mirror of
https://github.com/saymrwulf/curve25519-dalek-source.git
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8e0cef5b72
There is occasionally [a need](https://github.com/dalek-cryptography/curve25519-dalek/pull/519#issuecomment-1637770888) to multiply a non-prime-order Montgomery point by an integer. There's currently no way to do this, since our only methods are multiplication by `Scalar` (doesn't make sense in the non-prime-order case), and `MontgomeryPoint::mul_base_clamped` clamps the integer before multiplying. This defines `MontgomeryPoint::mul_bits_be`, which takes a big-endian representation of an integer and multiplies the point by that integer. Its usage is not recommended by default, but it is also not so unsafe as to be gated behind a `hazmat` feature.
660 lines
22 KiB
Rust
660 lines
22 KiB
Rust
// -*- mode: rust; -*-
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//
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// This file is part of curve25519-dalek.
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// Copyright (c) 2016-2021 isis lovecruft
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// Copyright (c) 2016-2019 Henry de Valence
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// See LICENSE for licensing information.
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//
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// Authors:
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// - isis agora lovecruft <isis@patternsinthevoid.net>
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// - Henry de Valence <hdevalence@hdevalence.ca>
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//! Scalar multiplication on the Montgomery form of Curve25519.
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//!
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//! To avoid notational confusion with the Edwards code, we use
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//! variables \\( u, v \\) for the Montgomery curve, so that “Montgomery
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//! \\(u\\)” here corresponds to “Montgomery \\(x\\)” elsewhere.
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//!
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//! Montgomery arithmetic works not on the curve itself, but on the
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//! \\(u\\)-line, which discards sign information and unifies the curve
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//! and its quadratic twist. See [_Montgomery curves and their
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//! arithmetic_][costello-smith] by Costello and Smith for more details.
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//!
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//! The `MontgomeryPoint` struct contains the affine \\(u\\)-coordinate
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//! \\(u\_0(P)\\) of a point \\(P\\) on either the curve or the twist.
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//! Here the map \\(u\_0 : \mathcal M \rightarrow \mathbb F\_p \\) is
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//! defined by \\(u\_0((u,v)) = u\\); \\(u\_0(\mathcal O) = 0\\). See
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//! section 5.4 of Costello-Smith for more details.
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//!
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//! # Scalar Multiplication
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//!
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//! Scalar multiplication on `MontgomeryPoint`s is provided by the `*`
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//! operator, which implements the Montgomery ladder.
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//!
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//! # Edwards Conversion
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//!
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//! The \\(2\\)-to-\\(1\\) map from the Edwards model to the Montgomery
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//! \\(u\\)-line is provided by `EdwardsPoint::to_montgomery()`.
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//!
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//! To lift a `MontgomeryPoint` to an `EdwardsPoint`, use
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//! `MontgomeryPoint::to_edwards()`, which takes a sign parameter.
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//! This function rejects `MontgomeryPoints` which correspond to points
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//! on the twist.
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//!
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//! [costello-smith]: https://eprint.iacr.org/2017/212.pdf
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// We allow non snake_case names because coordinates in projective space are
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// traditionally denoted by the capitalisation of their respective
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// counterparts in affine space. Yeah, you heard me, rustc, I'm gonna have my
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// affine and projective cakes and eat both of them too.
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#![allow(non_snake_case)]
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use core::{
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hash::{Hash, Hasher},
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ops::{Mul, MulAssign},
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};
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use crate::constants::{APLUS2_OVER_FOUR, MONTGOMERY_A, MONTGOMERY_A_NEG};
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use crate::edwards::{CompressedEdwardsY, EdwardsPoint};
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use crate::field::FieldElement;
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use crate::scalar::{clamp_integer, Scalar};
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use crate::traits::Identity;
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use subtle::Choice;
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use subtle::ConstantTimeEq;
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use subtle::{ConditionallyNegatable, ConditionallySelectable};
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#[cfg(feature = "zeroize")]
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use zeroize::Zeroize;
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/// Holds the \\(u\\)-coordinate of a point on the Montgomery form of
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/// Curve25519 or its twist.
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#[derive(Copy, Clone, Debug, Default)]
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#[cfg_attr(feature = "serde", derive(serde::Serialize, serde::Deserialize))]
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pub struct MontgomeryPoint(pub [u8; 32]);
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/// Equality of `MontgomeryPoint`s is defined mod p.
