+}
 
+impl<C: Curve> SecretShareMachine<C> {
   /// Continue generating a key
   /// Takes in everyone else's commitments, which are expected to be in a Vec where participant
   /// index = Vec index. An empty vector is expected at index 0 to allow for this. An empty vector
   /// is also expected at index i which is locally handled. Returns a byte vector representing a
   /// secret share for each other participant which should be encrypted before sending
   pub fn generate_secret_shares<R: RngCore + CryptoRng>(
-    &mut self,
+    self,
     rng: &mut R,
     commitments: HashMap<u16, Vec<u8>>,
-  ) -> Result<HashMap<u16, Vec<u8>>, FrostError> {
-    if self.state != State::GeneratedCoefficients {
-      Err(FrostError::InvalidKeyGenTransition(State::GeneratedCoefficients, self.state))?;
-    }
-
+  ) -> Result<(KeyMachine<C>, HashMap<u16, Vec<u8>>), FrostError> {
     let (secret, commitments, shares) = generate_key_r2::<R, C>(
       rng,
       &self.params,
       &self.context,
-      self.coefficients.take().unwrap(),
-      self.our_commitments.take().unwrap(),
+      self.coefficients,
+      self.our_commitments,
       commitments,
     )?;
-
-    self.secret = Some(secret);
-    self.commitments = Some(commitments);
-    self.state = State::GeneratedSecretShares;
-    Ok(shares)
+    Ok((KeyMachine { params: self.params, secret, commitments }, shares))
   }
+}
 
+impl<C: Curve> KeyMachine<C> {
   /// Complete key generation
   /// Takes in everyone elses' shares submitted to us as a Vec, expecting participant index =
   /// Vec index with an empty vector at index 0 and index i. Returns a byte vector representing the
@@ -367,31 +349,10 @@ impl<C: Curve> StateMachine<C> {
   /// must report completion without issue before this key can be considered usable, yet you should
   /// wait for all participants to report as such
   pub fn complete<R: RngCore + CryptoRng>(
-    &mut self,
+    self,
     rng: &mut R,
     shares: HashMap<u16, Vec<u8>>,
-  ) -> Result<MultisigKeys<C>, FrostError> {
-    if self.state != State::GeneratedSecretShares {
-      Err(FrostError::InvalidKeyGenTransition(State::GeneratedSecretShares, self.state))?;
-    }
-
-    let keys = complete_r2(
-      rng,
-      self.params,
-      self.secret.take().unwrap(),
-      self.commitments.take().unwrap(),
-      shares,
-    )?;
-
-    self.state = State::Complete;
-    Ok(keys)
-  }
-
-  pub fn params(&self) -> MultisigParams {
-    self.params.clone()
-  }
-
-  pub fn state(&self) -> State {
-    self.state
+  ) -> Result<FrostKeys<C>, FrostError> {
+    complete_r2(rng, self.params, self.secret, self.commitments, shares)
   }
 }

crypto/frost/src/lib.rs

@@ -1,124 +1,24 @@
-use core::{ops::Mul, fmt::Debug};
+use core::fmt::Debug;
 use std::collections::HashMap;
 
 use thiserror::Error;
 
-use ff::{Field, PrimeField};
-use group::{Group, GroupOps};
+use group::{ff::{Field, PrimeField}, GroupEncoding};
 
 mod schnorr;
 
+pub mod curve;
+use curve::{Curve, F_len, G_len, F_from_slice, G_from_slice};
 pub mod key_gen;
 pub mod algorithm;
 pub mod sign;
 
 pub mod tests;
 
-/// Set of errors for curve-related operations, namely encoding and decoding
-#[derive(Clone, Error, Debug)]
-pub enum CurveError {
-  #[error("invalid length for data (expected {0}, got {0})")]
-  InvalidLength(usize, usize),
-  #[error("invalid scalar")]
-  InvalidScalar,
-  #[error("invalid point")]
-  InvalidPoint,
-}
-
-/// Unified trait to manage a field/group
-// This should be moved into its own crate if the need for generic cryptography over ff/group
-// continues, which is the exact reason ff/group exists (to provide a generic interface)
-// elliptic-curve exists, yet it doesn't really serve the same role, nor does it use &[u8]/Vec<u8>
-// It uses GenericArray which will hopefully be deprecated as Rust evolves and doesn't offer enough
-// advantages in the modern day to be worth the hassle -- Kayaba
-pub trait Curve: Clone + Copy + PartialEq + Eq + Debug {
-  /// Field element type
-  // This is available via G::Scalar yet `C::G::Scalar` is ambiguous, forcing horrific accesses
-  type F: PrimeField;
-  /// Group element type
-  type G: Group<Scalar = Self::F> + GroupOps;
-  /// Precomputed table type
-  type T: Mul<Self::F, Output = Self::G>;
-
-  /// ID for this curve
-  fn id() -> String;
-  /// Byte length of the curve ID
-  // While curve.id().len() is trivial, this bounds it to u8 and lets us ignore the possibility it
-  // contains Unicode, therefore having a String length which is different from its byte length
-  fn id_len() -> u8;
-
-  /// Generator for the group
-  // While group does provide this in its API, Jubjub users will want to use a custom basepoint
-  fn generator() -> Self::G;
-
-  /// Table for the generator for the group
-  /// If there isn't a precomputed table available, the generator itself should be used
-  fn generator_table() -> Self::T;
-
-  /// If little endian is used for the scalar field's Repr
-  fn little_endian() -> bool;
-
-  /// Hash the message for the binding factor. H3 from the IETF draft
-  // This doesn't actually need to be part of Curve as it does nothing with the curve
-  // This also solely relates to FROST and with a proper Algorithm/HRAM, all projects using
-  // aggregatable signatures over this curve will work without issue
-  // It is kept here as Curve + H{1, 2, 3} is effectively a ciphersuite according to the IETF draft
-  // and moving it to Schnorr would force all of them into being ciphersuite-specific
-  // H2 is left to the Schnorr Algorithm as H2 is the H used in HRAM, which Schnorr further
-  // modularizes
-  fn hash_msg(msg: &[u8]) -> Vec<u8>;
-
-  /// Hash the commitments and message to calculate the binding factor. H1 from the IETF draft
-  fn hash_binding_factor(binding: &[u8]) -> Self::F;
-
-  // The following methods would optimally be F:: and G:: yet developers can't control F/G
-  // They can control a trait they pass into this library
-
-  /// Field element from hash. Used during key gen and by other crates under Serai as a general
-  /// utility
-  // Not parameterized by Digest as it's fine for it to use its own hash function as relevant to
-  // hash_msg and hash_binding_factor
-  #[allow(non_snake_case)]
-  fn hash_to_F(data: &[u8]) -> Self::F;
-
-  /// Constant size of a serialized field element
-  // The alternative way to grab this would be either serializing a junk element and getting its
-  // length or doing a naive division of its BITS property by 8 and assuming a lack of padding
-  #[allow(non_snake_case)]
-  fn F_len() -> usize;
-
-  /// Constant size of a serialized group element
-  // We could grab the serialization as described above yet a naive developer may use a
-  // non-constant size encoding, proving yet another reason to force this to be a provided constant
-  // A naive developer could still provide a constant for a variable length encoding, yet at least
-  // that is on them
-  #[allow(non_snake_case)]
-  fn G_len() -> usize;
-
-  /// Field element from slice. Preferred to be canonical yet does not have to be
-  // Required due to the lack of standardized encoding functions provided by ff/group
-  // While they do technically exist, their usage of Self::Repr breaks all potential library usage
-  // without helper functions like this
-  #[allow(non_snake_case)]
-  fn F_from_slice(slice: &[u8]) -> Result<Self::F, CurveError>;
-
-  /// Group element from slice. Must require canonicity or risks differing binding factors
-  #[allow(non_snake_case)]
-  fn G_from_slice(slice: &[u8]) -> Result<Self::G, CurveError>;
-
-  /// Obtain a vector of the byte encoding of F
-  #[allow(non_snake_case)]
-  fn F_to_bytes(f: &Self::F) -> Vec<u8>;
-
-  /// Obtain a vector of the byte encoding of G
-  #[allow(non_snake_case)]
-  fn G_to_bytes(g: &Self::G) -> Vec<u8>;
-}
-
 /// Parameters for a multisig
 // These fields can not be made public as they should be static
 #[derive(Clone, Copy, PartialEq, Eq, Debug)]
-pub struct MultisigParams {
+pub struct FrostParams {
   /// Participants needed to sign on behalf of the group
   t: u16,
   /// Amount of participants
@@ -127,12 +27,12 @@ pub struct MultisigParams {
   i: u16,
 }
 
-impl MultisigParams {
+impl FrostParams {
   pub fn new(
     t: u16,
     n: u16,
     i: u16
-  ) -> Result<MultisigParams, FrostError> {
+  ) -> Result<FrostParams, FrostError> {
     if (t == 0) || (n == 0) {
       Err(FrostError::ZeroParameter(t, n))?;
     }
@@ -146,7 +46,7 @@ impl MultisigParams {
       Err(FrostError::InvalidParticipantIndex(n, i))?;
     }
 
-    Ok(MultisigParams{ t, n, i })
+    Ok(FrostParams{ t, n, i })
   }
 
   pub fn t(&self) -> u16 { self.t }
@@ -179,11 +79,6 @@ pub enum FrostError {
   InvalidProofOfKnowledge(u16),
   #[error("invalid share (participant {0})")]
   InvalidShare(u16),
-  #[error("invalid key generation state machine transition (expected {0}, was {1})")]
-  InvalidKeyGenTransition(key_gen::State, key_gen::State),
-
-  #[error("invalid sign state machine transition (expected {0}, was {1})")]
-  InvalidSignTransition(sign::State, sign::State),
 
   #[error("internal error ({0})")]
   InternalError(String),
@@ -191,14 +86,14 @@ pub enum FrostError {
 
 // View of keys passable to algorithm implementations
 #[derive(Clone)]
-pub struct MultisigView<C: Curve> {
+pub struct FrostView<C: Curve> {
   group_key: C::G,
   included: Vec<u16>,
   secret_share: C::F,
   verification_shares: HashMap<u16, C::G>,
 }
 
-impl<C: Curve> MultisigView<C> {
+impl<C: Curve> FrostView<C> {
   pub fn group_key(&self) -> C::G {
     self.group_key
   }
@@ -239,9 +134,9 @@ pub fn lagrange<F: PrimeField>(
 }
 
 #[derive(Clone, PartialEq, Eq, Debug)]
-pub struct MultisigKeys<C: Curve> {
-  /// Multisig Parameters
-  params: MultisigParams,
+pub struct FrostKeys<C: Curve> {
+  /// FROST Parameters
+  params: FrostParams,
 
   /// Secret share key
   secret_share: C::F,
@@ -254,21 +149,26 @@ pub struct MultisigKeys<C: Curve> {
   offset: Option<C::F>,
 }
 
-impl<C: Curve> MultisigKeys<C> {
-  pub fn offset(&self, offset: C::F) -> MultisigKeys<C> {
+impl<C: Curve> FrostKeys<C> {
+  /// Offset the keys by a given scalar to allow for account and privacy schemes
+  /// This offset is ephemeral and will not be included when these keys are serialized
+  /// Keys offset multiple times will form a new offset of their sum
+  /// Not IETF compliant
+  pub fn offset(&self, offset: C::F) -> FrostKeys<C> {
     let mut res = self.clone();
     // Carry any existing offset
     // Enables schemes like Monero's subaddresses which have a per-subaddress offset and then a
     // one-time-key offset
     res.offset = Some(offset + res.offset.unwrap_or(C::F::zero()));
+    res.group_key += C::GENERATOR * offset;
     res
   }
 
-  pub fn params(&self) -> MultisigParams {
+  pub fn params(&self) -> FrostParams {
     self.params
   }
 
-  pub fn secret_share(&self) -> C::F {
+  fn secret_share(&self) -> C::F {
     self.secret_share
   }
 
@@ -276,11 +176,11 @@ impl<C: Curve> MultisigKeys<C> {
     self.group_key
   }
 
-  pub fn verification_shares(&self) -> HashMap<u16, C::G> {
+  fn verification_shares(&self) -> HashMap<u16, C::G> {
     self.verification_shares.clone()
   }
 
-  pub fn view(&self, included: &[u16]) -> Result<MultisigView<C>, FrostError> {
+  pub fn view(&self, included: &[u16]) -> Result<FrostView<C>, FrostError> {
     if (included.len() < self.params.t.into()) || (usize::from(self.params.n) < included.len()) {
       Err(FrostError::InvalidSigningSet("invalid amount of participants included".to_string()))?;
     }
@@ -289,13 +189,13 @@ impl<C: Curve> MultisigKeys<C> {
     let offset = self.offset.unwrap_or(C::F::zero());
     let offset_share = offset * C::F::from(included.len().try_into().unwrap()).invert().unwrap();
 
