//! This module provides an implementation of the Curve25519's scalar field $\mathbb{F}_q$
|
|
//! where `q = 2^252 + 27742317777372353535851937790883648493 = 0x1000000000000000 0000000000000000 14def9dea2f79cd6 5812631a5cf5d3ed`
|
|
//! The entire file is an adaptation from bls12-381 crate. We modify various constants (MODULUS, R, R2, etc.) to appropriate values for Curve25519 and update tests
|
|
//! We borrow the `invert` method from curve25519-dalek crate
|
|
//! See NOTICE.md for more details
|
|
|
|
use core::borrow::Borrow;
|
|
use core::convert::TryFrom;
|
|
use core::fmt;
|
|
use core::iter::{Product, Sum};
|
|
use core::ops::{Add, AddAssign, Mul, MulAssign, Neg, Sub, SubAssign};
|
|
use rand_core::{CryptoRng, RngCore};
|
|
use serde::{Deserialize, Serialize};
|
|
use subtle::{Choice, ConditionallySelectable, ConstantTimeEq, CtOption};
|
|
use zeroize::Zeroize;
|
|
|
|
// use crate::util::{adc, mac, sbb};
|
|
/// Compute a + b + carry, returning the result and the new carry over.
|
|
#[inline(always)]
|
|
pub const fn adc(a: u64, b: u64, carry: u64) -> (u64, u64) {
|
|
let ret = (a as u128) + (b as u128) + (carry as u128);
|
|
(ret as u64, (ret >> 64) as u64)
|
|
}
|
|
|
|
/// Compute a - (b + borrow), returning the result and the new borrow.
|
|
#[inline(always)]
|
|
pub const fn sbb(a: u64, b: u64, borrow: u64) -> (u64, u64) {
|
|
let ret = (a as u128).wrapping_sub((b as u128) + ((borrow >> 63) as u128));
|
|
(ret as u64, (ret >> 64) as u64)
|
|
}
|
|
|
|
/// Compute a + (b * c) + carry, returning the result and the new carry over.
|
|
#[inline(always)]
|
|
pub const fn mac(a: u64, b: u64, c: u64, carry: u64) -> (u64, u64) {
|
|
let ret = (a as u128) + ((b as u128) * (c as u128)) + (carry as u128);
|
|
(ret as u64, (ret >> 64) as u64)
|
|
}
|
|
|
|
macro_rules! impl_add_binop_specify_output {
|
|
($lhs:ident, $rhs:ident, $output:ident) => {
|
|
impl<'b> Add<&'b $rhs> for $lhs {
|
|
type Output = $output;
|
|
|
|
#[inline]
|
|
fn add(self, rhs: &'b $rhs) -> $output {
|
|
&self + rhs
|
|
}
|
|
}
|
|
|
|
impl<'a> Add<$rhs> for &'a $lhs {
|
|
type Output = $output;
|
|
|
|
#[inline]
|
|
fn add(self, rhs: $rhs) -> $output {
|
|
self + &rhs
|
|
}
|
|
}
|
|
|
|
impl Add<$rhs> for $lhs {
|
|
type Output = $output;
|
|
|
|
#[inline]
|
|
fn add(self, rhs: $rhs) -> $output {
|
|
&self + &rhs
|
|
}
|
|
}
|
|
};
|
|
}
|
|
|
|
macro_rules! impl_sub_binop_specify_output {
|
|
($lhs:ident, $rhs:ident, $output:ident) => {
|
|
impl<'b> Sub<&'b $rhs> for $lhs {
|
|
type Output = $output;
|
|
|
|
#[inline]
|
|
fn sub(self, rhs: &'b $rhs) -> $output {
|
|
&self - rhs
|
|
}
|
|
}
|
|
|
|
impl<'a> Sub<$rhs> for &'a $lhs {
|
|
type Output = $output;
|
|
|
|
#[inline]
|
|
fn sub(self, rhs: $rhs) -> $output {
|
|
self - &rhs
|
|
}
|
|
}
|
|
|
|
impl Sub<$rhs> for $lhs {
|
|
type Output = $output;
|
|
|
|
#[inline]
|
|
fn sub(self, rhs: $rhs) -> $output {
|
|
&self - &rhs
|
|
}
|
|
}
|
|
};
|
|
}
|
|
|
|
macro_rules! impl_binops_additive_specify_output {
|
|
($lhs:ident, $rhs:ident, $output:ident) => {
|
|
impl_add_binop_specify_output!($lhs, $rhs, $output);
|
|
impl_sub_binop_specify_output!($lhs, $rhs, $output);
|
|
};
|
|
}
|
|
|
|
macro_rules! impl_binops_multiplicative_mixed {
|
|
($lhs:ident, $rhs:ident, $output:ident) => {
|
|
impl<'b> Mul<&'b $rhs> for $lhs {
|
|
type Output = $output;
|
|
|
|
#[inline]
|
|
fn mul(self, rhs: &'b $rhs) -> $output {
|
|
&self * rhs
|
|
}
|
|
}
|
|
|
|
impl<'a> Mul<$rhs> for &'a $lhs {
|
|
type Output = $output;
|
|
|
|
#[inline]
|
|
fn mul(self, rhs: $rhs) -> $output {
|
|
self * &rhs
|
|
}
|
|
}
|
|
|
|
impl Mul<$rhs> for $lhs {
|
|
type Output = $output;
|
|
|
|
#[inline]
|
|
fn mul(self, rhs: $rhs) -> $output {
|
|
&self * &rhs
|
|
}
|
|
}
|
|
};
|
|
}
|
|
|
|
macro_rules! impl_binops_additive {
|
|
($lhs:ident, $rhs:ident) => {
|
|
impl_binops_additive_specify_output!($lhs, $rhs, $lhs);
|
|
|
|
impl SubAssign<$rhs> for $lhs {
|
|
#[inline]
|
|
fn sub_assign(&mut self, rhs: $rhs) {
|
|
*self = &*self - &rhs;
|
|
}
|
|
}
|
|
|
|
impl AddAssign<$rhs> for $lhs {
|
|
#[inline]
|
|
fn add_assign(&mut self, rhs: $rhs) {
|
|
*self = &*self + &rhs;
|
|
}
|
|
}
|
|
|
|
impl<'b> SubAssign<&'b $rhs> for $lhs {
|
|
#[inline]
|
|
fn sub_assign(&mut self, rhs: &'b $rhs) {
|
|
*self = &*self - rhs;
|
|
}
|
|
}
|
|
|
|
impl<'b> AddAssign<&'b $rhs> for $lhs {
|
|
#[inline]
|
|
fn add_assign(&mut self, rhs: &'b $rhs) {
|
|
*self = &*self + rhs;
|
|
}
|
|
}
|
|
};
|
|
}
|
|
|
|
macro_rules! impl_binops_multiplicative {
|
|
($lhs:ident, $rhs:ident) => {
|
|
impl_binops_multiplicative_mixed!($lhs, $rhs, $lhs);
|
|
|
|
impl MulAssign<$rhs> for $lhs {
|
|
#[inline]
|
|
fn mul_assign(&mut self, rhs: $rhs) {
|
|
*self = &*self * &rhs;
|
|
}
|
|
}
|
|
|
|
impl<'b> MulAssign<&'b $rhs> for $lhs {
|
|
#[inline]
|
|
fn mul_assign(&mut self, rhs: &'b $rhs) {
|
|
*self = &*self * rhs;
|
|
}
|
|
}
|
|
};
|
|
}
|
|
|
|
/// Represents an element of the scalar field $\mathbb{F}_q$ of the Curve25519 elliptic
|
|
/// curve construction.
