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k256: impl ReduceNonZero<U512> for Scalar #474

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merged 2 commits into from Dec 3, 2021
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k256: impl ReduceNonZero<U512> for Scalar #474

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0583d87
Add non-biased/non-zero constructors to Scalar
fjarri Sep 14, 2021
95d595c
k256: impl `ReduceNonZero<U512>` for `Scalar`
tarcieri Dec 3, 2021
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4 changes: 2 additions & 2 deletions Cargo.lock
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2 changes: 1 addition & 1 deletion k256/Cargo.toml
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Expand Up @@ -19,7 +19,7 @@ rust-version = "1.56"

[dependencies]
cfg-if = "1.0"
elliptic-curve = { version = "0.11", default-features = false, features = ["hazmat", "sec1"] }
elliptic-curve = { version = "0.11.3", default-features = false, features = ["hazmat", "sec1"] }
sec1 = { version = "0.2", default-features = false }

# optional dependencies
Expand Down
31 changes: 30 additions & 1 deletion k256/src/arithmetic/scalar.rs
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Expand Up @@ -12,7 +12,7 @@ use elliptic_curve::{
bigint::{nlimbs, prelude::*, Limb, LimbUInt, U256, U512},
generic_array::arr,
group::ff::{Field, PrimeField},
ops::Reduce,
ops::{Reduce, ReduceNonZero},
rand_core::{CryptoRng, RngCore},
subtle::{
Choice, ConditionallySelectable, ConstantTimeEq, ConstantTimeGreater, ConstantTimeLess,
Expand Down Expand Up @@ -581,6 +581,12 @@ impl Reduce<U512> for Scalar {
}
}

impl ReduceNonZero<U512> for Scalar {
fn from_uint_reduced_nonzero(w: U512) -> Self {
WideScalar(w).reduce_nonzero()
}
}

#[cfg(feature = "bits")]
#[cfg_attr(docsrs, doc(cfg(feature = "bits")))]
impl From<&Scalar> for ScalarBits {
Expand Down Expand Up @@ -628,7 +634,10 @@ mod tests {
use super::Scalar;
use crate::arithmetic::dev::{biguint_to_bytes, bytes_to_biguint};
use elliptic_curve::{
bigint::U512,
ff::{Field, PrimeField},
generic_array::GenericArray,
ops::Reduce,
IsHigh,
};
use num_bigint::{BigUint, ToBigUint};
Expand Down Expand Up @@ -745,6 +754,15 @@ mod tests {
assert_eq!((a - &a).is_zero().unwrap_u8(), 1);
}

#[test]
fn from_wide_bytes_reduced() {
let m = Scalar::modulus_as_biguint();
let b = [0xffu8; 64];
let s = <Scalar as Reduce<U512>>::from_be_bytes_reduced(GenericArray::clone_from_slice(&b));
let s_bu = s.to_biguint().unwrap();
assert!(s_bu < m);
}

prop_compose! {
fn scalar()(bytes in any::<[u8; 32]>()) -> Scalar {
let mut res = bytes_to_biguint(&bytes);
Expand Down Expand Up @@ -843,5 +861,16 @@ mod tests {
let m = Scalar::modulus_as_biguint();
assert_eq!((&inv_bi * &a_bi) % &m, 1.to_biguint().unwrap());
}

#[test]
fn fuzzy_from_wide_bytes_reduced(bytes_hi in any::<[u8; 32]>(), bytes_lo in any::<[u8; 32]>()) {
let m = Scalar::modulus_as_biguint();
let mut bytes = [0u8; 64];
bytes[0..32].clone_from_slice(&bytes_hi);
bytes[32..64].clone_from_slice(&bytes_lo);
let s = <Scalar as Reduce<U512>>::from_be_bytes_reduced(GenericArray::clone_from_slice(&bytes));
let s_bu = s.to_biguint().unwrap();
assert!(s_bu < m);
}
}
}
46 changes: 30 additions & 16 deletions k256/src/arithmetic/scalar/wide32.rs
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Expand Up @@ -230,8 +230,13 @@ impl WideScalar {
Scalar::conditional_select(&res, &res.add(&Scalar::ONE), Choice::from(c as u8))
}