-    Ok(MultisigView {
-      group_key: self.group_key + (C::generator_table() * offset),
+    Ok(FrostView {
+      group_key: self.group_key,
       secret_share: secret_share + offset_share,
       verification_shares: self.verification_shares.iter().map(
         |(l, share)| (
           *l,
-          (*share * lagrange::<C::F>(*l, &included)) + (C::generator_table() * offset_share)
+          (*share * lagrange::<C::F>(*l, &included)) + (C::GENERATOR * offset_share)
         )
       ).collect(),
       included: included.to_vec(),
@@ -303,84 +203,76 @@ impl<C: Curve> MultisigKeys<C> {
   }
 
   pub fn serialized_len(n: u16) -> usize {
-    1 + usize::from(C::id_len()) + (3 * 2) + C::F_len() + C::G_len() + (usize::from(n) * C::G_len())
+    8 + C::ID.len() + (3 * 2) + F_len::<C>() + G_len::<C>() + (usize::from(n) * G_len::<C>())
   }
 
   pub fn serialize(&self) -> Vec<u8> {
-    let mut serialized = Vec::with_capacity(
-      1 + usize::from(C::id_len()) + MultisigKeys::<C>::serialized_len(self.params.n)
-    );
-    serialized.push(C::id_len());
-    serialized.extend(C::id().as_bytes());
-    serialized.extend(&self.params.n.to_le_bytes());
-    serialized.extend(&self.params.t.to_le_bytes());
-    serialized.extend(&self.params.i.to_le_bytes());
-    serialized.extend(&C::F_to_bytes(&self.secret_share));
-    serialized.extend(&C::G_to_bytes(&self.group_key));
+    let mut serialized = Vec::with_capacity(FrostKeys::<C>::serialized_len(self.params.n));
+    serialized.extend(u64::try_from(C::ID.len()).unwrap().to_be_bytes());
+    serialized.extend(C::ID);
+    serialized.extend(&self.params.t.to_be_bytes());
+    serialized.extend(&self.params.n.to_be_bytes());
+    serialized.extend(&self.params.i.to_be_bytes());
+    serialized.extend(self.secret_share.to_repr().as_ref());
+    serialized.extend(self.group_key.to_bytes().as_ref());
     for l in 1 ..= self.params.n.into() {
-      serialized.extend(&C::G_to_bytes(&self.verification_shares[&l]));
+      serialized.extend(self.verification_shares[&l].to_bytes().as_ref());
     }
-
     serialized
   }
 
-  pub fn deserialize(serialized: &[u8]) -> Result<MultisigKeys<C>, FrostError> {
-    if serialized.len() < 1 {
-      Err(FrostError::InternalError("MultisigKeys serialization is empty".to_string()))?;
+  pub fn deserialize(serialized: &[u8]) -> Result<FrostKeys<C>, FrostError> {
+    let mut start = u64::try_from(C::ID.len()).unwrap().to_be_bytes().to_vec();
+    start.extend(C::ID);
+    let mut cursor = start.len();
+
+    if serialized.len() < (cursor + 4) {
+      Err(
+        FrostError::InternalError(
+          "FrostKeys serialization is missing its curve/participant quantities".to_string()
+        )
+      )?;
     }
-
-    let id_len: usize = serialized[0].into();
-    let mut cursor = 1;
-
-    if serialized.len() < (cursor + id_len) {
-      Err(FrostError::InternalError("ID wasn't included".to_string()))?;
-    }
-
-    let id = &serialized[cursor .. (cursor + id_len)];
-    if C::id().as_bytes() != id {
+    if &start != &serialized[.. cursor] {
       Err(
         FrostError::InternalError(
           "curve is distinct between serialization and deserialization".to_string()
         )
       )?;
     }
-    cursor += id_len;
 
-    if serialized.len() < (cursor + 8) {
-      Err(FrostError::InternalError("participant quantity wasn't included".to_string()))?;
-    }
-
-    let n = u16::from_le_bytes(serialized[cursor .. (cursor + 2)].try_into().unwrap());
+    let t = u16::from_be_bytes(serialized[cursor .. (cursor + 2)].try_into().unwrap());
     cursor += 2;
-    if serialized.len() != MultisigKeys::<C>::serialized_len(n) {
+
+    let n = u16::from_be_bytes(serialized[cursor .. (cursor + 2)].try_into().unwrap());
+    cursor += 2;
+    if serialized.len() != FrostKeys::<C>::serialized_len(n) {
       Err(FrostError::InternalError("incorrect serialization length".to_string()))?;
     }
 
-    let t = u16::from_le_bytes(serialized[cursor .. (cursor + 2)].try_into().unwrap());
-    cursor += 2;
-    let i = u16::from_le_bytes(serialized[cursor .. (cursor + 2)].try_into().unwrap());
+    let i = u16::from_be_bytes(serialized[cursor .. (cursor + 2)].try_into().unwrap());
     cursor += 2;
 
-    let secret_share = C::F_from_slice(&serialized[cursor .. (cursor + C::F_len())])
+    let secret_share = F_from_slice::<C::F>(&serialized[cursor .. (cursor + F_len::<C>())])
       .map_err(|_| FrostError::InternalError("invalid secret share".to_string()))?;
-    cursor += C::F_len();
-    let group_key = C::G_from_slice(&serialized[cursor .. (cursor + C::G_len())])
+    cursor += F_len::<C>();
+    let group_key = G_from_slice::<C::G>(&serialized[cursor .. (cursor + G_len::<C>())])
       .map_err(|_| FrostError::InternalError("invalid group key".to_string()))?;
-    cursor += C::G_len();
+    cursor += G_len::<C>();
 
     let mut verification_shares = HashMap::new();
     for l in 1 ..= n {
       verification_shares.insert(
         l,
-        C::G_from_slice(&serialized[cursor .. (cursor + C::G_len())])
+        G_from_slice::<C::G>(&serialized[cursor .. (cursor + G_len::<C>())])
           .map_err(|_| FrostError::InternalError("invalid verification share".to_string()))?
       );
-      cursor += C::G_len();
+      cursor += G_len::<C>();
     }
 
     Ok(
-      MultisigKeys {
-        params: MultisigParams::new(t, n, i)
+      FrostKeys {
+        params: FrostParams::new(t, n, i)
           .map_err(|_| FrostError::InternalError("invalid parameters".to_string()))?,
         secret_share,
         group_key,

crypto/frost/src/schnorr.rs

@@ -1,10 +1,10 @@
 use rand_core::{RngCore, CryptoRng};
 
-use ff::Field;
+use group::{ff::{Field, PrimeField}, GroupEncoding};
 
 use multiexp::BatchVerifier;
 
-use crate::Curve;
+use crate::{Curve, F_len, G_len};
 
 #[allow(non_snake_case)]
 #[derive(Clone, Copy, PartialEq, Eq, Debug)]
@@ -15,9 +15,9 @@ pub struct SchnorrSignature<C: Curve> {
 
 impl<C: Curve> SchnorrSignature<C> {
   pub fn serialize(&self) -> Vec<u8> {
-    let mut res = Vec::with_capacity(C::G_len() + C::F_len());
-    res.extend(C::G_to_bytes(&self.R));
-    res.extend(C::F_to_bytes(&self.s));
+    let mut res = Vec::with_capacity(G_len::<C>() + F_len::<C>());
+    res.extend(self.R.to_bytes().as_ref());
+    res.extend(self.s.to_repr().as_ref());
     res
   }
 }
@@ -28,25 +28,26 @@ pub(crate) fn sign<C: Curve>(
   challenge: C::F
 ) -> SchnorrSignature<C> {
   SchnorrSignature {
-    R: C::generator_table() * nonce,
+    R: C::GENERATOR * nonce,
     s: nonce + (private_key * challenge)
   }
 }
 
+#[must_use]
 pub(crate) fn verify<C: Curve>(
   public_key: C::G,
   challenge: C::F,
   signature: &SchnorrSignature<C>
 ) -> bool {
-  (C::generator_table() * signature.s) == (signature.R + (public_key * challenge))
+  (C::GENERATOR * signature.s) == (signature.R + (public_key * challenge))
 }
 
 pub(crate) fn batch_verify<C: Curve, R: RngCore + CryptoRng>(
   rng: &mut R,
   triplets: &[(u16, C::G, C::F, SchnorrSignature<C>)]
 ) -> Result<(), u16> {
-  let mut values = [(C::F::one(), C::generator()); 3];
-  let mut batch = BatchVerifier::new(triplets.len(), C::little_endian());
+  let mut values = [(C::F::one(), C::GENERATOR); 3];
+  let mut batch = BatchVerifier::new(triplets.len());
   for triple in triplets {
     // s = r + ca
     // sG == R + cA

crypto/frost/src/sign.rs

@@ -1,33 +1,35 @@
 use core::fmt;
-use std::{rc::Rc, collections::HashMap};
+use std::{sync::Arc, collections::HashMap};
 
 use rand_core::{RngCore, CryptoRng};
 
-use ff::Field;
+use group::{ff::{Field, PrimeField}, Group, GroupEncoding};
 
 use transcript::Transcript;
 
+use dleq::{Generators, DLEqProof};
+
 use crate::{
-  Curve,
+  curve::{Curve, F_len, G_len, F_from_slice, G_from_slice},
   FrostError,
-  MultisigParams, MultisigKeys, MultisigView,
+  FrostParams, FrostKeys, FrostView,
   algorithm::Algorithm,
   validate_map
 };
 
-/// Pairing of an Algorithm with a MultisigKeys instance and this specific signing set
+/// Pairing of an Algorithm with a FrostKeys instance and this specific signing set
 #[derive(Clone)]
 pub struct Params<C: Curve, A: Algorithm<C>> {
   algorithm: A,
-  keys: Rc<MultisigKeys<C>>,
-  view: MultisigView<C>,
+  keys: Arc<FrostKeys<C>>,
+  view: FrostView<C>,
 }
 
 // Currently public to enable more complex operations as desired, yet solely used in testing
 impl<C: Curve, A: Algorithm<C>> Params<C, A> {
   pub fn new(
     algorithm: A,
-    keys: Rc<MultisigKeys<C>>,
+    keys: Arc<FrostKeys<C>>,
     included: &[u16],
   ) -> Result<Params<C, A>, FrostError> {
     let mut included = included.to_vec();
@@ -60,18 +62,22 @@ impl<C: Curve, A: Algorithm<C>> Params<C, A> {
     Ok(Params { algorithm, view: keys.view(&included).unwrap(), keys })
   }
 
-  pub fn multisig_params(&self) -> MultisigParams {
+  pub fn multisig_params(&self) -> FrostParams {
     self.keys.params
   }
 
-  pub fn view(&self) -> MultisigView<C> {
+  pub fn view(&self) -> FrostView<C> {
     self.view.clone()
   }
 }
 
-struct PreprocessPackage<C: Curve> {
-  nonces: [C::F; 2],
-  serialized: Vec<u8>,
+fn nonce_transcript<T: Transcript>() -> T {
+  T::new(b"FROST_nonce_dleq")
+}
+
+pub(crate) struct PreprocessPackage<C: Curve> {
+  pub(crate) nonces: Vec<[C::F; 2]>,
+  pub(crate) serialized: Vec<u8>,
 }
 
 // This library unifies the preprocessing step with signing due to security concerns and to provide
@@ -80,27 +86,53 @@ fn preprocess<R: RngCore + CryptoRng, C: Curve, A: Algorithm<C>>(
   rng: &mut R,
   params: &mut Params<C, A>,
 ) -> PreprocessPackage<C> {
-  let nonces = [C::F::random(&mut *rng), C::F::random(&mut *rng)];
-  let commitments = [C::generator_table() * nonces[0], C::generator_table() * nonces[1]];
-  let mut serialized = C::G_to_bytes(&commitments[0]);
-  serialized.extend(&C::G_to_bytes(&commitments[1]));
+  let mut serialized = Vec::with_capacity(2 * G_len::<C>());
+  let nonces = params.algorithm.nonces().iter().cloned().map(
+    |mut generators| {
+      let nonces = [
+        C::random_nonce(params.view().secret_share(), &mut *rng),
+        C::random_nonce(params.view().secret_share(), &mut *rng)
+      ];
 
-  serialized.extend(
-    &params.algorithm.preprocess_addendum(
-      rng,
-      &params.view,
-      &nonces
-    )
-  );
+      let commit = |generator: C::G| {
+        let commitments = [generator * nonces[0], generator * nonces[1]];
+        [commitments[0].to_bytes().as_ref(), commitments[1].to_bytes().as_ref()].concat().to_vec()
+      };
+
+      let first = generators.remove(0);
+      serialized.extend(commit(first));
+
+      // Iterate over the rest
+      for generator in generators.iter() {
+        serialized.extend(commit(*generator));
+        // Provide a DLEq to verify these commitments are for the same nonce
+        // TODO: Provide a single DLEq. See https://github.com/serai-dex/serai/issues/34
+        for nonce in nonces {
+          DLEqProof::prove(
+            &mut *rng,
+            // Uses an independent transcript as each signer must do this now, yet we validate them
+            // sequentially by the global order. Avoids needing to clone the transcript around
+            &mut nonce_transcript::<A::Transcript>(),
+            Generators::new(first, *generator),
+            nonce
+          ).serialize(&mut serialized).unwrap();
+        }
+      }
+
+      nonces
+    }
+  ).collect::<Vec<_>>();
+
+  serialized.extend(&params.algorithm.preprocess_addendum(rng, &params.view));
 
   PreprocessPackage { nonces, serialized }
 }
 
 #[allow(non_snake_case)]
 struct Package<C: Curve> {
-  B: HashMap<u16, [C::G; 2]>,
+  B: HashMap<u16, Vec<Vec<[C::G; 2]>>>,
   binding: C::F,
-  R: C::G,
+  Rs: Vec<Vec<C::G>>,
   share: Vec<u8>
 }
 
@@ -126,7 +158,7 @@ fn sign_with_share<C: Curve, A: Algorithm<C>>(
     transcript.domain_separate(b"FROST");
     // Include the offset, if one exists
     if let Some(offset) = params.keys.offset {
-      transcript.append_message(b"offset", &C::F_to_bytes(&offset));
+      transcript.append_message(b"offset", offset.to_repr().as_ref());
     }
   }
 