|
|
// The internal representation of this type is four 64-bit unsigned
|
|
// integers in little-endian order. `Scalar` values are always in
|
|
// Montgomery form; i.e., Scalar(a) = aR mod q, with R = 2^256.
|
|
#[derive(Clone, Copy, Eq, Serialize, Deserialize)]
|
|
pub struct Scalar(pub(crate) [u64; 4]);
|
|
|
|
impl fmt::Debug for Scalar {
|
|
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
|
|
let tmp = self.to_bytes();
|
|
write!(f, "0x")?;
|
|
for &b in tmp.iter().rev() {
|
|
write!(f, "{:02x}", b)?;
|
|
}
|
|
Ok(())
|
|
}
|
|
}
|
|
|
|
impl From<u64> for Scalar {
|
|
fn from(val: u64) -> Scalar {
|
|
Scalar([val, 0, 0, 0]) * R2
|
|
}
|
|
}
|
|
|
|
impl ConstantTimeEq for Scalar {
|
|
fn ct_eq(&self, other: &Self) -> Choice {
|
|
self.0[0].ct_eq(&other.0[0])
|
|
& self.0[1].ct_eq(&other.0[1])
|
|
& self.0[2].ct_eq(&other.0[2])
|
|
& self.0[3].ct_eq(&other.0[3])
|
|
}
|
|
}
|
|
|
|
impl PartialEq for Scalar {
|
|
#[inline]
|
|
fn eq(&self, other: &Self) -> bool {
|
|
self.ct_eq(other).unwrap_u8() == 1
|
|
}
|
|
}
|
|
|
|
impl ConditionallySelectable for Scalar {
|
|
fn conditional_select(a: &Self, b: &Self, choice: Choice) -> Self {
|
|
Scalar([
|
|
u64::conditional_select(&a.0[0], &b.0[0], choice),
|
|
u64::conditional_select(&a.0[1], &b.0[1], choice),
|
|
u64::conditional_select(&a.0[2], &b.0[2], choice),
|
|
u64::conditional_select(&a.0[3], &b.0[3], choice),
|
|
])
|
|
}
|
|
}
|
|
|
|
/// Constant representing the modulus
|
|
/// q = 2^252 + 27742317777372353535851937790883648493
|
|
/// 0x1000000000000000 0000000000000000 14def9dea2f79cd6 5812631a5cf5d3ed
|
|
const MODULUS: Scalar = Scalar([
|
|
0x5812631a5cf5d3ed,
|
|
0x14def9dea2f79cd6,
|
|
0x0000000000000000,
|
|
0x1000000000000000,
|
|
]);
|
|
|
|
impl<'a> Neg for &'a Scalar {
|
|
type Output = Scalar;
|
|
|
|
#[inline]
|
|
fn neg(self) -> Scalar {
|
|
self.neg()
|
|
}
|
|
}
|
|
|
|
impl Neg for Scalar {
|
|
type Output = Scalar;
|
|
|
|
#[inline]
|
|
fn neg(self) -> Scalar {
|
|
-&self
|
|
}
|
|
}
|
|
|
|
impl<'a, 'b> Sub<&'b Scalar> for &'a Scalar {
|
|
type Output = Scalar;
|
|
|
|
#[inline]
|
|
fn sub(self, rhs: &'b Scalar) -> Scalar {
|
|
self.sub(rhs)
|
|
}
|
|
}
|
|
|
|
impl<'a, 'b> Add<&'b Scalar> for &'a Scalar {
|
|
type Output = Scalar;
|
|
|
|
#[inline]
|
|
fn add(self, rhs: &'b Scalar) -> Scalar {
|
|
self.add(rhs)
|
|
}
|
|
}
|
|
|
|
impl<'a, 'b> Mul<&'b Scalar> for &'a Scalar {
|
|
type Output = Scalar;
|
|
|
|
#[inline]
|
|
fn mul(self, rhs: &'b Scalar) -> Scalar {
|
|
self.mul(rhs)
|
|
}
|
|
}
|
|
|
|
impl_binops_additive!(Scalar, Scalar);
|
|
impl_binops_multiplicative!(Scalar, Scalar);
|
|
|
|
/// INV = -(q^{-1} mod 2^64) mod 2^64
|
|
const INV: u64 = 0xd2b51da312547e1b;
|
|
|
|
/// R = 2^256 mod q
|
|
const R: Scalar = Scalar([
|
|
0xd6ec31748d98951d,
|
|
0xc6ef5bf4737dcf70,
|
|
0xfffffffffffffffe,
|
|
0x0fffffffffffffff,
|
|
]);
|
|
|
|
/// R^2 = 2^512 mod q
|
|
const R2: Scalar = Scalar([
|
|
0xa40611e3449c0f01,
|
|
0xd00e1ba768859347,
|
|
0xceec73d217f5be65,
|
|
0x0399411b7c309a3d,
|
|
]);
|
|
|
|
/// R^3 = 2^768 mod q
|
|
const R3: Scalar = Scalar([
|
|
0x2a9e49687b83a2db,
|
|
0x278324e6aef7f3ec,
|
|
0x8065dc6c04ec5b65,
|
|
0xe530b773599cec7,
|
|
]);
|
|
|
|
impl Default for Scalar {
|
|
#[inline]
|
|
fn default() -> Self {
|
|
Self::zero()
|
|
}
|
|
}
|
|
|
|
impl<T> Product<T> for Scalar
|
|
where
|
|
T: Borrow<Scalar>,
|
|
{
|
|
fn product<I>(iter: I) -> Self
|
|
where
|
|
I: Iterator<Item = T>,
|
|
{
|
|
iter.fold(Scalar::one(), |acc, item| acc * item.borrow())
|
|
}
|
|
}
|
|
|
|
impl<T> Sum<T> for Scalar
|
|
where
|
|
T: Borrow<Scalar>,
|
|
{
|
|
fn sum<I>(iter: I) -> Self
|
|
where
|
|
I: Iterator<Item = T>,
|
|
{
|
|
iter.fold(Scalar::zero(), |acc, item| acc + item.borrow())
|
|
}
|
|
}
|
|
|
|
impl Zeroize for Scalar {
|
|
fn zeroize(&mut self) {
|
|
self.0 = [0u64; 4];
|
|
}
|
|
}
|
|
|
|
impl Scalar {
|
|
/// Returns zero, the additive identity.