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impl ConstantTimeEq for MontgomeryPoint {
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fn ct_eq(&self, other: &MontgomeryPoint) -> Choice {
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let self_fe = FieldElement::from_bytes(&self.0);
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let other_fe = FieldElement::from_bytes(&other.0);
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self_fe.ct_eq(&other_fe)
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}
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}
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impl PartialEq for MontgomeryPoint {
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fn eq(&self, other: &MontgomeryPoint) -> bool {
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self.ct_eq(other).into()
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}
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}
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impl Eq for MontgomeryPoint {}
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// Equal MontgomeryPoints must hash to the same value. So we have to get them into a canonical
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// encoding first
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impl Hash for MontgomeryPoint {
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fn hash<H: Hasher>(&self, state: &mut H) {
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// Do a round trip through a `FieldElement`. `as_bytes` is guaranteed to give a canonical
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// 32-byte encoding
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let canonical_bytes = FieldElement::from_bytes(&self.0).as_bytes();
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canonical_bytes.hash(state);
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}
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}
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impl Identity for MontgomeryPoint {
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/// Return the group identity element, which has order 4.
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fn identity() -> MontgomeryPoint {
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MontgomeryPoint([0u8; 32])
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}
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}
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#[cfg(feature = "zeroize")]
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impl Zeroize for MontgomeryPoint {
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fn zeroize(&mut self) {
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self.0.zeroize();
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}
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}
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impl MontgomeryPoint {
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/// Fixed-base scalar multiplication (i.e. multiplication by the base point).
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pub fn mul_base(scalar: &Scalar) -> Self {
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EdwardsPoint::mul_base(scalar).to_montgomery()
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}
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/// Multiply this point by `clamp_integer(bytes)`. For a description of clamping, see
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/// [`clamp_integer`].
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pub fn mul_clamped(self, bytes: [u8; 32]) -> Self {
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// We have to construct a Scalar that is not reduced mod l, which breaks scalar invariant
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// #2. But #2 is not necessary for correctness of variable-base multiplication. All that
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// needs to hold is invariant #1, i.e., the scalar is less than 2^255. This is guaranteed
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// by clamping.
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// Further, we don't do any reduction or arithmetic with this clamped value, so there's no
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// issues arising from the fact that the curve point is not necessarily in the prime-order
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// subgroup.
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let s = Scalar {
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bytes: clamp_integer(bytes),
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};
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s * self
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}
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/// Multiply the basepoint by `clamp_integer(bytes)`. For a description of clamping, see
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/// [`clamp_integer`].
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pub fn mul_base_clamped(bytes: [u8; 32]) -> Self {
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// See reasoning in Self::mul_clamped why it is OK to make an unreduced Scalar here. We
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// note that fixed-base multiplication is also defined for all values of `bytes` less than
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// 2^255.
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let s = Scalar {
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bytes: clamp_integer(bytes),
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};
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Self::mul_base(&s)
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}
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/// Given `self` \\( = u\_0(P) \\), and a big-endian bit representation of an integer
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/// \\(n\\), return \\( u\_0(\[n\]P) \\). This is constant time in the length of `bits`.
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///
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/// **NOTE:** You probably do not want to use this function. Almost every protocol built on
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/// Curve25519 uses _clamped multiplication_, explained
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/// [here](https://neilmadden.blog/2020/05/28/whats-the-curve25519-clamping-all-about/).
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/// When in doubt, use [`Self::mul_clamped`].
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pub fn mul_bits_be(&self, bits: impl Iterator<Item = bool>) -> MontgomeryPoint {
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// Algorithm 8 of Costello-Smith 2017
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let affine_u = FieldElement::from_bytes(&self.0);
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let mut x0 = ProjectivePoint::identity();
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let mut x1 = ProjectivePoint {
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U: affine_u,
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W: FieldElement::ONE,
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};
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// Go through the bits from most to least significant, using a sliding window of 2
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let mut prev_bit = false;
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for cur_bit in bits {
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let choice: u8 = (prev_bit ^ cur_bit) as u8;
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debug_assert!(choice == 0 || choice == 1);
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ProjectivePoint::conditional_swap(&mut x0, &mut x1, choice.into());
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differential_add_and_double(&mut x0, &mut x1, &affine_u);
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prev_bit = cur_bit;
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}
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// The final value of prev_bit above is scalar.bits()[0], i.e., the LSB of scalar
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ProjectivePoint::conditional_swap(&mut x0, &mut x1, Choice::from(prev_bit as u8));
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// Don't leave the bit in the stack
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#[cfg(feature = "zeroize")]
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prev_bit.zeroize();
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x0.as_affine()
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}
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/// View this `MontgomeryPoint` as an array of bytes.