@@ -134,61 +166,98 @@ fn sign_with_share<C: Curve, A: Algorithm<C>>(
   let mut B = HashMap::<u16, _>::with_capacity(params.view.included.len());
 
   // Get the binding factor
+  let nonces = params.algorithm.nonces();
   let mut addendums = HashMap::new();
   let binding = {
     let transcript = params.algorithm.transcript();
     // Parse the commitments
     for l in &params.view.included {
       transcript.append_message(b"participant", &l.to_be_bytes());
+      let serialized = commitments.remove(l).unwrap();
 
-      let commitments = commitments.remove(l).unwrap();
       let mut read_commitment = |c, label| {
-        let commitment = &commitments[c .. (c + C::G_len())];
+        let commitment = &serialized[c .. (c + G_len::<C>())];
         transcript.append_message(label, commitment);
-        C::G_from_slice(commitment).map_err(|_| FrostError::InvalidCommitment(*l))
+        G_from_slice::<C::G>(commitment).map_err(|_| FrostError::InvalidCommitment(*l))
       };
 
+      // While this doesn't note which nonce/basepoint this is for, those are expected to be
+      // static. Beyond that, they're committed to in the DLEq proof transcripts, ensuring
+      // consistency. While this is suboptimal, it maintains IETF compliance, and Algorithm is
+      // documented accordingly
       #[allow(non_snake_case)]
-      let mut read_D_E = || Ok(
-        [read_commitment(0, b"commitment_D")?, read_commitment(C::G_len(), b"commitment_E")?]
-      );
+      let mut read_D_E = |c| Ok([
+        read_commitment(c, b"commitment_D")?,
+        read_commitment(c + G_len::<C>(), b"commitment_E")?
+      ]);
 
-      B.insert(*l, read_D_E()?);
-      addendums.insert(*l, commitments[(C::G_len() * 2) ..].to_vec());
+      let mut c = 0;
+      let mut commitments = Vec::with_capacity(nonces.len());
+      for (n, nonce_generators) in nonces.clone().iter_mut().enumerate() {
+        commitments.push(Vec::with_capacity(nonce_generators.len()));
+
+        let first = nonce_generators.remove(0);
+        commitments[n].push(read_D_E(c)?);
+        c += 2 * G_len::<C>();
+
+        let mut c = 2 * G_len::<C>();
+        for generator in nonce_generators {
+          commitments[n].push(read_D_E(c)?);
+          c += 2 * G_len::<C>();
+          for de in 0 .. 2 {
+            DLEqProof::deserialize(
+              &mut std::io::Cursor::new(&serialized[c .. (c + (2 * F_len::<C>()))])
+            ).map_err(|_| FrostError::InvalidCommitment(*l))?.verify(
+              &mut nonce_transcript::<A::Transcript>(),
+              Generators::new(first, *generator),
+              (commitments[n][0][de], commitments[n][commitments[n].len() - 1][de])
+            ).map_err(|_| FrostError::InvalidCommitment(*l))?;
+            c += 2 * F_len::<C>();
+          }
+        }
+
+        addendums.insert(*l, serialized[c ..].to_vec());
+      }
+      B.insert(*l, commitments);
     }
 
     // Append the message to the transcript
     transcript.append_message(b"message", &C::hash_msg(&msg));
 
     // Calculate the binding factor
-    C::hash_binding_factor(&transcript.challenge(b"binding"))
+    C::hash_binding_factor(transcript.challenge(b"binding").as_ref())
   };
 
   // Process the addendums
   for l in &params.view.included {
-    params.algorithm.process_addendum(&params.view, *l, &B[l], &addendums[l])?;
+    params.algorithm.process_addendum(&params.view, *l, &addendums[l])?;
   }
 
   #[allow(non_snake_case)]
-  let R = {
-    B.values().map(|B| B[0]).sum::<C::G>() + (B.values().map(|B| B[1]).sum::<C::G>() * binding)
-  };
-  let share = C::F_to_bytes(
-    &params.algorithm.sign_share(
-      &params.view,
-      R,
-      binding,
-      our_preprocess.nonces[0] + (our_preprocess.nonces[1] * binding),
-      msg
-    )
-  );
+  let mut Rs = Vec::with_capacity(nonces.len());
+  for n in 0 .. nonces.len() {
+    Rs.push(vec![C::G::identity(); nonces[n].len()]);
+    #[allow(non_snake_case)]
+    for g in 0 .. nonces[n].len() {
+      Rs[n][g] = {
+        B.values().map(|B| B[n][g][0]).sum::<C::G>() +
+          (B.values().map(|B| B[n][g][1]).sum::<C::G>() * binding)
+      };
+    }
+  }
 
-  Ok((Package { B, binding, R, share: share.clone() }, share))
+  let share = params.algorithm.sign_share(
+    &params.view,
+    &Rs,
+    &our_preprocess.nonces.iter().map(
+      |nonces| nonces[0] + (nonces[1] * binding)
+    ).collect::<Vec<_>>(),
+    msg
+  ).to_repr().as_ref().to_vec();
+
+  Ok((Package { B, binding, Rs, share: share.clone() }, share))
 }
 
-// This doesn't check the signing set is as expected and unexpected changes can cause false blames
-// if legitimate participants are still using the original, expected, signing set. This library
-// could be made more robust in that regard
 fn complete<C: Curve, A: Algorithm<C>>(
   sign_params: &Params<C, A>,
   sign: Package<C>,
@@ -200,7 +269,7 @@ fn complete<C: Curve, A: Algorithm<C>>(
   let mut responses = HashMap::new();
   let mut sum = C::F::zero();
   for l in &sign_params.view.included {
-    let part = C::F_from_slice(&shares[l]).map_err(|_| FrostError::InvalidShare(*l))?;
+    let part = F_from_slice::<C::F>(&shares[l]).map_err(|_| FrostError::InvalidShare(*l))?;
     sum += part;
     responses.insert(*l, part);
   }
@@ -208,7 +277,7 @@ fn complete<C: Curve, A: Algorithm<C>>(
   // Perform signature validation instead of individual share validation
   // For the success route, which should be much more frequent, this should be faster
   // It also acts as an integrity check of this library's signing function
-  let res = sign_params.algorithm.verify(sign_params.view.group_key, sign.R, sum);
+  let res = sign_params.algorithm.verify(sign_params.view.group_key, &sign.Rs, sum);
   if let Some(res) = res {
     return Ok(res);
   }
@@ -219,7 +288,11 @@ fn complete<C: Curve, A: Algorithm<C>>(
     if !sign_params.algorithm.verify_share(
       *l,
       sign_params.view.verification_share(*l),
-      sign.B[l][0] + (sign.B[l][1] * sign.binding),
+      &sign.B[l].iter().map(
+        |nonces| nonces.iter().map(
+          |commitments| commitments[0] + (commitments[1] * sign.binding)
+        ).collect()
+      ).collect::<Vec<_>>(),
       responses[l]
     ) {
       Err(FrostError::InvalidShare(*l))?;
@@ -234,31 +307,21 @@ fn complete<C: Curve, A: Algorithm<C>>(
   )
 }
 
-/// State of a Sign machine
-#[derive(Clone, Copy, PartialEq, Eq, Debug)]
-pub enum State {
-  Fresh,
-  Preprocessed,
-  Signed,
-  Complete,
-}
-
-impl fmt::Display for State {
-  fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
-    write!(f, "{:?}", self)
-  }
-}
-
-pub trait StateMachine {
+pub trait PreprocessMachine {
   type Signature: Clone + PartialEq + fmt::Debug;
+  type SignMachine: SignMachine<Self::Signature>;
 
   /// Perform the preprocessing round required in order to sign
   /// Returns a byte vector which must be transmitted to all parties selected for this signing
   /// process, over an authenticated channel
   fn preprocess<R: RngCore + CryptoRng>(
-    &mut self,
+    self,
     rng: &mut R
-  ) -> Result<Vec<u8>, FrostError>;
+  ) -> (Self::SignMachine, Vec<u8>);
+}
+
+pub trait SignMachine<S> {
+  type SignatureMachine: SignatureMachine<S>;
 
   /// Sign a message
   /// Takes in the participant's commitments, which are expected to be in a Vec where participant
@@ -266,107 +329,88 @@ pub trait StateMachine {
   /// index i which is locally handled. Returns a byte vector representing a share of the signature
   /// for every other participant to receive, over an authenticated channel
   fn sign(
-    &mut self,
+    self,
     commitments: HashMap<u16, Vec<u8>>,
     msg: &[u8],
-  ) -> Result<Vec<u8>, FrostError>;
+  ) -> Result<(Self::SignatureMachine, Vec<u8>), FrostError>;
+}
 
+pub trait SignatureMachine<S> {
   /// Complete signing
   /// Takes in everyone elses' shares submitted to us as a Vec, expecting participant index =
   /// Vec index with None at index 0 and index i. Returns a byte vector representing the serialized
   /// signature
-  fn complete(&mut self, shares: HashMap<u16, Vec<u8>>) -> Result<Self::Signature, FrostError>;
-
-  fn multisig_params(&self) -> MultisigParams;
-
-  fn state(&self) -> State;
+  fn complete(self, shares: HashMap<u16, Vec<u8>>) -> Result<S, FrostError>;
 }
 
 /// State machine which manages signing for an arbitrary signature algorithm
-#[allow(non_snake_case)]
 pub struct AlgorithmMachine<C: Curve, A: Algorithm<C>> {
+  params: Params<C, A>
+}
+
+pub struct AlgorithmSignMachine<C: Curve, A: Algorithm<C>> {
   params: Params<C, A>,
-  state: State,
-  preprocess: Option<PreprocessPackage<C>>,
-  sign: Option<Package<C>>,
+  preprocess: PreprocessPackage<C>,
+}
+
+pub struct AlgorithmSignatureMachine<C: Curve, A: Algorithm<C>> {
+  params: Params<C, A>,
+  sign: Package<C>,
 }
 
 impl<C: Curve, A: Algorithm<C>> AlgorithmMachine<C, A> {
   /// Creates a new machine to generate a key for the specified curve in the specified multisig
   pub fn new(
     algorithm: A,
-    keys: Rc<MultisigKeys<C>>,
+    keys: Arc<FrostKeys<C>>,
     included: &[u16],
   ) -> Result<AlgorithmMachine<C, A>, FrostError> {
-    Ok(
-      AlgorithmMachine {
-        params: Params::new(algorithm, keys, included)?,
-        state: State::Fresh,
-        preprocess: None,
-        sign: None,
-      }
-    )
+    Ok(AlgorithmMachine { params: Params::new(algorithm, keys, included)? })
+  }
+
+  pub(crate) fn unsafe_override_preprocess(
+    self,
+    preprocess: PreprocessPackage<C>
+  ) -> (AlgorithmSignMachine<C, A>, Vec<u8>) {
+    let serialized = preprocess.serialized.clone();
+    (AlgorithmSignMachine { params: self.params, preprocess }, serialized)
   }
 }
 
-impl<C: Curve, A: Algorithm<C>> StateMachine for AlgorithmMachine<C, A> {
+impl<C: Curve, A: Algorithm<C>> PreprocessMachine for AlgorithmMachine<C, A> {
   type Signature = A::Signature;
+  type SignMachine = AlgorithmSignMachine<C, A>;
 
   fn preprocess<R: RngCore + CryptoRng>(
-    &mut self,
+    self,
     rng: &mut R
-  ) -> Result<Vec<u8>, FrostError> {
-    if self.state != State::Fresh {
-      Err(FrostError::InvalidSignTransition(State::Fresh, self.state))?;
-    }
-    let preprocess = preprocess::<R, C, A>(rng, &mut self.params);
+  ) -> (Self::SignMachine, Vec<u8>) {
+    let mut params = self.params;
+    let preprocess = preprocess::<R, C, A>(rng, &mut params);
     let serialized = preprocess.serialized.clone();
-    self.preprocess = Some(preprocess);
-    self.state = State::Preprocessed;
-    Ok(serialized)
-  }
-
-  fn sign(
-    &mut self,
-    commitments: HashMap<u16, Vec<u8>>,
-    msg: &[u8],
-  ) -> Result<Vec<u8>, FrostError> {
-    if self.state != State::Preprocessed {
-      Err(FrostError::InvalidSignTransition(State::Preprocessed, self.state))?;
-    }
-
-    let (sign, serialized) = sign_with_share(
-      &mut self.params,
-      self.preprocess.take().unwrap(),
-      commitments,
-      msg,
-    )?;
-
-    self.sign = Some(sign);
-    self.state = State::Signed;
-    Ok(serialized)
-  }
-
-  fn complete(&mut self, shares: HashMap<u16, Vec<u8>>) -> Result<A::Signature, FrostError> {
-    if self.state != State::Signed {
-      Err(FrostError::InvalidSignTransition(State::Signed, self.state))?;
-    }
-
-    let signature = complete(
-      &self.params,
-      self.sign.take().unwrap(),
-      shares,
-    )?;
-
-    self.state = State::Complete;
-    Ok(signature)
-  }
-
-  fn multisig_params(&self) -> MultisigParams {
-    self.params.multisig_params().clone()
-  }
-
-  fn state(&self) -> State {
-    self.state
+    (AlgorithmSignMachine { params, preprocess }, serialized)
+  }
+}
+
+impl<C: Curve, A: Algorithm<C>> SignMachine<A::Signature> for AlgorithmSignMachine<C, A> {
+  type SignatureMachine = AlgorithmSignatureMachine<C, A>;
+
+  fn sign(
+    self,
+    commitments: HashMap<u16, Vec<u8>>,
+    msg: &[u8]
+  ) -> Result<(Self::SignatureMachine, Vec<u8>), FrostError> {
+    let mut params = self.params;
+    let (sign, serialized) = sign_with_share(&mut params, self.preprocess, commitments, msg)?;
+    Ok((AlgorithmSignatureMachine { params, sign }, serialized))
+  }
+}
+
+impl<
+  C: Curve,
+  A: Algorithm<C>
+> SignatureMachine<A::Signature> for AlgorithmSignatureMachine<C, A> {
+  fn complete(self, shares: HashMap<u16, Vec<u8>>) -> Result<A::Signature, FrostError> {
+    complete(&self.params, self.sign, shares)
   }
 }

crypto/frost/src/tests/curve.rs

@@ -1,9 +1,8 @@
 use rand_core::{RngCore, CryptoRng};
 