#[inline(always)] // only used in Scalar::mul(), so won't cause binary bloat
pub(super) fn reduce(&self) -> Scalar {
pub(super) fn reduce_impl(&self, modulus_minus_one: bool) -> Scalar {
let neg_modulus0 = if modulus_minus_one {
NEG_MODULUS[0] + 1
} else {
NEG_MODULUS[0]
};

let w = self.0.to_uint_array();
let n0 = w[8];
let n1 = w[9];
Expand All @@ -249,46 +254,46 @@ impl WideScalar {
let c0 = w[0];
let c1 = 0;
let c2 = 0;
let (c0, c1) = muladd_fast(n0, NEG_MODULUS[0], c0, c1);
let (c0, c1) = muladd_fast(n0, neg_modulus0, c0, c1);
let (m0, c0, c1) = (c0, c1, 0);
let (c0, c1) = sumadd_fast(w[1], c0, c1);
let (c0, c1, c2) = muladd(n1, NEG_MODULUS[0], c0, c1, c2);
let (c0, c1, c2) = muladd(n1, neg_modulus0, c0, c1, c2);
let (c0, c1, c2) = muladd(n0, NEG_MODULUS[1], c0, c1, c2);
let (m1, c0, c1, c2) = (c0, c1, c2, 0);
let (c0, c1, c2) = sumadd(w[2], c0, c1, c2);
let (c0, c1, c2) = muladd(n2, NEG_MODULUS[0], c0, c1, c2);
let (c0, c1, c2) = muladd(n2, neg_modulus0, c0, c1, c2);
let (c0, c1, c2) = muladd(n1, NEG_MODULUS[1], c0, c1, c2);
let (c0, c1, c2) = muladd(n0, NEG_MODULUS[2], c0, c1, c2);
let (m2, c0, c1, c2) = (c0, c1, c2, 0);
let (c0, c1, c2) = sumadd(w[3], c0, c1, c2);
let (c0, c1, c2) = muladd(n3, NEG_MODULUS[0], c0, c1, c2);
let (c0, c1, c2) = muladd(n3, neg_modulus0, c0, c1, c2);
let (c0, c1, c2) = muladd(n2, NEG_MODULUS[1], c0, c1, c2);
let (c0, c1, c2) = muladd(n1, NEG_MODULUS[2], c0, c1, c2);
let (c0, c1, c2) = muladd(n0, NEG_MODULUS[3], c0, c1, c2);
let (m3, c0, c1, c2) = (c0, c1, c2, 0);
let (c0, c1, c2) = sumadd(w[4], c0, c1, c2);
let (c0, c1, c2) = muladd(n4, NEG_MODULUS[0], c0, c1, c2);
let (c0, c1, c2) = muladd(n4, neg_modulus0, c0, c1, c2);
let (c0, c1, c2) = muladd(n3, NEG_MODULUS[1], c0, c1, c2);
let (c0, c1, c2) = muladd(n2, NEG_MODULUS[2], c0, c1, c2);
let (c0, c1, c2) = muladd(n1, NEG_MODULUS[3], c0, c1, c2);
let (c0, c1, c2) = sumadd(n0, c0, c1, c2);
let (m4, c0, c1, c2) = (c0, c1, c2, 0);
let (c0, c1, c2) = sumadd(w[5], c0, c1, c2);
let (c0, c1, c2) = muladd(n5, NEG_MODULUS[0], c0, c1, c2);
let (c0, c1, c2) = muladd(n5, neg_modulus0, c0, c1, c2);
let (c0, c1, c2) = muladd(n4, NEG_MODULUS[1], c0, c1, c2);
let (c0, c1, c2) = muladd(n3, NEG_MODULUS[2], c0, c1, c2);
let (c0, c1, c2) = muladd(n2, NEG_MODULUS[3], c0, c1, c2);
let (c0, c1, c2) = sumadd(n1, c0, c1, c2);
let (m5, c0, c1, c2) = (c0, c1, c2, 0);
let (c0, c1, c2) = sumadd(w[6], c0, c1, c2);
let (c0, c1, c2) = muladd(n6, NEG_MODULUS[0], c0, c1, c2);
let (c0, c1, c2) = muladd(n6, neg_modulus0, c0, c1, c2);
let (c0, c1, c2) = muladd(n5, NEG_MODULUS[1], c0, c1, c2);
let (c0, c1, c2) = muladd(n4, NEG_MODULUS[2], c0, c1, c2);
let (c0, c1, c2) = muladd(n3, NEG_MODULUS[3], c0, c1, c2);
let (c0, c1, c2) = sumadd(n2, c0, c1, c2);
let (m6, c0, c1, c2) = (c0, c1, c2, 0);
let (c0, c1, c2) = sumadd(w[7], c0, c1, c2);
let (c0, c1, c2) = muladd(n7, NEG_MODULUS[0], c0, c1, c2);
let (c0, c1, c2) = muladd(n7, neg_modulus0, c0, c1, c2);
let (c0, c1, c2) = muladd(n6, NEG_MODULUS[1], c0, c1, c2);
let (c0, c1, c2) = muladd(n5, NEG_MODULUS[2], c0, c1, c2);
let (c0, c1, c2) = muladd(n4, NEG_MODULUS[3], c0, c1, c2);
Expand Down Expand Up @@ -316,25 +321,25 @@ impl WideScalar {
let c0 = m0;
let c1 = 0;
let c2 = 0;
let (c0, c1) = muladd_fast(m8, NEG_MODULUS[0], c0, c1);
let (c0, c1) = muladd_fast(m8, neg_modulus0, c0, c1);
let (p0, c0, c1) = (c0, c1, 0);
let (c0, c1) = sumadd_fast(m1, c0, c1);
let (c0, c1, c2) = muladd(m9, NEG_MODULUS[0], c0, c1, c2);
let (c0, c1, c2) = muladd(m9, neg_modulus0, c0, c1, c2);
let (c0, c1, c2) = muladd(m8, NEG_MODULUS[1], c0, c1, c2);
let (p1, c0, c1, c2) = (c0, c1, c2, 0);
let (c0, c1, c2) = sumadd(m2, c0, c1, c2);
let (c0, c1, c2) = muladd(m10, NEG_MODULUS[0], c0, c1, c2);
let (c0, c1, c2) = muladd(m10, neg_modulus0, c0, c1, c2);
let (c0, c1, c2) = muladd(m9, NEG_MODULUS[1], c0, c1, c2);
let (c0, c1, c2) = muladd(m8, NEG_MODULUS[2], c0, c1, c2);
let (p2, c0, c1, c2) = (c0, c1, c2, 0);
let (c0, c1, c2) = sumadd(m3, c0, c1, c2);
let (c0, c1, c2) = muladd(m11, NEG_MODULUS[0], c0, c1, c2);
let (c0, c1, c2) = muladd(m11, neg_modulus0, c0, c1, c2);
let (c0, c1, c2) = muladd(m10, NEG_MODULUS[1], c0, c1, c2);
let (c0, c1, c2) = muladd(m9, NEG_MODULUS[2], c0, c1, c2);
let (c0, c1, c2) = muladd(m8, NEG_MODULUS[3], c0, c1, c2);
let (p3, c0, c1, c2) = (c0, c1, c2, 0);
let (c0, c1, c2) = sumadd(m4, c0, c1, c2);
let (c0, c1, c2) = muladd(m12, NEG_MODULUS[0], c0, c1, c2);
let (c0, c1, c2) = muladd(m12, neg_modulus0, c0, c1, c2);
let (c0, c1, c2) = muladd(m11, NEG_MODULUS[1], c0, c1, c2);
let (c0, c1, c2) = muladd(m10, NEG_MODULUS[2], c0, c1, c2);
let (c0, c1, c2) = muladd(m9, NEG_MODULUS[3], c0, c1, c2);
Expand All @@ -360,7 +365,7 @@ impl WideScalar {