|
|
#[inline]
|
|
pub const fn zero() -> Scalar {
|
|
Scalar([0, 0, 0, 0])
|
|
}
|
|
|
|
/// Returns one, the multiplicative identity.
|
|
#[inline]
|
|
pub const fn one() -> Scalar {
|
|
R
|
|
}
|
|
|
|
pub fn random<Rng: RngCore + CryptoRng>(rng: &mut Rng) -> Self {
|
|
let mut limbs = [0u64; 8];
|
|
for i in 0..8 {
|
|
limbs[i] = rng.next_u64();
|
|
}
|
|
Scalar::from_u512(limbs)
|
|
}
|
|
|
|
/// Doubles this field element.
|
|
#[inline]
|
|
pub const fn double(&self) -> Scalar {
|
|
// TODO: This can be achieved more efficiently with a bitshift.
|
|
self.add(self)
|
|
}
|
|
|
|
/// Attempts to convert a little-endian byte representation of
|
|
/// a scalar into a `Scalar`, failing if the input is not canonical.
|
|
pub fn from_bytes(bytes: &[u8; 32]) -> CtOption<Scalar> {
|
|
let mut tmp = Scalar([0, 0, 0, 0]);
|
|
|
|
tmp.0[0] = u64::from_le_bytes(<[u8; 8]>::try_from(&bytes[0..8]).unwrap());
|
|
tmp.0[1] = u64::from_le_bytes(<[u8; 8]>::try_from(&bytes[8..16]).unwrap());
|
|
tmp.0[2] = u64::from_le_bytes(<[u8; 8]>::try_from(&bytes[16..24]).unwrap());
|
|
tmp.0[3] = u64::from_le_bytes(<[u8; 8]>::try_from(&bytes[24..32]).unwrap());
|
|
|
|
// Try to subtract the modulus
|
|
let (_, borrow) = sbb(tmp.0[0], MODULUS.0[0], 0);
|
|
let (_, borrow) = sbb(tmp.0[1], MODULUS.0[1], borrow);
|
|
let (_, borrow) = sbb(tmp.0[2], MODULUS.0[2], borrow);
|
|
let (_, borrow) = sbb(tmp.0[3], MODULUS.0[3], borrow);
|
|
|
|
// If the element is smaller than MODULUS then the
|
|
// subtraction will underflow, producing a borrow value
|
|
// of 0xffff...ffff. Otherwise, it'll be zero.
|
|
let is_some = (borrow as u8) & 1;
|
|
|
|
// Convert to Montgomery form by computing
|
|
// (a.R^0 * R^2) / R = a.R
|
|
tmp *= &R2;
|
|
|
|
CtOption::new(tmp, Choice::from(is_some))
|
|
}
|
|
|
|
/// Converts an element of `Scalar` into a byte representation in
|
|
/// little-endian byte order.
|
|
pub fn to_bytes(&self) -> [u8; 32] {
|
|
// Turn into canonical form by computing
|
|
// (a.R) / R = a
|
|
let tmp = Scalar::montgomery_reduce(self.0[0], self.0[1], self.0[2], self.0[3], 0, 0, 0, 0);
|
|
|
|
let mut res = [0; 32];
|
|
res[0..8].copy_from_slice(&tmp.0[0].to_le_bytes());
|
|
res[8..16].copy_from_slice(&tmp.0[1].to_le_bytes());
|
|
res[16..24].copy_from_slice(&tmp.0[2].to_le_bytes());
|
|
res[24..32].copy_from_slice(&tmp.0[3].to_le_bytes());
|
|
|
|
res
|
|
}
|
|
|
|
/// Converts a 512-bit little endian integer into
|
|
/// a `Scalar` by reducing by the modulus.
|
|
pub fn from_bytes_wide(bytes: &[u8; 64]) -> Scalar {
|
|
Scalar::from_u512([
|
|
u64::from_le_bytes(<[u8; 8]>::try_from(&bytes[0..8]).unwrap()),
|
|
u64::from_le_bytes(<[u8; 8]>::try_from(&bytes[8..16]).unwrap()),
|
|
u64::from_le_bytes(<[u8; 8]>::try_from(&bytes[16..24]).unwrap()),
|
|
u64::from_le_bytes(<[u8; 8]>::try_from(&bytes[24..32]).unwrap()),
|
|
u64::from_le_bytes(<[u8; 8]>::try_from(&bytes[32..40]).unwrap()),
|
|
u64::from_le_bytes(<[u8; 8]>::try_from(&bytes[40..48]).unwrap()),
|
|
u64::from_le_bytes(<[u8; 8]>::try_from(&bytes[48..56]).unwrap()),
|
|
u64::from_le_bytes(<[u8; 8]>::try_from(&bytes[56..64]).unwrap()),
|
|
])
|
|
}
|
|
|
|
fn from_u512(limbs: [u64; 8]) -> Scalar {
|
|
// We reduce an arbitrary 512-bit number by decomposing it into two 256-bit digits
|
|
// with the higher bits multiplied by 2^256. Thus, we perform two reductions
|
|
//
|
|
// 1. the lower bits are multiplied by R^2, as normal
|
|
// 2. the upper bits are multiplied by R^2 * 2^256 = R^3
|
|
//
|
|
// and computing their sum in the field. It remains to see that arbitrary 256-bit
|
|
// numbers can be placed into Montgomery form safely using the reduction. The
|
|
// reduction works so long as the product is less than R=2^256 multipled by
|
|
// the modulus. This holds because for any `c` smaller than the modulus, we have
|
|
// that (2^256 - 1)*c is an acceptable product for the reduction. Therefore, the
|
|
// reduction always works so long as `c` is in the field; in this case it is either the
|
|
// constant `R2` or `R3`.