-use crate::{
-  Curve, MultisigKeys,
-  tests::{schnorr::{sign, verify, batch_verify}, key_gen}
-};
+use group::{ff::Field, Group};
+
+use crate::{Curve, FrostKeys, tests::key_gen};
 
 // Test generation of FROST keys
 fn key_generation<R: RngCore + CryptoRng, C: Curve>(rng: &mut R) {
@@ -14,21 +13,30 @@ fn key_generation<R: RngCore + CryptoRng, C: Curve>(rng: &mut R) {
 // Test serialization of generated keys
 fn keys_serialization<R: RngCore + CryptoRng, C: Curve>(rng: &mut R) {
   for (_, keys) in key_gen::<_, C>(rng) {
-    assert_eq!(&MultisigKeys::<C>::deserialize(&keys.serialize()).unwrap(), &*keys);
+    assert_eq!(&FrostKeys::<C>::deserialize(&keys.serialize()).unwrap(), &*keys);
   }
 }
 
 pub fn test_curve<R: RngCore + CryptoRng, C: Curve>(rng: &mut R) {
   // TODO: Test the Curve functions themselves
 
-  // Test Schnorr signatures work as expected
-  // This is a bit unnecessary, as they should for any valid curve, yet this provides tests with
-  // meaning, which the above tests won't have
-  sign::<_, C>(rng);
-  verify::<_, C>(rng);
-  batch_verify::<_, C>(rng);
+  // Test successful multiexp, with enough pairs to trigger its variety of algorithms
+  // Multiexp has its own tests, yet only against k256 and Ed25519 (which should be sufficient
+  // as-is to prove multiexp), and this doesn't hurt
+  {
+    let mut pairs = Vec::with_capacity(1000);
+    let mut sum = C::G::identity();
+    for _ in 0 .. 10 {
+      for _ in 0 .. 100 {
+        pairs.push((C::F::random(&mut *rng), C::GENERATOR * C::F::random(&mut *rng)));
+        sum += pairs[pairs.len() - 1].1 * pairs[pairs.len() - 1].0;
+      }
+      assert_eq!(multiexp::multiexp(&pairs), sum);
+      assert_eq!(multiexp::multiexp_vartime(&pairs), sum);
+    }
+  }
 
-  // Test FROST key generation and serialization of MultisigKeys works as expected
+  // Test FROST key generation and serialization of FrostKeys works as expected
   key_generation::<_, C>(rng);
   keys_serialization::<_, C>(rng);
 }

crypto/frost/src/tests/literal/dalek.rs

@@ -0,0 +1,77 @@
+use rand::rngs::OsRng;
+
+use crate::{curve, tests::vectors::{Vectors, test_with_vectors}};
+
+#[cfg(any(test, feature = "ristretto"))]
+#[test]
+fn ristretto_vectors() {
+  test_with_vectors::<_, curve::Ristretto, curve::IetfRistrettoHram>(
+    &mut OsRng,
+    Vectors {
+      threshold: 2,
+      shares: &[
+        "5c3430d391552f6e60ecdc093ff9f6f4488756aa6cebdbad75a768010b8f830e",
+        "b06fc5eac20b4f6e1b271d9df2343d843e1e1fb03c4cbb673f2872d459ce6f01",
+        "f17e505f0e2581c6acfe54d3846a622834b5e7b50cad9a2109a97ba7a80d5c04"
+      ],
+      group_secret: "1b25a55e463cfd15cf14a5d3acc3d15053f08da49c8afcf3ab265f2ebc4f970b",
+      group_key: "e2a62f39eede11269e3bd5a7d97554f5ca384f9f6d3dd9c3c0d05083c7254f57",
+
+      msg: "74657374",
+      included: &[1, 3],
+      nonces: &[
+        [
+          "b358743151e33d84bf00c12f71808f4103957c3e2cabab7b895c436b5e70f90c",
+          "7bd112153b9ae1ab9b31f5e78f61f5c4ca9ee67b7ea6d1181799c409d14c350c"
+        ],
+        [
+          "22acad88478e0d0373a991092a322ebd1b9a2dad90451a976d0db3215426af0e",
+          "9155e3d7bcf7cd468b980c7e20b2c77cbdfbe33a1dcae031fd8bc6b1403f4b04"
+        ]
+      ],
+      sig_shares: &[
+        "ff801b4e0839faa67f16dee4127b9f7fbcf5fd007900257b0e2bbc02cbe5e709",
+        "afdf5481023c855bf3411a5c8a5fafa92357296a078c3b80dc168f294cb4f504"
+      ],
+      sig: "deae61af10e8ee48ba492573592fba547f5debeff6bd6e2024e8673584746f5e".to_owned() +
+           "ae6070cf0a757f027358f8409dda4e29e04c276b808c60fbea414b2c179add0e"
+    }
+  );
+}
+
+#[cfg(feature = "ed25519")]
+#[test]
+fn ed25519_vectors() {
+  test_with_vectors::<_, curve::Ed25519, curve::IetfEd25519Hram>(
+    &mut OsRng,
+    Vectors {
+      threshold: 2,
+      shares: &[
+        "929dcc590407aae7d388761cddb0c0db6f5627aea8e217f4a033f2ec83d93509",
+        "a91e66e012e4364ac9aaa405fcafd370402d9859f7b6685c07eed76bf409e80d",
+        "d3cb090a075eb154e82fdb4b3cb507f110040905468bb9c46da8bdea643a9a02"
+      ],
+      group_secret: "7b1c33d3f5291d85de664833beb1ad469f7fb6025a0ec78b3a790c6e13a98304",
+      group_key: "15d21ccd7ee42959562fc8aa63224c8851fb3ec85a3faf66040d380fb9738673",
+
+      msg: "74657374",
+      included: &[1, 3],
+      nonces: &[
+        [
+          "8c76af04340e83bb5fc427c117d38347fc8ef86d5397feea9aa6412d96c05b0a",
+          "14a37ddbeae8d9e9687369e5eb3c6d54f03dc19d76bb54fb5425131bc37a600b"
+        ],
+        [
+          "5ca39ebab6874f5e7b5089f3521819a2aa1e2cf738bae6974ee80555de2ef70e",
+          "0afe3650c4815ff37becd3c6948066e906e929ea9b8f546c74e10002dbcc150c"
+        ]
+      ],
+      sig_shares: &[
+        "4369474a398aa10357b60d683da91ea6a767dcf53fd541a8ed6b4d780827ea0a",
+        "32fcc690d926075e45d2dfb746bab71447943cddbefe80d122c39174aa2e1004"
+      ],
+      sig: "2b8d9c6995333c5990e3a3dd6568785539d3322f7f0376452487ea35cfda587b".to_owned() +
+           "75650edb12b1a8619c88ed1f8463d6baeefb18d3fed3c279102fdfecb255fa0e"
+    }
+  );
+}

crypto/frost/src/tests/literal/kp256.rs

@@ -0,0 +1,55 @@
+use rand::rngs::OsRng;
+
+#[cfg(feature = "secp256k1")]
+use crate::tests::{curve::test_curve, schnorr::test_schnorr};
+#[cfg(feature = "secp256k1")]
+use crate::curve::Secp256k1;
+
+#[cfg(feature = "p256")]
+use crate::tests::vectors::{Vectors, test_with_vectors};
+#[cfg(feature = "p256")]
+use crate::curve::{P256, IetfP256Hram};
+
+#[cfg(feature = "secp256k1")]
+#[test]
+fn secp256k1_non_ietf() {
+  test_curve::<_, Secp256k1>(&mut OsRng);
+  test_schnorr::<_, Secp256k1>(&mut OsRng);
+}
+
+#[cfg(feature = "p256")]
+#[test]
+fn p256_vectors() {
+  test_with_vectors::<_, P256, IetfP256Hram>(
+    &mut OsRng,
+    Vectors {
+      threshold: 2,
+      shares: &[
+        "0c9c1a0fe806c184add50bbdcac913dda73e482daf95dcb9f35dbb0d8a9f7731",
+        "8d8e787bef0ff6c2f494ca45f4dad198c6bee01212d6c84067159c52e1863ad5",
+        "0e80d6e8f6192c003b5488ce1eec8f5429587d48cf001541e713b2d53c09d928"
+      ],
+      group_secret: "8ba9bba2e0fd8c4767154d35a0b7562244a4aaf6f36c8fb8735fa48b301bd8de",
+      group_key: "023a309ad94e9fe8a7ba45dfc58f38bf091959d3c99cfbd02b4dc00585ec45ab70",
+
+      msg: "74657374",
+      included: &[1, 3],
+      nonces: &[
+        [
+          "081617b24375e069b39f649d4c4ce2fba6e38b73e7c16759de0b6079a22c4c7e",
+          "4de5fb77d99f03a2491a83a6a4cb91ca3c82a3f34ce94cec939174f47c9f95dd"
+        ],
+        [
+          "d186ea92593f83ea83181b184d41aa93493301ac2bc5b4b1767e94d2db943e38",
+          "486e2ee25a3fbc8e6399d748b077a2755fde99fa85cc24fa647ea4ebf5811a15"
+        ]
+      ],
+      sig_shares: &[
+        "9e4d8865faf8c7b3193a3b35eda3d9e12118447114b1e7d5b4809ea28067f8a9",
+        "b7d094eab6305ae74daeed1acd31abba9ab81f638d38b72c132cb25a5dfae1fc"
+      ],
+      sig: "0342c14c77f9d4ef9b8bd64fb0d7bbfdb9f8216a44e5f7bbe6ac0f3ed5e1a57367".to_owned() +
+        "561e1d51b129229966e92850bad5859bfee96926fad3007cd3f38639e1ffb554"
+    }
+  );
+}

crypto/frost/src/tests/literal/mod.rs

@@ -1,2 +1,4 @@
-mod secp256k1;
-mod schnorr;
+#[cfg(any(test, feature = "dalek"))]
+mod dalek;
+#[cfg(feature = "kp256")]
+mod kp256;

crypto/frost/src/tests/literal/schnorr.rs

@@ -1,42 +0,0 @@
-use std::rc::Rc;
-
-use rand::rngs::OsRng;
-
-use crate::{
-  Curve, schnorr, algorithm::{Hram, Schnorr},
-  tests::{key_gen, algorithm_machines, sign as sign_test, literal::secp256k1::{Secp256k1, TestHram}}
-};
-
-const MESSAGE: &[u8] = b"Hello World";
-
-#[test]
-fn sign() {
-  sign_test(
-    &mut OsRng,
-    algorithm_machines(
-      &mut OsRng,
-      Schnorr::<Secp256k1, TestHram>::new(),
-      &key_gen::<_, Secp256k1>(&mut OsRng)
-    ),
-    MESSAGE
-  );
-}
-
-#[test]
-fn sign_with_offset() {
-  let mut keys = key_gen::<_, Secp256k1>(&mut OsRng);
-  let group_key = keys[&1].group_key();
-
-  let offset = Secp256k1::hash_to_F(b"offset");
-  for i in 1 ..= u16::try_from(keys.len()).unwrap() {
-    keys.insert(i, Rc::new(keys[&i].offset(offset)));
-  }
-  let offset_key = group_key + (Secp256k1::generator_table() * offset);
-
-  let sig = sign_test(
-    &mut OsRng,
-    algorithm_machines(&mut OsRng, Schnorr::<Secp256k1, TestHram>::new(), &keys),
-    MESSAGE
-  );
-  assert!(schnorr::verify(offset_key, TestHram::hram(&sig.R, &offset_key, MESSAGE), &sig));
-}