// Reduce 258 bits into 256.
// r[0..7] = p[0..7] + p[8] * NEG_MODULUS.
let mut c = p0 as u64 + (NEG_MODULUS[0] as u64) * (p8 as u64);
let mut c = p0 as u64 + (neg_modulus0 as u64) * (p8 as u64);
let r0 = (c & 0xFFFFFFFFu64) as u32;
c >>= 32;
c += p1 as u64 + (NEG_MODULUS[1] as u64) * (p8 as u64);
Expand Down Expand Up @@ -392,6 +397,15 @@ impl WideScalar {
let underflow = Choice::from((underflow.0 >> 31) as u8);
Scalar(U256::conditional_select(&r, &r2, !underflow | high_bit))
}

#[inline(always)] // only used in Scalar::mul(), so won't cause binary bloat
pub(super) fn reduce(&self) -> Scalar {
self.reduce_impl(false)
}

pub(super) fn reduce_nonzero(&self) -> Scalar {
self.reduce_impl(true) + Scalar::ONE
}
}

/// Constant-time comparison.
Expand Down
40 changes: 27 additions & 13 deletions k256/src/arithmetic/scalar/wide64.rs
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Expand Up @@ -118,32 +118,37 @@ impl WideScalar {
Scalar::conditional_select(&res, &res.add(&Scalar::ONE), Choice::from(c as u8))
}

#[inline(always)] // only used in Scalar::mul(), so won't cause binary bloat
pub(super) fn reduce(&self) -> Scalar {
fn reduce_impl(&self, modulus_minus_one: bool) -> Scalar {
let neg_modulus0 = if modulus_minus_one {
NEG_MODULUS[0] + 1
} else {
NEG_MODULUS[0]
};

let w = self.0.to_uint_array();
let n0 = w[4];
let n1 = w[5];
let n2 = w[6];
let n3 = w[7];