|
|
let d0 = Scalar([limbs[0], limbs[1], limbs[2], limbs[3]]);
|
|
let d1 = Scalar([limbs[4], limbs[5], limbs[6], limbs[7]]);
|
|
// Convert to Montgomery form
|
|
d0 * R2 + d1 * R3
|
|
}
|
|
|
|
/// Converts from an integer represented in little endian
|
|
/// into its (congruent) `Scalar` representation.
|
|
pub const fn from_raw(val: [u64; 4]) -> Self {
|
|
(&Scalar(val)).mul(&R2)
|
|
}
|
|
|
|
/// Squares this element.
|
|
#[inline]
|
|
pub const fn square(&self) -> Scalar {
|
|
let (r1, carry) = mac(0, self.0[0], self.0[1], 0);
|
|
let (r2, carry) = mac(0, self.0[0], self.0[2], carry);
|
|
let (r3, r4) = mac(0, self.0[0], self.0[3], carry);
|
|
|
|
let (r3, carry) = mac(r3, self.0[1], self.0[2], 0);
|
|
let (r4, r5) = mac(r4, self.0[1], self.0[3], carry);
|
|
|
|
let (r5, r6) = mac(r5, self.0[2], self.0[3], 0);
|
|
|
|
let r7 = r6 >> 63;
|
|
let r6 = (r6 << 1) | (r5 >> 63);
|
|
let r5 = (r5 << 1) | (r4 >> 63);
|
|
let r4 = (r4 << 1) | (r3 >> 63);
|
|
let r3 = (r3 << 1) | (r2 >> 63);
|
|
let r2 = (r2 << 1) | (r1 >> 63);
|
|
let r1 = r1 << 1;
|
|
|
|
let (r0, carry) = mac(0, self.0[0], self.0[0], 0);
|
|
let (r1, carry) = adc(0, r1, carry);
|
|
let (r2, carry) = mac(r2, self.0[1], self.0[1], carry);
|
|
let (r3, carry) = adc(0, r3, carry);
|
|
let (r4, carry) = mac(r4, self.0[2], self.0[2], carry);
|
|
let (r5, carry) = adc(0, r5, carry);
|
|
let (r6, carry) = mac(r6, self.0[3], self.0[3], carry);
|
|
let (r7, _) = adc(0, r7, carry);
|
|
|
|
Scalar::montgomery_reduce(r0, r1, r2, r3, r4, r5, r6, r7)
|
|
}
|
|
|
|
/// Exponentiates `self` by `by`, where `by` is a
|
|
/// little-endian order integer exponent.
|
|
pub fn pow(&self, by: &[u64; 4]) -> Self {
|
|
let mut res = Self::one();
|
|
for e in by.iter().rev() {
|
|
for i in (0..64).rev() {
|
|
res = res.square();
|
|
let mut tmp = res;
|
|
tmp *= self;
|
|
res.conditional_assign(&tmp, (((*e >> i) & 0x1) as u8).into());
|
|
}
|
|
}
|
|
res
|
|
}
|
|
|
|
/// Exponentiates `self` by `by`, where `by` is a
|
|
/// little-endian order integer exponent.
|
|
///
|
|
/// **This operation is variable time with respect
|
|
/// to the exponent.** If the exponent is fixed,
|
|
/// this operation is effectively constant time.
|
|
pub fn pow_vartime(&self, by: &[u64; 4]) -> Self {
|
|
let mut res = Self::one();
|
|
for e in by.iter().rev() {
|
|
for i in (0..64).rev() {
|
|
res = res.square();
|
|
|
|
if ((*e >> i) & 1) == 1 {
|
|
res.mul_assign(self);
|
|
}
|
|
}
|
|
}
|
|
res
|
|
}
|
|
|
|
pub fn invert(&self) -> CtOption<Self> {
|
|
// Uses the addition chain from
|
|
// https://briansmith.org/ecc-inversion-addition-chains-01#curve25519_scalar_inversion
|
|
// implementation adapted from curve25519-dalek
|
|
let _1 = self;
|
|
let _10 = _1.square();
|
|
let _100 = _10.square();
|
|
let _11 = &_10 * _1;
|
|
let _101 = &_10 * &_11;
|
|
let _111 = &_10 * &_101;
|
|
let _1001 = &_10 * &_111;
|
|
let _1011 = &_10 * &_1001;
|
|
let _1111 = &_100 * &_1011;
|
|
|
|
// _10000
|
|
let mut y = &_1111 * _1;
|
|
|
|
#[inline]
|
|
fn square_multiply(y: &mut Scalar, squarings: usize, x: &Scalar) {
|
|
for _ in 0..squarings {
|
|
*y = y.square();
|
|
}
|
|
*y = y.mul(x);
|
|
}
|
|
|
|
square_multiply(&mut y, 123 + 3, &_101);
|
|
square_multiply(&mut y, 2 + 2, &_11);
|
|
square_multiply(&mut y, 1 + 4, &_1111);
|
|
square_multiply(&mut y, 1 + 4, &_1111);
|
|
square_multiply(&mut y, 4, &_1001);
|
|
square_multiply(&mut y, 2, &_11);
|
|
square_multiply(&mut y, 1 + 4, &_1111);
|
|
square_multiply(&mut y, 1 + 3, &_101);
|
|
square_multiply(&mut y, 3 + 3, &_101);
|
|
square_multiply(&mut y, 3, &_111);
|
|
square_multiply(&mut y, 1 + 4, &_1111);
|
|
square_multiply(&mut y, 2 + 3, &_111);
|
|
square_multiply(&mut y, 2 + 2, &_11);
|
|
square_multiply(&mut y, 1 + 4, &_1011);
|
|
square_multiply(&mut y, 2 + 4, &_1011);
|
|
square_multiply(&mut y, 6 + 4, &_1001);
|
|
square_multiply(&mut y, 2 + 2, &_11);
|
|
square_multiply(&mut y, 3 + 2, &_11);
|
|
square_multiply(&mut y, 3 + 2, &_11);
|
|
square_multiply(&mut y, 1 + 4, &_1001);
|
|
square_multiply(&mut y, 1 + 3, &_111);
|
|
square_multiply(&mut y, 2 + 4, &_1111);
|
|
square_multiply(&mut y, 1 + 4, &_1011);
|
|
square_multiply(&mut y, 3, &_101);
|
|
square_multiply(&mut y, 2 + 4, &_1111);
|
|
square_multiply(&mut y, 3, &_101);
|
|
square_multiply(&mut y, 1 + 2, &_11);
|
|
|
|
CtOption::new(y, !self.ct_eq(&Self::zero()))
|
|
}
|
|
|
|
pub fn batch_invert(inputs: &mut [Scalar]) -> Scalar {
|
|
// This code is essentially identical to the FieldElement
|
|
// implementation, and is documented there. Unfortunately,
|
|
// it's not easy to write it generically, since here we want
|
|
// to use `UnpackedScalar`s internally, and `Scalar`s
|
|
// externally, but there's no corresponding distinction for
|
|
// field elements.