crypto/frost/src/tests/literal/secp256k1.rs

@@ -1,120 +0,0 @@
-use core::convert::TryInto;
-
-use rand::rngs::OsRng;
-
-use ff::PrimeField;
-use group::GroupEncoding;
-
-use sha2::{Digest, Sha256, Sha512};
-
-use k256::{
-  elliptic_curve::{generic_array::GenericArray, bigint::{ArrayEncoding, U512}, ops::Reduce},
-  Scalar,
-  ProjectivePoint
-};
-
-use crate::{CurveError, Curve, algorithm::Hram, tests::curve::test_curve};
-
-#[derive(Clone, Copy, PartialEq, Eq, Debug)]
-pub struct Secp256k1;
-impl Curve for Secp256k1 {
-  type F = Scalar;
-  type G = ProjectivePoint;
-  type T = ProjectivePoint;
-
-  fn id() -> String {
-    "secp256k1".to_string()
-  }
-
-  fn id_len() -> u8 {
-    u8::try_from(Self::id().len()).unwrap()
-  }
-
-  fn generator() -> Self::G {
-    Self::G::GENERATOR
-  }
-
-  fn generator_table() -> Self::T {
-    Self::G::GENERATOR
-  }
-
-  fn little_endian() -> bool {
-    false
-  }
-
-  // The IETF draft doesn't specify a secp256k1 ciphersuite
-  // This test just uses the simplest ciphersuite which would still be viable to deploy
-  // The comparable P-256 curve uses hash_to_field from the Hash To Curve IETF draft with a context
-  // string and further DST for H1 ("rho") and H3 ("digest"). It's not currently worth it to add
-  // that weight, yet if secp256k1 is ever officially acknowledged (not just a testing curve), it
-  // must be properly implemented.
-  fn hash_msg(msg: &[u8]) -> Vec<u8> {
-    (&Sha256::digest(msg)).to_vec()
-  }
-
-  fn hash_binding_factor(binding: &[u8]) -> Self::F {
-    Self::hash_to_F(&[b"rho", binding].concat())
-  }
-
-  // Use wide reduction for security
-  fn hash_to_F(data: &[u8]) -> Self::F {
-    Scalar::from_uint_reduced(U512::from_be_byte_array(Sha512::digest(data)))
-  }
-
-  fn F_len() -> usize {
-    32
-  }
-
-  fn G_len() -> usize {
-    33
-  }
-
-  fn F_from_slice(slice: &[u8]) -> Result<Self::F, CurveError> {
-    let bytes: [u8; 32] = slice.try_into()
-      .map_err(|_| CurveError::InvalidLength(32, slice.len()))?;
-    let scalar = Scalar::from_repr(bytes.into());
-    if scalar.is_none().unwrap_u8() == 1 {
-      Err(CurveError::InvalidScalar)?;
-    }
-    Ok(scalar.unwrap())
-  }
-
-  fn G_from_slice(slice: &[u8]) -> Result<Self::G, CurveError> {
-    let point = ProjectivePoint::from_bytes(GenericArray::from_slice(slice));
-    if point.is_none().unwrap_u8() == 1 {
-      Err(CurveError::InvalidScalar)?;
-    }
-    Ok(point.unwrap())
-  }
-
-  fn F_to_bytes(f: &Self::F) -> Vec<u8> {
-    (&f.to_bytes()).to_vec()
-  }
-
-  fn G_to_bytes(g: &Self::G) -> Vec<u8> {
-    (&g.to_bytes()).to_vec()
-  }
-}
-
-#[allow(non_snake_case)]
-#[derive(Clone)]
-pub struct TestHram {}
-impl Hram<Secp256k1> for TestHram {
-  #[allow(non_snake_case)]
-  fn hram(R: &ProjectivePoint, A: &ProjectivePoint, m: &[u8]) -> Scalar {
-    Scalar::from_uint_reduced(
-      U512::from_be_byte_array(
-        Sha512::new()
-          .chain_update(Secp256k1::G_to_bytes(R))
-          .chain_update(Secp256k1::G_to_bytes(A))
-          .chain_update(m)
-          .finalize()
-      )
-    )
-  }
-}
-
-#[test]
-fn secp256k1_curve() {
-  test_curve::<_, Secp256k1>(&mut OsRng);
-}

crypto/frost/src/tests/mod.rs

@@ -1,23 +1,22 @@
-use std::{rc::Rc, collections::HashMap};
+use std::{sync::Arc, collections::HashMap};
 
 use rand_core::{RngCore, CryptoRng};
 
-use ff::Field;
+use group::ff::Field;
 
 use crate::{
   Curve,
-  MultisigParams, MultisigKeys,
+  FrostParams, FrostKeys,
   lagrange,
-  key_gen,
+  key_gen::KeyGenMachine,
   algorithm::Algorithm,
-  sign::{StateMachine, AlgorithmMachine}
+  sign::{PreprocessMachine, SignMachine, SignatureMachine, AlgorithmMachine}
 };
 
-// Internal tests
-mod schnorr;
-
 // Test suites for public usage
 pub mod curve;
+pub mod schnorr;
+pub mod vectors;
 
 // Literal test definitions to run during `cargo test`
 #[cfg(test)]
@@ -37,50 +36,37 @@ pub fn clone_without<K: Clone + std::cmp::Eq + std::hash::Hash, V: Clone>(
 
 pub fn key_gen<R: RngCore + CryptoRng, C: Curve>(
   rng: &mut R
-) -> HashMap<u16, Rc<MultisigKeys<C>>> {
-  let mut params = HashMap::new();
+) -> HashMap<u16, Arc<FrostKeys<C>>> {
   let mut machines = HashMap::new();
-
   let mut commitments = HashMap::new();
   for i in 1 ..= PARTICIPANTS {
-    params.insert(
-      i,
-      MultisigParams::new(
-        THRESHOLD,
-        PARTICIPANTS,
-        i
-      ).unwrap()
-    );
-    machines.insert(
-      i,
-      key_gen::StateMachine::<C>::new(
-        params[&i],
-        "FROST test key_gen".to_string()
-      )
-    );
-    commitments.insert(
-      i,
-      machines.get_mut(&i).unwrap().generate_coefficients(rng).unwrap()
+    let machine = KeyGenMachine::<C>::new(
+      FrostParams::new(THRESHOLD, PARTICIPANTS, i).unwrap(),
+      "FROST Test key_gen".to_string()
     );
+    let (machine, these_commitments) = machine.generate_coefficients(rng);
+    machines.insert(i, machine);
+    commitments.insert(i, these_commitments);
   }
 
   let mut secret_shares = HashMap::new();
-  for (l, machine) in machines.iter_mut() {
-    secret_shares.insert(
-      *l,
+  let mut machines = machines.drain().map(|(l, machine)| {
+    let (machine, shares) = machine.generate_secret_shares(
+      rng,
       // clone_without isn't necessary, as this machine's own data will be inserted without
       // conflict, yet using it ensures the machine's own data is actually inserted as expected
-      machine.generate_secret_shares(rng, clone_without(&commitments, l)).unwrap()
-    );
-  }
+      clone_without(&commitments, &l)
+    ).unwrap();
+    secret_shares.insert(l, shares);
+    (l, machine)
+  }).collect::<HashMap<_, _>>();
 
   let mut verification_shares = None;
   let mut group_key = None;
-  let mut keys = HashMap::new();
-  for (i, machine) in machines.iter_mut() {
+  machines.drain().map(|(i, machine)| {
     let mut our_secret_shares = HashMap::new();
     for (l, shares) in &secret_shares {
-      if i == l {
+      if i == *l {
         continue;
       }
       our_secret_shares.insert(*l, shares[&i].clone());
@@ -99,13 +85,11 @@ pub fn key_gen<R: RngCore + CryptoRng, C: Curve>(
     }
     assert_eq!(group_key.unwrap(), these_keys.group_key());
 
-    keys.insert(*i, Rc::new(these_keys));
-  }
-
-  keys
+    (i, Arc::new(these_keys))
+  }).collect::<HashMap<_, _>>()
 }
 
-pub fn recover<C: Curve>(keys: &HashMap<u16, MultisigKeys<C>>) -> C::F {
+pub fn recover<C: Curve>(keys: &HashMap<u16, FrostKeys<C>>) -> C::F {
   let first = keys.values().next().expect("no keys provided");
   assert!(keys.len() >= first.params().t().into(), "not enough keys provided");
   let included = keys.keys().cloned().collect::<Vec<_>>();
@@ -114,14 +98,14 @@ pub fn recover<C: Curve>(keys: &HashMap<u16, MultisigKeys<C>>) -> C::F {
     C::F::zero(),
     |accum, (i, keys)| accum + (keys.secret_share() * lagrange::<C::F>(*i, &included))
   );
-  assert_eq!(C::generator_table() * group_private, first.group_key(), "failed to recover keys");
+  assert_eq!(C::GENERATOR * group_private, first.group_key(), "failed to recover keys");
   group_private
 }
 
 pub fn algorithm_machines<R: RngCore, C: Curve, A: Algorithm<C>>(
   rng: &mut R,
   algorithm: A,
-  keys: &HashMap<u16, Rc<MultisigKeys<C>>>,
+  keys: &HashMap<u16, Arc<FrostKeys<C>>>,
 ) -> HashMap<u16, AlgorithmMachine<C, A>> {
   let mut included = vec![];
   while included.len() < usize::from(keys[&1].params().t()) {
@@ -148,27 +132,28 @@ pub fn algorithm_machines<R: RngCore, C: Curve, A: Algorithm<C>>(
   ).collect()
 }
 
-pub fn sign<R: RngCore + CryptoRng, M: StateMachine>(
+pub fn sign<R: RngCore + CryptoRng, M: PreprocessMachine>(
   rng: &mut R,
   mut machines: HashMap<u16, M>,
   msg: &[u8]
 ) -> M::Signature {
   let mut commitments = HashMap::new();
-  for (i, machine) in machines.iter_mut() {
-    commitments.insert(*i, machine.preprocess(rng).unwrap());
-  }
+  let mut machines = machines.drain().map(|(i, machine)| {
+    let (machine, preprocess) = machine.preprocess(rng);
+    commitments.insert(i, preprocess);
+    (i, machine)
+  }).collect::<HashMap<_, _>>();
 
   let mut shares = HashMap::new();
-  for (i, machine) in machines.iter_mut() {
-    shares.insert(
-      *i,
-      machine.sign(clone_without(&commitments, i), msg).unwrap()
-    );
-  }
+  let mut machines = machines.drain().map(|(i, machine)| {
+    let (machine, share) = machine.sign(clone_without(&commitments, &i), msg).unwrap();
+    shares.insert(i, share);
+    (i, machine)
+  }).collect::<HashMap<_, _>>();
 
   let mut signature = None;
-  for (i, machine) in machines.iter_mut() {
-    let sig = machine.complete(clone_without(&shares, i)).unwrap();
+  for (i, machine) in machines.drain() {
+    let sig = machine.complete(clone_without(&shares, &i)).unwrap();
     if signature.is_none() {
       signature = Some(sig.clone());
     }

crypto/frost/src/tests/schnorr.rs

@@ -1,16 +1,21 @@
+use std::{marker::PhantomData, sync::Arc, collections::HashMap};
+
 use rand_core::{RngCore, CryptoRng};
 
-use ff::Field;
+use group::{ff::Field, GroupEncoding};
 
-use crate::{Curve, schnorr, algorithm::SchnorrSignature};
+use crate::{
+  Curve, FrostKeys, schnorr::{self, SchnorrSignature}, algorithm::{Hram, Schnorr},
+  tests::{key_gen, algorithm_machines, sign as sign_test}
+};
 
-pub(crate) fn sign<R: RngCore + CryptoRng, C: Curve>(rng: &mut R) {
+pub(crate) fn core_sign<R: RngCore + CryptoRng, C: Curve>(rng: &mut R) {
   let private_key = C::F::random(&mut *rng);
   let nonce = C::F::random(&mut *rng);
   let challenge = C::F::random(rng); // Doesn't bother to craft an HRAM
   assert!(
     schnorr::verify::<C>(
-      C::generator_table() * private_key,
+      C::GENERATOR * private_key,
       challenge,
       &schnorr::sign(private_key, nonce, challenge)
     )
@@ -20,17 +25,17 @@ pub(crate) fn sign<R: RngCore + CryptoRng, C: Curve>(rng: &mut R) {
 // The above sign function verifies signing works
 // This verifies invalid signatures don't pass, using zero signatures, which should effectively be
 // random
-pub(crate) fn verify<R: RngCore + CryptoRng, C: Curve>(rng: &mut R) {
+pub(crate) fn core_verify<R: RngCore + CryptoRng, C: Curve>(rng: &mut R) {
   assert!(
     !schnorr::verify::<C>(
-      C::generator_table() * C::F::random(&mut *rng),
+      C::GENERATOR * C::F::random(&mut *rng),
       C::F::random(rng),
-      &SchnorrSignature { R: C::generator_table() * C::F::zero(), s: C::F::zero() }
+      &SchnorrSignature { R: C::GENERATOR * C::F::zero(), s: C::F::zero() }
     )
   );
 }
 
-pub(crate) fn batch_verify<R: RngCore + CryptoRng, C: Curve>(rng: &mut R) {
+pub(crate) fn core_batch_verify<R: RngCore + CryptoRng, C: Curve>(rng: &mut R) {
   // Create 5 signatures
   let mut keys = vec![];
   let mut challenges = vec![];
@@ -43,7 +48,7 @@ pub(crate) fn batch_verify<R: RngCore + CryptoRng, C: Curve>(rng: &mut R) {
 
   // Batch verify
   let triplets = (0 .. 5).map(
-    |i| (u16::try_from(i + 1).unwrap(), C::generator_table() * keys[i], challenges[i], sigs[i])
+    |i| (u16::try_from(i + 1).unwrap(), C::GENERATOR * keys[i], challenges[i], sigs[i])
   ).collect::<Vec<_>>();
   schnorr::batch_verify(rng, &triplets).unwrap();
 