// Reduce 512 bits into 385.
// m[0..6] = self[0..3] + n[0..3] * NEG_MODULUS.
// m[0..6] = self[0..3] + n[0..3] * neg_modulus.
let c0 = w[0];
let c1 = 0;
let c2 = 0;
let (c0, c1) = muladd_fast(n0, NEG_MODULUS[0], c0, c1);
let (c0, c1) = muladd_fast(n0, neg_modulus0, c0, c1);
let (m0, c0, c1) = (c0, c1, 0);
let (c0, c1) = sumadd_fast(w[1], c0, c1);
let (c0, c1, c2) = muladd(n1, NEG_MODULUS[0], c0, c1, c2);
let (c0, c1, c2) = muladd(n1, neg_modulus0, c0, c1, c2);
let (c0, c1, c2) = muladd(n0, NEG_MODULUS[1], c0, c1, c2);
let (m1, c0, c1, c2) = (c0, c1, c2, 0);
let (c0, c1, c2) = sumadd(w[2], c0, c1, c2);
let (c0, c1, c2) = muladd(n2, NEG_MODULUS[0], c0, c1, c2);
let (c0, c1, c2) = muladd(n2, neg_modulus0, c0, c1, c2);
let (c0, c1, c2) = muladd(n1, NEG_MODULUS[1], c0, c1, c2);
let (c0, c1, c2) = sumadd(n0, c0, c1, c2);
let (m2, c0, c1, c2) = (c0, c1, c2, 0);
let (c0, c1, c2) = sumadd(w[3], c0, c1, c2);
let (c0, c1, c2) = muladd(n3, NEG_MODULUS[0], c0, c1, c2);
let (c0, c1, c2) = muladd(n3, neg_modulus0, c0, c1, c2);
let (c0, c1, c2) = muladd(n2, NEG_MODULUS[1], c0, c1, c2);
let (c0, c1, c2) = sumadd(n1, c0, c1, c2);
let (m3, c0, c1, c2) = (c0, c1, c2, 0);
Expand All @@ -156,18 +161,18 @@ impl WideScalar {
let m6 = c0;

// Reduce 385 bits into 258.
// p[0..4] = m[0..3] + m[4..6] * NEG_MODULUS.
// p[0..4] = m[0..3] + m[4..6] * neg_modulus.
let c0 = m0;
let c1 = 0;
let c2 = 0;
let (c0, c1) = muladd_fast(m4, NEG_MODULUS[0], c0, c1);
let (c0, c1) = muladd_fast(m4, neg_modulus0, c0, c1);
let (p0, c0, c1) = (c0, c1, 0);
let (c0, c1) = sumadd_fast(m1, c0, c1);
let (c0, c1, c2) = muladd(m5, NEG_MODULUS[0], c0, c1, c2);
let (c0, c1, c2) = muladd(m5, neg_modulus0, c0, c1, c2);
let (c0, c1, c2) = muladd(m4, NEG_MODULUS[1], c0, c1, c2);
let (p1, c0, c1) = (c0, c1, 0);
let (c0, c1, c2) = sumadd(m2, c0, c1, c2);
let (c0, c1, c2) = muladd(m6, NEG_MODULUS[0], c0, c1, c2);
let (c0, c1, c2) = muladd(m6, neg_modulus0, c0, c1, c2);
let (c0, c1, c2) = muladd(m5, NEG_MODULUS[1], c0, c1, c2);
let (c0, c1, c2) = sumadd(m4, c0, c1, c2);
let (p2, c0, c1, _c2) = (c0, c1, c2, 0);
Expand All @@ -179,8 +184,8 @@ impl WideScalar {
debug_assert!(p4 <= 2);

// Reduce 258 bits into 256.
// r[0..3] = p[0..3] + p[4] * NEG_MODULUS.
let mut c = (p0 as u128) + (NEG_MODULUS[0] as u128) * (p4 as u128);
// r[0..3] = p[0..3] + p[4] * neg_modulus.
let mut c = (p0 as u128) + (neg_modulus0 as u128) * (p4 as u128);
let r0 = (c & 0xFFFFFFFFFFFFFFFFu128) as u64;
c >>= 64;
c += (p1 as u128) + (NEG_MODULUS[1] as u128) * (p4 as u128);
Expand All @@ -200,6 +205,15 @@ impl WideScalar {
let underflow = Choice::from((underflow.0 >> 63) as u8);
Scalar(U256::conditional_select(&r, &r2, !underflow | high_bit))
}

#[inline(always)] // only used in Scalar::mul(), so won't cause binary bloat
pub(super) fn reduce(&self) -> Scalar {
self.reduce_impl(false)
}

pub(super) fn reduce_nonzero(&self) -> Scalar {
self.reduce_impl(true) + Scalar::ONE
}
}

/// Constant-time comparison.
Expand Down