|
|
|
|
use zeroize::Zeroizing;
|
|
|
|
let n = inputs.len();
|
|
let one = Scalar::one();
|
|
|
|
// Place scratch storage in a Zeroizing wrapper to wipe it when
|
|
// we pass out of scope.
|
|
let scratch_vec = vec![one; n];
|
|
let mut scratch = Zeroizing::new(scratch_vec);
|
|
|
|
// Keep an accumulator of all of the previous products
|
|
let mut acc = Scalar::one();
|
|
|
|
// Pass through the input vector, recording the previous
|
|
// products in the scratch space
|
|
for (input, scratch) in inputs.iter().zip(scratch.iter_mut()) {
|
|
*scratch = acc;
|
|
|
|
acc = acc * input;
|
|
}
|
|
|
|
// acc is nonzero iff all inputs are nonzero
|
|
debug_assert!(acc != Scalar::zero());
|
|
|
|
// Compute the inverse of all products
|
|
acc = acc.invert().unwrap();
|
|
|
|
// We need to return the product of all inverses later
|
|
let ret = acc;
|
|
|
|
// Pass through the vector backwards to compute the inverses
|
|
// in place
|
|
for (input, scratch) in inputs.iter_mut().rev().zip(scratch.iter().rev()) {
|
|
let tmp = &acc * input.clone();
|
|
*input = &acc * scratch;
|
|
acc = tmp;
|
|
}
|
|
|
|
ret
|
|
}
|
|
|
|
#[inline(always)]
|
|
const fn montgomery_reduce(
|
|
r0: u64,
|
|
r1: u64,
|
|
r2: u64,
|
|
r3: u64,
|
|
r4: u64,
|
|
r5: u64,
|
|
r6: u64,
|
|
r7: u64,
|
|
) -> Self {
|
|
// The Montgomery reduction here is based on Algorithm 14.32 in
|
|
// Handbook of Applied Cryptography
|
|
// <http://cacr.uwaterloo.ca/hac/about/chap14.pdf>.
|
|
|
|
let k = r0.wrapping_mul(INV);
|
|
let (_, carry) = mac(r0, k, MODULUS.0[0], 0);
|
|
let (r1, carry) = mac(r1, k, MODULUS.0[1], carry);
|
|
let (r2, carry) = mac(r2, k, MODULUS.0[2], carry);
|
|
let (r3, carry) = mac(r3, k, MODULUS.0[3], carry);
|
|
let (r4, carry2) = adc(r4, 0, carry);
|
|
|
|
let k = r1.wrapping_mul(INV);
|
|
let (_, carry) = mac(r1, k, MODULUS.0[0], 0);
|
|
let (r2, carry) = mac(r2, k, MODULUS.0[1], carry);
|
|
let (r3, carry) = mac(r3, k, MODULUS.0[2], carry);
|
|
let (r4, carry) = mac(r4, k, MODULUS.0[3], carry);
|
|
let (r5, carry2) = adc(r5, carry2, carry);
|
|
|
|
let k = r2.wrapping_mul(INV);
|
|
let (_, carry) = mac(r2, k, MODULUS.0[0], 0);
|
|
let (r3, carry) = mac(r3, k, MODULUS.0[1], carry);
|
|
let (r4, carry) = mac(r4, k, MODULUS.0[2], carry);
|
|
let (r5, carry) = mac(r5, k, MODULUS.0[3], carry);
|
|
let (r6, carry2) = adc(r6, carry2, carry);
|
|
|
|
let k = r3.wrapping_mul(INV);
|
|
let (_, carry) = mac(r3, k, MODULUS.0[0], 0);
|
|
let (r4, carry) = mac(r4, k, MODULUS.0[1], carry);
|
|
let (r5, carry) = mac(r5, k, MODULUS.0[2], carry);
|
|
let (r6, carry) = mac(r6, k, MODULUS.0[3], carry);
|
|
let (r7, _) = adc(r7, carry2, carry);
|
|
|
|
// Result may be within MODULUS of the correct value
|
|
(&Scalar([r4, r5, r6, r7])).sub(&MODULUS)
|
|
}
|
|
|
|
/// Multiplies `rhs` by `self`, returning the result.
|
|
#[inline]
|
|
pub const fn mul(&self, rhs: &Self) -> Self {
|
|
// Schoolbook multiplication
|
|
|
|
let (r0, carry) = mac(0, self.0[0], rhs.0[0], 0);
|
|
let (r1, carry) = mac(0, self.0[0], rhs.0[1], carry);
|
|
let (r2, carry) = mac(0, self.0[0], rhs.0[2], carry);
|
|
let (r3, r4) = mac(0, self.0[0], rhs.0[3], carry);
|
|
|
|
let (r1, carry) = mac(r1, self.0[1], rhs.0[0], 0);
|
|
let (r2, carry) = mac(r2, self.0[1], rhs.0[1], carry);
|
|
let (r3, carry) = mac(r3, self.0[1], rhs.0[2], carry);
|
|
let (r4, r5) = mac(r4, self.0[1], rhs.0[3], carry);
|
|
|
|
let (r2, carry) = mac(r2, self.0[2], rhs.0[0], 0);
|
|
let (r3, carry) = mac(r3, self.0[2], rhs.0[1], carry);
|
|
let (r4, carry) = mac(r4, self.0[2], rhs.0[2], carry);
|
|
let (r5, r6) = mac(r5, self.0[2], rhs.0[3], carry);
|
|
|
|
let (r3, carry) = mac(r3, self.0[3], rhs.0[0], 0);
|
|
let (r4, carry) = mac(r4, self.0[3], rhs.0[1], carry);
|
|
let (r5, carry) = mac(r5, self.0[3], rhs.0[2], carry);
|
|
let (r6, r7) = mac(r6, self.0[3], rhs.0[3], carry);
|
|
|
|
Scalar::montgomery_reduce(r0, r1, r2, r3, r4, r5, r6, r7)
|
|
}
|
|
|
|
/// Subtracts `rhs` from `self`, returning the result.