@@ -71,3 +76,56 @@ pub(crate) fn batch_verify<R: RngCore + CryptoRng, C: Curve>(rng: &mut R) {
     }
   }
 }
+
+fn sign_core<R: RngCore + CryptoRng, C: Curve>(
+  rng: &mut R,
+  group_key: C::G,
+  keys: &HashMap<u16, Arc<FrostKeys<C>>>
+) {
+  const MESSAGE: &'static [u8] = b"Hello, World!";
+
+  let machines = algorithm_machines(rng, Schnorr::<C, TestHram<C>>::new(), keys);
+  let sig = sign_test(&mut *rng, machines, MESSAGE);
+  assert!(schnorr::verify(group_key, TestHram::<C>::hram(&sig.R, &group_key, MESSAGE), &sig));
+}
+
+#[derive(Clone)]
+pub struct TestHram<C: Curve> {
+  _curve: PhantomData<C>
+}
+impl<C: Curve> Hram<C> for TestHram<C> {
+  #[allow(non_snake_case)]
+  fn hram(R: &C::G, A: &C::G, m: &[u8]) -> C::F {
+    C::hash_to_F(b"challenge", &[R.to_bytes().as_ref(), A.to_bytes().as_ref(), m].concat())
+  }
+}
+
+fn sign<R: RngCore + CryptoRng, C: Curve>(rng: &mut R) {
+  let keys = key_gen::<_, C>(&mut *rng);
+  sign_core(rng, keys[&1].group_key(), &keys);
+}
+
+fn sign_with_offset<R: RngCore + CryptoRng, C: Curve>(rng: &mut R) {
+  let mut keys = key_gen::<_, C>(&mut *rng);
+  let group_key = keys[&1].group_key();
+
+  let offset = C::hash_to_F(b"FROST Test sign_with_offset", b"offset");
+  for i in 1 ..= u16::try_from(keys.len()).unwrap() {
+    keys.insert(i, Arc::new(keys[&i].offset(offset)));
+  }
+  let offset_key = group_key + (C::GENERATOR * offset);
+
+  sign_core(rng, offset_key, &keys);
+}
+
+pub fn test_schnorr<R: RngCore + CryptoRng, C: Curve>(rng: &mut R) {
+  // Test Schnorr signatures work as expected
+  // This is a bit unnecessary, as they should for any valid curve, yet this establishes sanity
+  core_sign::<_, C>(rng);
+  core_verify::<_, C>(rng);
+  core_batch_verify::<_, C>(rng);
+
+  // Test Schnorr signatures under FROST
+  sign::<_, C>(rng);
+  sign_with_offset::<_, C>(rng);
+}

crypto/frost/src/tests/vectors.rs

@@ -0,0 +1,136 @@
+use std::{sync::Arc, collections::HashMap};
+
+use rand_core::{RngCore, CryptoRng};
+
+use group::{ff::PrimeField, GroupEncoding};
+
+use crate::{
+  curve::{Curve, F_from_slice, G_from_slice}, FrostKeys,
+  algorithm::{Schnorr, Hram},
+  sign::{PreprocessPackage, SignMachine, SignatureMachine, AlgorithmMachine},
+  tests::{curve::test_curve, schnorr::test_schnorr, recover}
+};
+
+pub struct Vectors {
+  pub threshold: u16,
+  pub shares: &'static [&'static str],
+  pub group_secret: &'static str,
+  pub group_key: &'static str,
+
+  pub msg: &'static str,
+  pub included: &'static [u16],
+  pub nonces: &'static [[&'static str; 2]],
+  pub sig_shares: &'static [&'static str],
+  pub sig: String
+}
+
+// Load these vectors into FrostKeys using a custom serialization it'll deserialize
+fn vectors_to_multisig_keys<C: Curve>(vectors: &Vectors) -> HashMap<u16, FrostKeys<C>> {
+  let shares = vectors.shares.iter().map(
+    |secret| F_from_slice::<C::F>(&hex::decode(secret).unwrap()).unwrap()
+  ).collect::<Vec<_>>();
+  let verification_shares = shares.iter().map(
+    |secret| C::GENERATOR * secret
+  ).collect::<Vec<_>>();
+
+  let mut keys = HashMap::new();
+  for i in 1 ..= u16::try_from(shares.len()).unwrap() {
+    let mut serialized = vec![];
+    serialized.extend(u64::try_from(C::ID.len()).unwrap().to_be_bytes());
+    serialized.extend(C::ID);
+    serialized.extend(vectors.threshold.to_be_bytes());
+    serialized.extend(u16::try_from(shares.len()).unwrap().to_be_bytes());
+    serialized.extend(i.to_be_bytes());
+    serialized.extend(shares[usize::from(i) - 1].to_repr().as_ref());
+    serialized.extend(&hex::decode(vectors.group_key).unwrap());
+    for share in &verification_shares {
+      serialized.extend(share.to_bytes().as_ref());
+    }
+
+    let these_keys = FrostKeys::<C>::deserialize(&serialized).unwrap();
+    assert_eq!(these_keys.params().t(), vectors.threshold);
+    assert_eq!(usize::from(these_keys.params().n()), shares.len());
+    assert_eq!(these_keys.params().i(), i);
+    assert_eq!(these_keys.secret_share(), shares[usize::from(i - 1)]);
+    assert_eq!(&hex::encode(these_keys.group_key().to_bytes().as_ref()), vectors.group_key);
+    keys.insert(i, these_keys);
+  }
+
+  keys
+}
+
+pub fn test_with_vectors<
+  R: RngCore + CryptoRng,
+  C: Curve,
+  H: Hram<C>
+>(rng: &mut R, vectors: Vectors) {
+  // Do basic tests before trying the vectors
+  test_curve::<_, C>(&mut *rng);
+  test_schnorr::<_, C>(rng);
+
+  // Test against the vectors
+  let keys = vectors_to_multisig_keys::<C>(&vectors);
+  let group_key = G_from_slice::<C::G>(&hex::decode(vectors.group_key).unwrap()).unwrap();
+  assert_eq!(
+    C::GENERATOR * F_from_slice::<C::F>(&hex::decode(vectors.group_secret).unwrap()).unwrap(),
+    group_key
+  );
+  assert_eq!(
+    recover(&keys),
+    F_from_slice::<C::F>(&hex::decode(vectors.group_secret).unwrap()).unwrap()
+  );
+
+  let mut machines = vec![];
+  for i in vectors.included {
+    machines.push((
+      *i,
+      AlgorithmMachine::new(
+        Schnorr::<C, H>::new(),
+        Arc::new(keys[i].clone()),
+        vectors.included.clone()
+      ).unwrap()
+    ));
+  }
+
+  let mut commitments = HashMap::new();
+  let mut c = 0;
+  let mut machines = machines.drain(..).map(|(i, machine)| {
+    let nonces = [
+      F_from_slice::<C::F>(&hex::decode(vectors.nonces[c][0]).unwrap()).unwrap(),
+      F_from_slice::<C::F>(&hex::decode(vectors.nonces[c][1]).unwrap()).unwrap()
+    ];
+    c += 1;
+
+    let mut serialized = (C::GENERATOR * nonces[0]).to_bytes().as_ref().to_vec();
+    serialized.extend((C::GENERATOR * nonces[1]).to_bytes().as_ref());
+
+    let (machine, serialized) = machine.unsafe_override_preprocess(
+      PreprocessPackage { nonces: vec![nonces], serialized: serialized.clone() }
+    );
+
+    commitments.insert(i, serialized);
+    (i, machine)
+  }).collect::<Vec<_>>();
+
+  let mut shares = HashMap::new();
+  c = 0;
+  let mut machines = machines.drain(..).map(|(i, machine)| {
+    let (machine, share) = machine.sign(
+      commitments.clone(),
+      &hex::decode(vectors.msg).unwrap()
+    ).unwrap();
+
+    assert_eq!(share, hex::decode(vectors.sig_shares[c]).unwrap());
+    c += 1;
+
+    shares.insert(i, share);
+    (i, machine)
+  }).collect::<HashMap<_, _>>();
+
+  for (_, machine) in machines.drain() {
+    let sig = machine.complete(shares.clone()).unwrap();
+    let mut serialized = sig.R.to_bytes().as_ref().to_vec();
+    serialized.extend(sig.s.to_repr().as_ref());
+    assert_eq!(hex::encode(serialized), vectors.sig);
+  }
+}

crypto/multiexp/Cargo.toml

@@ -3,13 +3,22 @@ name = "multiexp"
 version = "0.1.0"
 description = "Multiexponentation algorithms for ff/group"
 license = "MIT"
+repository = "https://github.com/serai-dex/serai"
 authors = ["Luke Parker <lukeparker5132@gmail.com>"]
+keywords = ["multiexp", "ff", "group"]
 edition = "2021"
 
 [dependencies]
-group = "0.11"
+ff = "0.12"
+group = "0.12"
 
 rand_core = { version = "0.6", optional = true }
 
+[dev-dependencies]
+rand_core = "0.6"
+
+k256 = { version = "0.11", features = ["bits"] }
+dalek-ff-group = { path = "../dalek-ff-group" }
+
 [features]
 batch = ["rand_core"]

crypto/multiexp/README.md

@@ -0,0 +1,6 @@
+# Multiexp
+
+A multiexp implementation for ff/group implementing Straus and Pippenger. A
+batch verification API is also available via the "batch" feature, which enables
+secure multiexponentation batch verification given a series of values which
+should sum to 0, identifying which doesn't via binary search if they don't.

crypto/multiexp/src/batch.rs

@@ -0,0 +1,84 @@
+use rand_core::{RngCore, CryptoRng};
+
+use ff::{Field, PrimeFieldBits};
+use group::Group;
+
+use crate::{multiexp, multiexp_vartime};
+
+#[cfg(feature = "batch")]
+pub struct BatchVerifier<Id: Copy, G: Group>(Vec<(Id, Vec<(G::Scalar, G)>)>);
+
+#[cfg(feature = "batch")]
+impl<Id: Copy, G: Group> BatchVerifier<Id, G> where <G as Group>::Scalar: PrimeFieldBits {
+  pub fn new(capacity: usize) -> BatchVerifier<Id, G> {
+    BatchVerifier(Vec::with_capacity(capacity))
+  }
+
+  pub fn queue<
+    R: RngCore + CryptoRng,
+    I: IntoIterator<Item = (G::Scalar, G)>
+  >(&mut self, rng: &mut R, id: Id, pairs: I) {
+    // Define a unique scalar factor for this set of variables so individual items can't overlap
+    let u = if self.0.len() == 0 {
+      G::Scalar::one()
+    } else {
+      let mut weight;
+      // Ensure it's non-zero, as a zero scalar would cause this item to pass no matter what
+      while {
+        weight = G::Scalar::random(&mut *rng);
+        weight.is_zero().into()
+      } {}
+      weight
+    };
+    self.0.push((id, pairs.into_iter().map(|(scalar, point)| (scalar * u, point)).collect()));
+  }
+
+  #[must_use]
+  pub fn verify(&self) -> bool {
+    multiexp(
+      &self.0.iter().flat_map(|pairs| pairs.1.iter()).cloned().collect::<Vec<_>>()
+    ).is_identity().into()
+  }
+
+  #[must_use]
+  pub fn verify_vartime(&self) -> bool {
+    multiexp_vartime(
+      &self.0.iter().flat_map(|pairs| pairs.1.iter()).cloned().collect::<Vec<_>>()
+    ).is_identity().into()
+  }
+
+  // A constant time variant may be beneficial for robust protocols
+  pub fn blame_vartime(&self) -> Option<Id> {
+    let mut slice = self.0.as_slice();
+    while slice.len() > 1 {
+      let split = slice.len() / 2;
+      if multiexp_vartime(
+        &slice[.. split].iter().flat_map(|pairs| pairs.1.iter()).cloned().collect::<Vec<_>>()
+      ).is_identity().into() {
+        slice = &slice[split ..];
+      } else {
+        slice = &slice[.. split];
+      }
+    }
+
+    slice.get(0).filter(
+      |(_, value)| !bool::from(multiexp_vartime(value).is_identity())
+    ).map(|(id, _)| *id)
+  }
+
+  pub fn verify_with_vartime_blame(&self) -> Result<(), Id> {
+    if self.verify() {
+      Ok(())
+    } else {
+      Err(self.blame_vartime().unwrap())
+    }
+  }
+
+  pub fn verify_vartime_with_vartime_blame(&self) -> Result<(), Id> {
+    if self.verify_vartime() {
+      Ok(())
+    } else {
+      Err(self.blame_vartime().unwrap())
+    }
+  }
+}

crypto/multiexp/src/lib.rs

@@ -1,156 +1,176 @@
-use group::{ff::PrimeField, Group};
+use ff::PrimeFieldBits;
+use group::Group;
+
+mod straus;
+use straus::*;
+
+mod pippenger;
+use pippenger::*;
 
 #[cfg(feature = "batch")]
-use group::ff::Field;
+mod batch;
 #[cfg(feature = "batch")]
-use rand_core::{RngCore, CryptoRng};
+pub use batch::BatchVerifier;
 
-fn prep<
-  G: Group,
-  I: IntoIterator<Item = (G::Scalar, G)>
->(pairs: I, little: bool) -> (Vec<Vec<u8>>, Vec<[G; 16]>) {
-  let mut nibbles = vec![];
-  let mut tables = vec![];
-  for pair in pairs.into_iter() {
-    let p = nibbles.len();
-    nibbles.push(vec![]);
-    {
-      let mut repr = pair.0.to_repr();
-      let bytes = repr.as_mut();
-      if !little {
-        bytes.reverse();
-      }
+#[cfg(test)]
+mod tests;
 