|
|
#[inline]
|
|
pub const fn sub(&self, rhs: &Self) -> Self {
|
|
let (d0, borrow) = sbb(self.0[0], rhs.0[0], 0);
|
|
let (d1, borrow) = sbb(self.0[1], rhs.0[1], borrow);
|
|
let (d2, borrow) = sbb(self.0[2], rhs.0[2], borrow);
|
|
let (d3, borrow) = sbb(self.0[3], rhs.0[3], borrow);
|
|
|
|
// If underflow occurred on the final limb, borrow = 0xfff...fff, otherwise
|
|
// borrow = 0x000...000. Thus, we use it as a mask to conditionally add the modulus.
|
|
let (d0, carry) = adc(d0, MODULUS.0[0] & borrow, 0);
|
|
let (d1, carry) = adc(d1, MODULUS.0[1] & borrow, carry);
|
|
let (d2, carry) = adc(d2, MODULUS.0[2] & borrow, carry);
|
|
let (d3, _) = adc(d3, MODULUS.0[3] & borrow, carry);
|
|
|
|
Scalar([d0, d1, d2, d3])
|
|
}
|
|
|
|
/// Adds `rhs` to `self`, returning the result.
|
|
#[inline]
|
|
pub const fn add(&self, rhs: &Self) -> Self {
|
|
let (d0, carry) = adc(self.0[0], rhs.0[0], 0);
|
|
let (d1, carry) = adc(self.0[1], rhs.0[1], carry);
|
|
let (d2, carry) = adc(self.0[2], rhs.0[2], carry);
|
|
let (d3, _) = adc(self.0[3], rhs.0[3], carry);
|
|
|
|
// Attempt to subtract the modulus, to ensure the value
|
|
// is smaller than the modulus.
|
|
(&Scalar([d0, d1, d2, d3])).sub(&MODULUS)
|
|
}
|
|
|
|
/// Negates `self`.
|
|
#[inline]
|
|
pub const fn neg(&self) -> Self {
|
|
// Subtract `self` from `MODULUS` to negate. Ignore the final
|
|
// borrow because it cannot underflow; self is guaranteed to
|
|
// be in the field.
|
|
let (d0, borrow) = sbb(MODULUS.0[0], self.0[0], 0);
|
|
let (d1, borrow) = sbb(MODULUS.0[1], self.0[1], borrow);
|
|
let (d2, borrow) = sbb(MODULUS.0[2], self.0[2], borrow);
|
|
let (d3, _) = sbb(MODULUS.0[3], self.0[3], borrow);
|
|
|
|
// `tmp` could be `MODULUS` if `self` was zero. Create a mask that is
|
|
// zero if `self` was zero, and `u64::max_value()` if self was nonzero.
|
|
let mask = (((self.0[0] | self.0[1] | self.0[2] | self.0[3]) == 0) as u64).wrapping_sub(1);
|
|
|
|
Scalar([d0 & mask, d1 & mask, d2 & mask, d3 & mask])
|
|
}
|
|
}
|
|
|
|
impl<'a> From<&'a Scalar> for [u8; 32] {
|
|
fn from(value: &'a Scalar) -> [u8; 32] {
|
|
value.to_bytes()
|
|
}
|
|
}
|
|
|
|
#[cfg(test)]
|
|
mod tests {
|
|
use super::*;
|
|
|
|
#[test]
|
|
fn test_inv() {
|
|
// Compute -(q^{-1} mod 2^64) mod 2^64 by exponentiating
|
|
// by totient(2**64) - 1
|
|
|
|
let mut inv = 1u64;
|
|
for _ in 0..63 {
|
|
inv = inv.wrapping_mul(inv);
|
|
inv = inv.wrapping_mul(MODULUS.0[0]);
|
|
}
|
|
inv = inv.wrapping_neg();
|
|
|
|
assert_eq!(inv, INV);
|
|
}
|
|
|
|
#[cfg(feature = "std")]
|
|
#[test]
|
|
fn test_debug() {
|
|
assert_eq!(
|
|
format!("{:?}", Scalar::zero()),
|
|
"0x0000000000000000000000000000000000000000000000000000000000000000"
|
|
);
|
|
assert_eq!(
|
|
format!("{:?}", Scalar::one()),
|
|
"0x0000000000000000000000000000000000000000000000000000000000000001"
|
|
);
|
|
assert_eq!(
|
|
format!("{:?}", R2),
|
|
"0x1824b159acc5056f998c4fefecbc4ff55884b7fa0003480200000001fffffffe"
|
|
);
|
|
}
|
|
|
|
#[test]
|
|
fn test_equality() {
|
|
assert_eq!(Scalar::zero(), Scalar::zero());
|
|
assert_eq!(Scalar::one(), Scalar::one());
|
|
assert_eq!(R2, R2);
|
|
|
|
assert!(Scalar::zero() != Scalar::one());
|
|
assert!(Scalar::one() != R2);
|
|
}
|
|
|
|
#[test]
|
|
fn test_to_bytes() {
|
|
assert_eq!(
|
|
Scalar::zero().to_bytes(),
|
|
[
|
|
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
|
|
0, 0
|
|
]
|
|
);
|
|
|
|
assert_eq!(
|
|
Scalar::one().to_bytes(),
|
|
[
|
|
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
|
|
0, 0
|
|
]
|
|
);
|
|
|
|
assert_eq!(
|
|
R2.to_bytes(),
|
|
[
|
|
29, 149, 152, 141, 116, 49, 236, 214, 112, 207, 125, 115, 244, 91, 239, 198, 254, 255, 255,
|
|
255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 15
|
|
]
|
|
);
|
|
|
|
assert_eq!(
|
|
(-&Scalar::one()).to_bytes(),
|
|
[
|
|
236, 211, 245, 92, 26, 99, 18, 88, 214, 156, 247, 162, 222, 249, 222, 20, 0, 0, 0, 0, 0, 0,
|
|
0, 0, 0, 0, 0, 0, 0, 0, 0, 16
|
|
]
|
|
);
|
|
}
|
|
|
|
#[test]
|
|
fn test_from_bytes() {
|
|
assert_eq!(
|
|
Scalar::from_bytes(&[
|
|
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
|
|
0, 0
|
|
])
|
|
.unwrap(),
|
|
Scalar::zero()
|
|
);
|
|
|
|
assert_eq!(
|
|
Scalar::from_bytes(&[
|
|
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
|
|
0, 0
|
|
])
|
|
.unwrap(),
|
|
Scalar::one()
|
|
);
|
|
|
|
assert_eq!(
|
|
Scalar::from_bytes(&[
|
|
29, 149, 152, 141, 116, 49, 236, 214, 112, 207, 125, 115, 244, 91, 239, 198, 254, 255, 255,
|
|
255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 15
|
|
])
|
|
.unwrap(),
|
|
R2
|
|
);
|
|
|
|
// -1 should work
|
|
assert!(
|
|
Scalar::from_bytes(&[
|
|
236, 211, 245, 92, 26, 99, 18, 88, 214, 156, 247, 162, 222, 249, 222, 20, 0, 0, 0, 0, 0, 0,
|
|
0, 0, 0, 0, 0, 0, 0, 0, 0, 16
|
|
])
|
|
.is_some()
|
|
.unwrap_u8()
|
|
== 1
|
|
);
|
|
|
|
// modulus is invalid
|
|
assert!(
|
|
Scalar::from_bytes(&[
|
|
1, 0, 0, 0, 255, 255, 255, 255, 254, 91, 254, 255, 2, 164, 189, 83, 5, 216, 161, 9, 8, 216,
|
|
57, 51, 72, 125, 157, 41, 83, 167, 237, 115
|
|
])
|
|
.is_none()
|
|
.unwrap_u8()
|
|
== 1
|
|
);
|
|
|
|
// Anything larger than the modulus is invalid
|
|
assert!(
|
|
Scalar::from_bytes(&[
|
|
2, 0, 0, 0, 255, 255, 255, 255, 254, 91, 254, 255, 2, 164, 189, 83, 5, 216, 161, 9, 8, 216,
|
|
57, 51, 72, 125, 157, 41, 83, 167, 237, 115
|
|
])
|
|
.is_none()
|
|
.unwrap_u8()
|
|
== 1
|
|
);
|
|
assert!(
|
|
Scalar::from_bytes(&[
|
|
1, 0, 0, 0, 255, 255, 255, 255, 254, 91, 254, 255, 2, 164, 189, 83, 5, 216, 161, 9, 8, 216,
|
|
58, 51, 72, 125, 157, 41, 83, 167, 237, 115
|
|
])
|
|
.is_none()
|
|
.unwrap_u8()
|
|
== 1
|
|
);
|
|
assert!(
|
|
Scalar::from_bytes(&[
|
|
1, 0, 0, 0, 255, 255, 255, 255, 254, 91, 254, 255, 2, 164, 189, 83, 5, 216, 161, 9, 8, 216,
|
|
57, 51, 72, 125, 157, 41, 83, 167, 237, 116
|
|
])
|
|
.is_none()
|
|
.unwrap_u8()
|
|
== 1
|
|
);
|
|
}
|
|
|
|
#[test]
|
|
fn test_from_u512_zero() {
|
|
assert_eq!(
|
|
Scalar::zero(),
|
|
Scalar::from_u512([
|
|
MODULUS.0[0],
|
|
MODULUS.0[1],
|
|
MODULUS.0[2],
|
|
MODULUS.0[3],
|
|
0,
|
|
0,
|
|
0,
|
|
0
|
|
])
|
|
);
|
|
}
|
|
|
|
#[test]
|
|
fn test_from_u512_r() {
|
|
assert_eq!(R, Scalar::from_u512([1, 0, 0, 0, 0, 0, 0, 0]));
|
|
}
|
|
|
|
#[test]
|
|
fn test_from_u512_r2() {
|
|
assert_eq!(R2, Scalar::from_u512([0, 0, 0, 0, 1, 0, 0, 0]));
|
|
}
|
|
|
|
#[test]
|
|
fn test_from_u512_max() {
|
|
let max_u64 = 0xffffffffffffffff;
|
|
assert_eq!(
|
|
R3 - R,
|
|
Scalar::from_u512([max_u64, max_u64, max_u64, max_u64, max_u64, max_u64, max_u64, max_u64])
|
|
);
|
|
}
|
|
|
|
#[test]
|
|
fn test_from_bytes_wide_r2() {
|
|
assert_eq!(
|
|
R2,
|
|
Scalar::from_bytes_wide(&[
|
|
29, 149, 152, 141, 116, 49, 236, 214, 112, 207, 125, 115, 244, 91, 239, 198, 254, 255, 255,
|
|
255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0,
|
|
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
|
|
])
|
|
);
|
|
}
|
|
|
|
#[test]
|
|
fn test_from_bytes_wide_negative_one() {
|
|
assert_eq!(
|
|
-&Scalar::one(),
|
|
Scalar::from_bytes_wide(&[
|
|
236, 211, 245, 92, 26, 99, 18, 88, 214, 156, 247, 162, 222, 249, 222, 20, 0, 0, 0, 0, 0, 0,
|
|
0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
|
|
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
|
|
])
|
|
);
|
|
}
|
|
|
|
#[test]
|
|
fn test_from_bytes_wide_maximum() {
|
|
assert_eq!(
|
|
Scalar::from_raw([
|
|
0xa40611e3449c0f00,
|
|
0xd00e1ba768859347,
|
|
0xceec73d217f5be65,
|
|
0x0399411b7c309a3d
|
|
]),
|
|
Scalar::from_bytes_wide(&[0xff; 64])
|
|
);
|
|
}
|
|
|
|
#[test]
|
|
fn test_zero() {
|
|
assert_eq!(Scalar::zero(), -&Scalar::zero());
|
|