-      nibbles[p].resize(bytes.len() * 2, 0);
-      for i in 0 .. bytes.len() {
-        nibbles[p][i * 2] = bytes[i] & 0b1111;
-        nibbles[p][(i * 2) + 1] = (bytes[i] >> 4) & 0b1111;
-      }
+pub(crate) fn prep_bits<G: Group>(
+  pairs: &[(G::Scalar, G)],
+  window: u8
+) -> Vec<Vec<u8>> where G::Scalar: PrimeFieldBits {
+  let w_usize = usize::from(window);
+
+  let mut groupings = vec![];
+  for pair in pairs {
+    let p = groupings.len();
+    let bits = pair.0.to_le_bits();
+    groupings.push(vec![0; (bits.len() + (w_usize - 1)) / w_usize]);
+
+    for (i, bit) in bits.into_iter().enumerate() {
+      let bit = bit as u8;
+      debug_assert_eq!(bit | 1, 1);
+      groupings[p][i / w_usize] |= bit << (i % w_usize);
     }
+  }
 
-    tables.push([G::identity(); 16]);
+  groupings
+}
+
+pub(crate) fn prep_tables<G: Group>(
+  pairs: &[(G::Scalar, G)],
+  window: u8
+) -> Vec<Vec<G>> {
+  let mut tables = Vec::with_capacity(pairs.len());
+  for pair in pairs {
+    let p = tables.len();
+    tables.push(vec![G::identity(); 2_usize.pow(window.into())]);
     let mut accum = G::identity();
-    for i in 1 .. 16 {
+    for i in 1 .. tables[p].len() {
       accum += pair.1;
       tables[p][i] = accum;
     }
   }
-
-  (nibbles, tables)
+  tables
 }
 
-// An implementation of Straus, with a extremely minimal API that lets us add other algorithms in
-// the future. Takes in an iterator of scalars and points with a boolean for if the scalars are
-// little endian encoded in their Reprs or not
-pub fn multiexp<
-  G: Group,
-  I: IntoIterator<Item = (G::Scalar, G)>
->(pairs: I, little: bool) -> G {
-  let (nibbles, tables) = prep(pairs, little);
-
-  let mut res = G::identity();
-  for b in (0 .. nibbles[0].len()).rev() {
-    for _ in 0 .. 4 {
-      res = res.double();
-    }
-
-    for s in 0 .. tables.len() {
-      res += tables[s][usize::from(nibbles[s][b])];
-    }
-  }
-  res
+#[derive(Clone, Copy, PartialEq, Eq, Debug)]
+enum Algorithm {
+  Null,
+  Single,
+  Straus(u8),
+  Pippenger(u8)
 }
 
-pub fn multiexp_vartime<
-  G: Group,
-  I: IntoIterator<Item = (G::Scalar, G)>
->(pairs: I, little: bool) -> G {
-  let (nibbles, tables) = prep(pairs, little);
+/*
+Release (with runs 20, so all of these are off by 20x):
 
-  let mut res = G::identity();
-  for b in (0 .. nibbles[0].len()).rev() {
-    for _ in 0 .. 4 {
-      res = res.double();
-    }
+k256
+Straus 3 is more efficient at 5 with 678µs per
+Straus 4 is more efficient at 10 with 530µs per
+Straus 5 is more efficient at 35 with 467µs per
 
-    for s in 0 .. tables.len() {
-      if nibbles[s][b] != 0 {
-        res += tables[s][usize::from(nibbles[s][b])];
-      }
-    }
-  }
-  res
-}
+Pippenger 5 is more efficient at 125 with 431µs per
+Pippenger 6 is more efficient at 275 with 349µs per
+Pippenger 7 is more efficient at 375 with 360µs per
 
-#[cfg(feature = "batch")]
-pub struct BatchVerifier<Id: Copy, G: Group>(Vec<(Id, Vec<(G::Scalar, G)>)>, bool);
+dalek
+Straus 3 is more efficient at 5 with 519µs per
+Straus 4 is more efficient at 10 with 376µs per
+Straus 5 is more efficient at 170 with 330µs per
 
-#[cfg(feature = "batch")]
-impl<Id: Copy, G: Group> BatchVerifier<Id, G> {
-  pub fn new(capacity: usize, endian: bool) -> BatchVerifier<Id, G> {
-    BatchVerifier(Vec::with_capacity(capacity), endian)
+Pippenger 5 is more efficient at 125 with 305µs per
+Pippenger 6 is more efficient at 275 with 250µs per
+Pippenger 7 is more efficient at 450 with 205µs per
+Pippenger 8 is more efficient at 800 with 213µs per
+
+Debug (with runs 5, so...):
+
+k256
+Straus 3 is more efficient at 5 with 2532µs per
+Straus 4 is more efficient at 10 with 1930µs per
+Straus 5 is more efficient at 80 with 1632µs per
+
+Pippenger 5 is more efficient at 150 with 1441µs per
+Pippenger 6 is more efficient at 300 with 1235µs per
+Pippenger 7 is more efficient at 475 with 1182µs per
+Pippenger 8 is more efficient at 625 with 1170µs per
+
+dalek:
+Straus 3 is more efficient at 5 with 971µs per
+Straus 4 is more efficient at 10 with 782µs per
+Straus 5 is more efficient at 75 with 778µs per
+Straus 6 is more efficient at 165 with 867µs per
+
+Pippenger 5 is more efficient at 125 with 677µs per
+Pippenger 6 is more efficient at 250 with 655µs per
+Pippenger 7 is more efficient at 475 with 500µs per
+Pippenger 8 is more efficient at 875 with 499µs per
+*/
+fn algorithm(len: usize) -> Algorithm {
+  #[cfg(not(debug_assertions))]
+  if len == 0 {
+    Algorithm::Null
+  } else if len == 1 {
+    Algorithm::Single
+  } else if len < 10 {
+    // Straus 2 never showed a performance benefit, even with just 2 elements
+    Algorithm::Straus(3)
+  } else if len < 20 {
+    Algorithm::Straus(4)
+  } else if len < 50 {
+    Algorithm::Straus(5)
+  } else if len < 100 {
+    Algorithm::Pippenger(4)
+  } else if len < 125 {
+    Algorithm::Pippenger(5)
+  } else if len < 275 {
+    Algorithm::Pippenger(6)
+  } else if len < 400 {
+    Algorithm::Pippenger(7)
+  } else {
+    Algorithm::Pippenger(8)
   }
 
-  pub fn queue<
-    R: RngCore + CryptoRng,
-    I: IntoIterator<Item = (G::Scalar, G)>
-  >(&mut self, rng: &mut R, id: Id, pairs: I) {
-    // Define a unique scalar factor for this set of variables so individual items can't overlap
-    let u = if self.0.len() == 0 {
-      G::Scalar::one()
-    } else {
-      G::Scalar::random(rng)
-    };
-    self.0.push((id, pairs.into_iter().map(|(scalar, point)| (scalar * u, point)).collect()));
-  }
-
-  pub fn verify(&self) -> bool {
-    multiexp(
-      self.0.iter().flat_map(|pairs| pairs.1.iter()).cloned(),
-      self.1
-    ).is_identity().into()
-  }
-
-  pub fn verify_vartime(&self) -> bool {
-    multiexp_vartime(
-      self.0.iter().flat_map(|pairs| pairs.1.iter()).cloned(),
-      self.1
-    ).is_identity().into()
-  }
-
-  // A constant time variant may be beneficial for robust protocols
-  pub fn blame_vartime(&self) -> Option<Id> {
-    let mut slice = self.0.as_slice();
-    while slice.len() > 1 {
-      let split = slice.len() / 2;
-      if multiexp_vartime(
-        slice[.. split].iter().flat_map(|pairs| pairs.1.iter()).cloned(),
-        self.1
-      ).is_identity().into() {
-        slice = &slice[split ..];
-      } else {
-        slice = &slice[.. split];
-      }
-    }
-
-    slice.get(0).filter(
-      |(_, value)| !bool::from(multiexp_vartime(value.clone(), self.1).is_identity())
-    ).map(|(id, _)| *id)
-  }
-
-  pub fn verify_with_vartime_blame(&self) -> Result<(), Id> {
-    if self.verify() {
-      Ok(())
-    } else {
-      Err(self.blame_vartime().unwrap())
-    }
-  }
-
-  pub fn verify_vartime_with_vartime_blame(&self) -> Result<(), Id> {
-    if self.verify_vartime() {
-      Ok(())
-    } else {
-      Err(self.blame_vartime().unwrap())
-    }
+  #[cfg(debug_assertions)]
+  if len == 0 {
+    Algorithm::Null
+  } else if len == 1 {
+    Algorithm::Single
+  } else if len < 10 {
+    Algorithm::Straus(3)
+  } else if len < 80 {
+    Algorithm::Straus(4)
+  } else if len < 100 {
+    Algorithm::Straus(5)
+  } else if len < 125 {
+    Algorithm::Pippenger(4)
+  } else if len < 275 {
+    Algorithm::Pippenger(5)
+  } else if len < 475 {
+    Algorithm::Pippenger(6)
+  } else if len < 750 {
+    Algorithm::Pippenger(7)
+  } else {
+    Algorithm::Pippenger(8)
+  }
+}
+
+// Performs a multiexp, automatically selecting the optimal algorithm based on amount of pairs
+pub fn multiexp<G: Group>(pairs: &[(G::Scalar, G)]) -> G where G::Scalar: PrimeFieldBits {
+  match algorithm(pairs.len()) {
+    Algorithm::Null => Group::identity(),
+    Algorithm::Single => pairs[0].1 * pairs[0].0,
+    Algorithm::Straus(window) => straus(pairs, window),
+    Algorithm::Pippenger(window) => pippenger(pairs, window)
+  }
+}
+
+pub fn multiexp_vartime<G: Group>(pairs: &[(G::Scalar, G)]) -> G where G::Scalar: PrimeFieldBits {
+  match algorithm(pairs.len()) {
+    Algorithm::Null => Group::identity(),
+    Algorithm::Single => pairs[0].1 * pairs[0].0,
+    Algorithm::Straus(window) => straus_vartime(pairs, window),
+    Algorithm::Pippenger(window) => pippenger_vartime(pairs, window)
   }
 }

crypto/multiexp/src/pippenger.rs

@@ -0,0 +1,63 @@
+use ff::PrimeFieldBits;
+use group::Group;
+
+use crate::prep_bits;
+
+pub(crate) fn pippenger<G: Group>(
+  pairs: &[(G::Scalar, G)],
+  window: u8
+) -> G where G::Scalar: PrimeFieldBits {
+  let bits = prep_bits(pairs, window);
+
+  let mut res = G::identity();
+  for n in (0 .. bits[0].len()).rev() {
+    for _ in 0 .. window {
+      res = res.double();
+    }
+
+    let mut buckets = vec![G::identity(); 2_usize.pow(window.into())];
+    for p in 0 .. bits.len() {
+      buckets[usize::from(bits[p][n])] += pairs[p].1;
+    }
+
+    let mut intermediate_sum = G::identity();
+    for b in (1 .. buckets.len()).rev() {
+      intermediate_sum += buckets[b];
+      res += intermediate_sum;
+    }
+  }
+
+  res
+}
+
+pub(crate) fn pippenger_vartime<G: Group>(
+  pairs: &[(G::Scalar, G)],
+  window: u8
+) -> G where G::Scalar: PrimeFieldBits {
+  let bits = prep_bits(pairs, window);
+
+  let mut res = G::identity();
+  for n in (0 .. bits[0].len()).rev() {
+    if n != (bits[0].len() - 1) {
+      for _ in 0 .. window {
+        res = res.double();
+      }
+    }
+
+    let mut buckets = vec![G::identity(); 2_usize.pow(window.into())];
+    for p in 0 .. bits.len() {
+      let nibble = usize::from(bits[p][n]);
+      if nibble != 0 {
+        buckets[nibble] += pairs[p].1;
+      }
+    }
+
+    let mut intermediate_sum = G::identity();
+    for b in (1 .. buckets.len()).rev() {
+      intermediate_sum += buckets[b];
+      res += intermediate_sum;
+    }
+  }
+
+  res
+}

crypto/multiexp/src/straus.rs

@@ -0,0 +1,49 @@
+use ff::PrimeFieldBits;
+use group::Group;
+
+use crate::{prep_bits, prep_tables};
+
+pub(crate) fn straus<G: Group>(
+  pairs: &[(G::Scalar, G)],
+  window: u8
+) -> G where G::Scalar: PrimeFieldBits {
+  let groupings = prep_bits(pairs, window);
+  let tables = prep_tables(pairs, window);
+
+  let mut res = G::identity();
+  for b in (0 .. groupings[0].len()).rev() {
+    for _ in 0 .. window {
+      res = res.double();
+    }
+
+    for s in 0 .. tables.len() {
+      res += tables[s][usize::from(groupings[s][b])];
+    }
+  }
+  res
+}
+
+pub(crate) fn straus_vartime<G: Group>(
+  pairs: &[(G::Scalar, G)],
+  window: u8
+) -> G where G::Scalar: PrimeFieldBits {
+  let groupings = prep_bits(pairs, window);
+  let tables = prep_tables(pairs, window);
+
+  let mut res = G::identity();
+  for b in (0 .. groupings[0].len()).rev() {
+    if b != (groupings[0].len() - 1) {
+      for _ in 0 .. window {
+        res = res.double();
+      }
+    }
+
+    for s in 0 .. tables.len() {
+      if groupings[s][b] != 0 {
+        res += tables[s][usize::from(groupings[s][b])];
+      }
+    }
+  }
+
+  res
+}