assert_eq!(Scalar::zero(), Scalar::zero() + Scalar::zero());
|
|
assert_eq!(Scalar::zero(), Scalar::zero() - Scalar::zero());
|
|
assert_eq!(Scalar::zero(), Scalar::zero() * Scalar::zero());
|
|
}
|
|
|
|
const LARGEST: Scalar = Scalar([
|
|
0x5812631a5cf5d3ec,
|
|
0x14def9dea2f79cd6,
|
|
0x0000000000000000,
|
|
0x1000000000000000,
|
|
]);
|
|
|
|
#[test]
|
|
fn test_addition() {
|
|
let mut tmp = LARGEST;
|
|
tmp += &LARGEST;
|
|
|
|
assert_eq!(
|
|
tmp,
|
|
Scalar([
|
|
0x5812631a5cf5d3eb,
|
|
0x14def9dea2f79cd6,
|
|
0x0000000000000000,
|
|
0x1000000000000000,
|
|
])
|
|
);
|
|
|
|
let mut tmp = LARGEST;
|
|
tmp += &Scalar([1, 0, 0, 0]);
|
|
|
|
assert_eq!(tmp, Scalar::zero());
|
|
}
|
|
|
|
#[test]
|
|
fn test_negation() {
|
|
let tmp = -&LARGEST;
|
|
|
|
assert_eq!(tmp, Scalar([1, 0, 0, 0]));
|
|
|
|
let tmp = -&Scalar::zero();
|
|
assert_eq!(tmp, Scalar::zero());
|
|
let tmp = -&Scalar([1, 0, 0, 0]);
|
|
assert_eq!(tmp, LARGEST);
|
|
}
|
|
|
|
#[test]
|
|
fn test_subtraction() {
|
|
let mut tmp = LARGEST;
|
|
tmp -= &LARGEST;
|
|
|
|
assert_eq!(tmp, Scalar::zero());
|
|
|
|
let mut tmp = Scalar::zero();
|
|
tmp -= &LARGEST;
|
|
|
|
let mut tmp2 = MODULUS;
|
|
tmp2 -= &LARGEST;
|
|
|
|
assert_eq!(tmp, tmp2);
|
|
}
|
|
|
|
#[test]
|
|
fn test_multiplication() {
|
|
let mut cur = LARGEST;
|
|
|
|
for _ in 0..100 {
|
|
let mut tmp = cur;
|
|
tmp *= &cur;
|
|
|
|
let mut tmp2 = Scalar::zero();
|
|
for b in cur
|
|
.to_bytes()
|
|
.iter()
|
|
.rev()
|
|
.flat_map(|byte| (0..8).rev().map(move |i| ((byte >> i) & 1u8) == 1u8))
|
|
{
|
|
let tmp3 = tmp2;
|
|
tmp2.add_assign(&tmp3);
|
|
|
|
if b {
|
|
tmp2.add_assign(&cur);
|
|
}
|
|
}
|
|
|
|
assert_eq!(tmp, tmp2);
|
|
|
|
cur.add_assign(&LARGEST);
|
|
}
|
|
}
|
|
|
|
#[test]
|
|
fn test_squaring() {
|
|
let mut cur = LARGEST;
|
|
|
|
for _ in 0..100 {
|
|
let mut tmp = cur;
|
|
tmp = tmp.square();
|
|
|
|
let mut tmp2 = Scalar::zero();
|
|
for b in cur
|
|
.to_bytes()
|
|
.iter()
|
|
.rev()
|
|
.flat_map(|byte| (0..8).rev().map(move |i| ((byte >> i) & 1u8) == 1u8))
|
|
{
|
|
let tmp3 = tmp2;
|
|
tmp2.add_assign(&tmp3);
|
|
|
|
if b {
|
|
tmp2.add_assign(&cur);
|
|
}
|
|
}
|
|
|
|
assert_eq!(tmp, tmp2);
|
|
|
|
cur.add_assign(&LARGEST);
|
|
}
|
|
}
|
|
|
|
#[test]
|
|
fn test_inversion() {
|
|
assert_eq!(Scalar::zero().invert().is_none().unwrap_u8(), 1);
|
|
assert_eq!(Scalar::one().invert().unwrap(), Scalar::one());
|
|
assert_eq!((-&Scalar::one()).invert().unwrap(), -&Scalar::one());
|
|
|
|
let mut tmp = R2;
|
|
|
|
for _ in 0..100 {
|
|
let mut tmp2 = tmp.invert().unwrap();
|
|
tmp2.mul_assign(&tmp);
|
|
|
|
assert_eq!(tmp2, Scalar::one());
|
|
|
|
tmp.add_assign(&R2);
|
|
}
|
|
}
|
|
|
|
#[test]
|
|
fn test_invert_is_pow() {
|
|
let q_minus_2 = [
|
|
0x5812631a5cf5d3eb,
|
|
0x14def9dea2f79cd6,
|
|
0x0000000000000000,
|
|
0x1000000000000000,
|
|
];
|
|
|
|
let mut r1 = R;
|
|
let mut r2 = R;
|
|
let mut r3 = R;
|
|
|
|
for _ in 0..100 {
|
|
r1 = r1.invert().unwrap();
|
|
r2 = r2.pow_vartime(&q_minus_2);
|
|
r3 = r3.pow(&q_minus_2);
|
|
|
|
assert_eq!(r1, r2);
|
|
assert_eq!(r2, r3);
|
|
// Add R so we check something different next time around
|
|
r1.add_assign(&R);
|
|
r2 = r1;
|
|
r3 = r1;
|
|
}
|
|
}
|
|
|
|
#[test]
|
|
fn test_from_raw() {
|
|
assert_eq!(
|
|
Scalar::from_raw([
|
|
0xd6ec31748d98951c,
|
|
0xc6ef5bf4737dcf70,
|
|
0xfffffffffffffffe,
|
|
0x0fffffffffffffff
|
|
]),
|
|
Scalar::from_raw([0xffffffffffffffff; 4])
|
|
);
|
|
|
|
assert_eq!(Scalar::from_raw(MODULUS.0), Scalar::zero());
|
|
|
|
assert_eq!(Scalar::from_raw([1, 0, 0, 0]), R);
|
|
}
|
|
|
|
#[test]
|
|
fn test_double() {
|
|
let a = Scalar::from_raw([
|
|
0x1fff3231233ffffd,
|
|
0x4884b7fa00034802,
|
|
0x998c4fefecbc4ff3,
|
|
0x1824b159acc50562,
|
|
]);
|
|
|
|
assert_eq!(a.double(), a + a);
|
|
}
|
|
}
|