crypto/multiexp/src/tests/mod.rs

@@ -0,0 +1,112 @@
+use std::time::Instant;
+
+use rand_core::OsRng;
+
+use ff::{Field, PrimeFieldBits};
+use group::Group;
+
+use k256::ProjectivePoint;
+use dalek_ff_group::EdwardsPoint;
+
+use crate::{straus, pippenger, multiexp, multiexp_vartime};
+
+#[allow(dead_code)]
+fn benchmark_internal<G: Group>(straus_bool: bool) where G::Scalar: PrimeFieldBits {
+  let runs: usize = 20;
+
+  let mut start = 0;
+  let mut increment: usize = 5;
+  let mut total: usize = 250;
+  let mut current = 2;
+
+  if !straus_bool {
+    start = 100;
+    increment = 25;
+    total = 1000;
+    current = 4;
+  };
+
+  let mut pairs = Vec::with_capacity(total);
+  let mut sum = G::identity();
+
+  for _ in 0 .. start {
+    pairs.push((G::Scalar::random(&mut OsRng), G::generator() * G::Scalar::random(&mut OsRng)));
+    sum += pairs[pairs.len() - 1].1 * pairs[pairs.len() - 1].0;
+  }
+
+  for _ in 0 .. (total / increment) {
+    for _ in 0 .. increment {
+      pairs.push((G::Scalar::random(&mut OsRng), G::generator() * G::Scalar::random(&mut OsRng)));
+      sum += pairs[pairs.len() - 1].1 * pairs[pairs.len() - 1].0;
+    }
+
+    let now = Instant::now();
+    for _ in 0 .. runs {
+      if straus_bool {
+        assert_eq!(straus(&pairs, current), sum);
+      } else {
+        assert_eq!(pippenger(&pairs, current), sum);
+      }
+    }
+    let current_per = now.elapsed().as_micros() / u128::try_from(pairs.len()).unwrap();
+
+    let now = Instant::now();
+    for _ in 0 .. runs {
+      if straus_bool {
+        assert_eq!(straus(&pairs, current + 1), sum);
+      } else {
+        assert_eq!(pippenger(&pairs, current + 1), sum);
+      }
+    }
+    let next_per = now.elapsed().as_micros() / u128::try_from(pairs.len()).unwrap();
+
+    if next_per < current_per {
+      current += 1;
+      println!(
+        "{} {} is more efficient at {} with {}µs per",
+        if straus_bool { "Straus" } else { "Pippenger" }, current, pairs.len(), next_per
+      );
+      if current >= 8 {
+        return;
+      }
+    }
+  }
+}
+
+fn test_multiexp<G: Group>() where G::Scalar: PrimeFieldBits {
+  let mut pairs = Vec::with_capacity(1000);
+  let mut sum = G::identity();
+  for _ in 0 .. 10 {
+    for _ in 0 .. 100 {
+      pairs.push((G::Scalar::random(&mut OsRng), G::generator() * G::Scalar::random(&mut OsRng)));
+      sum += pairs[pairs.len() - 1].1 * pairs[pairs.len() - 1].0;
+    }
+    assert_eq!(multiexp(&pairs), sum);
+    assert_eq!(multiexp_vartime(&pairs), sum);
+  }
+}
+
+#[test]
+fn test_secp256k1() {
+  test_multiexp::<ProjectivePoint>();
+}
+
+#[test]
+fn test_ed25519() {
+  test_multiexp::<EdwardsPoint>();
+}
+
+#[ignore]
+#[test]
+fn benchmark() {
+  // Activate the processor's boost clock
+  for _ in 0 .. 30 {
+    test_multiexp::<ProjectivePoint>();
+  }
+
+  benchmark_internal::<ProjectivePoint>(true);
+  benchmark_internal::<ProjectivePoint>(false);
+
+  benchmark_internal::<EdwardsPoint>(true);
+  benchmark_internal::<EdwardsPoint>(false);
+}

crypto/transcript/Cargo.toml

@@ -1,15 +1,19 @@
 [package]
-name = "transcript"
-version = "0.1.0"
-description = "A simple transcript definition"
+name = "flexible-transcript"
+version = "0.1.2"
+description = "A simple transcript trait definition, along with viable options"
 license = "MIT"
+repository = "https://github.com/serai-dex/serai"
 authors = ["Luke Parker <lukeparker5132@gmail.com>"]
+keywords = ["transcript"]
 edition = "2021"
 
 [dependencies]
 digest = "0.10"
 
+blake2 = { version = "0.10", optional = true }
 merlin = { version = "3", optional = true }
 
 [features]
+recommended = ["blake2"]
 merlin = ["dep:merlin"]

crypto/transcript/README.md

@@ -0,0 +1,27 @@
+# Flexible Transcript
+
+Flexible Transcript is a crate offering:
+- `Transcript`, a trait offering functions transcripts should implement.
+- `DigestTranscript`, a competent transcript format instantiated against a
+provided hash function.
+- `MerlinTranscript`, a wrapper of `merlin` into the trait (available via the
+`merlin` feature).
+- `RecommendedTranscript`, a transcript recommended for usage in applications.
+  Currently, this is `DigestTranscript<Blake2b512>` (available via the
+  `recommended` feature).
+
+The trait was created while working on an IETF draft which defined an incredibly
+simple transcript format. Extensions of the protocol would quickly require a
+more competent format, yet implementing the one specified was mandatory to meet
+the specification. Accordingly, the library implementing the draft defined an
+`IetfTranscript`, dropping labels and not allowing successive challenges, yet
+thanks to the trait, allowed protocols building on top to provide their own
+transcript format as needed.
+
+`DigestTranscript` takes in any hash function implementing `Digest`, offering a
+secure transcript format around it. All items are prefixed by a flag, denoting
+their type, and their length.
+
+`MerlinTranscript` was used to justify the API, and if any issues existed with
+`DigestTranscript`, enable a fallback. It was also meant as a way to be
+compatible with existing Rust projects using `merlin`.

crypto/transcript/src/lib.rs

@@ -1,57 +1,101 @@
-use core::{marker::PhantomData, fmt::Debug};
+#![no_std]
 
-#[cfg(features = "merlin")]
+#[cfg(feature = "merlin")]
 mod merlin;
-#[cfg(features = "merlin")]
-pub use merlin::MerlinTranscript;
+#[cfg(feature = "merlin")]
+pub use crate::merlin::MerlinTranscript;
 
-use digest::Digest;
+use digest::{typenum::type_operators::IsGreaterOrEqual, consts::U256, Digest, Output};
 
 pub trait Transcript {
-  fn domain_separate(&mut self, label: &[u8]);
+  type Challenge: Clone + Send + Sync + AsRef<[u8]>;
+
+  /// Create a new transcript with the specified name
+  fn new(name: &'static [u8]) -> Self;
+
+  /// Apply a domain separator to the transcript
+  fn domain_separate(&mut self, label: &'static [u8]);
+
+  /// Append a message to the transcript
   fn append_message(&mut self, label: &'static [u8], message: &[u8]);
-  fn challenge(&mut self, label: &'static [u8]) -> Vec<u8>;
+
+  /// Produce a challenge. This MUST update the transcript as it does so, preventing the same
+  /// challenge from being generated multiple times
+  fn challenge(&mut self, label: &'static [u8]) -> Self::Challenge;
+
+  /// Produce a RNG seed. Helper function for parties needing to generate random data from an
+  /// agreed upon state. Internally calls the challenge function for the needed bytes, converting
+  /// them to the seed format rand_core expects
   fn rng_seed(&mut self, label: &'static [u8]) -> [u8; 32];
 }
 
+enum DigestTranscriptMember {
+  Name,
+  Domain,
+  Label,
+  Value,
+  Challenge
+}
+
+impl DigestTranscriptMember {
+  fn as_u8(&self) -> u8 {
+    match self {
+      DigestTranscriptMember::Name => 0,
+      DigestTranscriptMember::Domain => 1,
+      DigestTranscriptMember::Label => 2,
+      DigestTranscriptMember::Value => 3,
+      DigestTranscriptMember::Challenge => 4
+    }
+  }
+}
+
+/// A trait defining Digests with at least a 256-byte output size, assuming at least a 128-bit
+/// level of security accordingly
+pub trait SecureDigest: Clone + Digest {}
+impl<D: Clone + Digest> SecureDigest for D where D::OutputSize: IsGreaterOrEqual<U256> {}
+
+/// A simple transcript format constructed around the specified hash algorithm
 #[derive(Clone, Debug)]
-pub struct DigestTranscript<D: Digest>(Vec<u8>, PhantomData<D>);
+pub struct DigestTranscript<D: SecureDigest>(D);
 
-impl<D: Digest> PartialEq for DigestTranscript<D> {
-  fn eq(&self, other: &DigestTranscript<D>) -> bool {
-    self.0 == other.0
+impl<D: SecureDigest> DigestTranscript<D> {
+  fn append(&mut self, kind: DigestTranscriptMember, value: &[u8]) {
+    self.0.update(&[kind.as_u8()]);
+    // Assumes messages don't exceed 16 exabytes
+    self.0.update(u64::try_from(value.len()).unwrap().to_le_bytes());
+    self.0.update(value);
   }
 }
 
-impl<D: Digest> DigestTranscript<D> {
-  pub fn new(label: Vec<u8>) -> Self {
-    DigestTranscript(label, PhantomData)
-  }
-}
+impl<D: SecureDigest> Transcript for DigestTranscript<D> {
+  type Challenge = Output<D>;
+
+  fn new(name: &'static [u8]) -> Self {
+    let mut res = DigestTranscript(D::new());
+    res.append(DigestTranscriptMember::Name, name);
+    res
+  }
 
-impl<D: Digest> Transcript for DigestTranscript<D> {
-  // It may be beneficial for each domain to be a nested transcript which is itself length prefixed
-  // This would go further than Merlin though and require an accurate end_domain function which has
-  // frustrations not worth bothering with when this shouldn't actually be meaningful
   fn domain_separate(&mut self, label: &[u8]) {
-    self.append_message(b"domain", label);
+    self.append(DigestTranscriptMember::Domain, label);
   }
 
   fn append_message(&mut self, label: &'static [u8], message: &[u8]) {
-    self.0.extend(label);
-    // Assumes messages don't exceed 16 exabytes
-    self.0.extend(u64::try_from(message.len()).unwrap().to_le_bytes());
-    self.0.extend(message);
+    self.append(DigestTranscriptMember::Label, label);
+    self.append(DigestTranscriptMember::Value, message);
   }
 
-  fn challenge(&mut self, label: &'static [u8]) -> Vec<u8> {
-    self.0.extend(label);
-    D::new().chain_update(&self.0).finalize().to_vec()
+  fn challenge(&mut self, label: &'static [u8]) -> Self::Challenge {
+    self.append(DigestTranscriptMember::Challenge, label);
+    self.0.clone().finalize()
   }
 
   fn rng_seed(&mut self, label: &'static [u8]) -> [u8; 32] {
     let mut seed = [0; 32];
-    seed.copy_from_slice(&self.challenge(label)[0 .. 32]);
+    seed.copy_from_slice(&self.challenge(label)[.. 32]);
     seed
   }
 }
+
+#[cfg(feature = "recommended")]
+pub type RecommendedTranscript = DigestTranscript<blake2::Blake2b512>;

crypto/transcript/src/merlin.rs

@@ -1,16 +1,27 @@
-use core::{marker::PhantomData, fmt::{Debug, Formatter}};
+use core::fmt::{Debug, Formatter};
 
-use digest::Digest;
+use crate::Transcript;
 
-#[derive(Clone, PartialEq)]
+#[derive(Clone)]
 pub struct MerlinTranscript(pub merlin::Transcript);
 // Merlin doesn't implement Debug so provide a stub which won't panic
 impl Debug for MerlinTranscript {
-  fn fmt(&self, _: &mut Formatter<'_>) -> Result<(), std::fmt::Error> { Ok(()) }
+  fn fmt(&self, _: &mut Formatter<'_>) -> Result<(), core::fmt::Error> { Ok(()) }
 }
 
 impl Transcript for MerlinTranscript {
-  fn domain_separate(&mut self, label: &[u8]) {
+  // Uses a challenge length of 64 bytes to support wide reduction on generated scalars
+  // From a security level standpoint, this should just be 32 bytes
+  // From a Merlin standpoint, this should be variable per call
+  // From a practical standpoint, this is a demo file not planned to be used and anything using
+  // this wrapper should be secure with this setting
+  type Challenge = [u8; 64];
+
+  fn new(name: &'static [u8]) -> Self {
+    MerlinTranscript(merlin::Transcript::new(name))
+  }
+
+  fn domain_separate(&mut self, label: &'static [u8]) {
     self.append_message(b"dom-sep", label);
   }
 
@@ -18,21 +29,15 @@ impl Transcript for MerlinTranscript {
     self.0.append_message(label, message);
   }
 
-  fn challenge(&mut self, label: &'static [u8]) -> Vec<u8> {
-    let mut challenge = vec![];
-    // Uses a challenge length of 64 bytes to support wide reduction on generated scalars
-    // From a security level standpoint, this should just be 32 bytes
-    // From a Merlin standpoint, this should be variable per call
-    // From a practical standpoint, this is a demo file not planned to be used and anything using
-    // this wrapper is fine without any settings it uses
-    challenge.resize(64, 0);
+  fn challenge(&mut self, label: &'static [u8]) -> Self::Challenge {
+    let mut challenge = [0; 64];
     self.0.challenge_bytes(label, &mut challenge);
     challenge
   }
 
   fn rng_seed(&mut self, label: &'static [u8]) -> [u8; 32] {
     let mut seed = [0; 32];
-    transcript.challenge_bytes(label, &mut seed);
+    seed.copy_from_slice(&self.challenge(label)[.. 32]);
     seed
   }
 }