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pub const fn as_bytes(&self) -> &[u8; 32] {
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&self.0
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}
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/// Convert this `MontgomeryPoint` to an array of bytes.
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pub const fn to_bytes(&self) -> [u8; 32] {
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self.0
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}
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/// Attempt to convert to an `EdwardsPoint`, using the supplied
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/// choice of sign for the `EdwardsPoint`.
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///
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/// # Inputs
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///
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/// * `sign`: a `u8` donating the desired sign of the resulting
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/// `EdwardsPoint`. `0` denotes positive and `1` negative.
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///
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/// # Return
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///
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/// * `Some(EdwardsPoint)` if `self` is the \\(u\\)-coordinate of a
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/// point on (the Montgomery form of) Curve25519;
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///
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/// * `None` if `self` is the \\(u\\)-coordinate of a point on the
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/// twist of (the Montgomery form of) Curve25519;
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///
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pub fn to_edwards(&self, sign: u8) -> Option<EdwardsPoint> {
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// To decompress the Montgomery u coordinate to an
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// `EdwardsPoint`, we apply the birational map to obtain the
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// Edwards y coordinate, then do Edwards decompression.
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//
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// The birational map is y = (u-1)/(u+1).
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//
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// The exceptional points are the zeros of the denominator,
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// i.e., u = -1.
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//
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// But when u = -1, v^2 = u*(u^2+486662*u+1) = 486660.
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//
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// Since this is nonsquare mod p, u = -1 corresponds to a point
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// on the twist, not the curve, so we can reject it early.
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let u = FieldElement::from_bytes(&self.0);
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if u == FieldElement::MINUS_ONE {
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return None;
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}
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let one = FieldElement::ONE;
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let y = &(&u - &one) * &(&u + &one).invert();
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let mut y_bytes = y.as_bytes();
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y_bytes[31] ^= sign << 7;
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CompressedEdwardsY(y_bytes).decompress()
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}
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}
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/// Perform the Elligator2 mapping to a Montgomery point.
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///
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/// See <https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-10#section-6.7.1>
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//
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// TODO Determine how much of the hash-to-group API should be exposed after the CFRG
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// draft gets into a more polished/accepted state.
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#[allow(unused)]
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pub(crate) fn elligator_encode(r_0: &FieldElement) -> MontgomeryPoint {
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let one = FieldElement::ONE;
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let d_1 = &one + &r_0.square2(); /* 2r^2 */
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let d = &MONTGOMERY_A_NEG * &(d_1.invert()); /* A/(1+2r^2) */
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let d_sq = &d.square();
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let au = &MONTGOMERY_A * &d;
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let inner = &(d_sq + &au) + &one;
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let eps = &d * &inner; /* eps = d^3 + Ad^2 + d */
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let (eps_is_sq, _eps) = FieldElement::sqrt_ratio_i(&eps, &one);
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let zero = FieldElement::ZERO;
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let Atemp = FieldElement::conditional_select(&MONTGOMERY_A, &zero, eps_is_sq); /* 0, or A if nonsquare*/
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let mut u = &d + &Atemp; /* d, or d+A if nonsquare */
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u.conditional_negate(!eps_is_sq); /* d, or -d-A if nonsquare */
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MontgomeryPoint(u.as_bytes())
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}
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/// A `ProjectivePoint` holds a point on the projective line
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/// \\( \mathbb P(\mathbb F\_p) \\), which we identify with the Kummer
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/// line of the Montgomery curve.
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#[derive(Copy, Clone, Debug)]
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struct ProjectivePoint {
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pub U: FieldElement,
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pub W: FieldElement,
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}
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impl Identity for ProjectivePoint {
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fn identity() -> ProjectivePoint {
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ProjectivePoint {
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U: FieldElement::ONE,
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W: FieldElement::ZERO,
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}
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}
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}
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impl Default for ProjectivePoint {
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fn default() -> ProjectivePoint {
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ProjectivePoint::identity()
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}
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}
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impl ConditionallySelectable for ProjectivePoint {
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fn conditional_select(
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a: &ProjectivePoint,
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b: &ProjectivePoint,
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choice: Choice,
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) -> ProjectivePoint {
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ProjectivePoint {
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U: FieldElement::conditional_select(&a.U, &b.U, choice),
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W: FieldElement::conditional_select(&a.W, &b.W, choice),
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}
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}
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}
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impl ProjectivePoint {
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/// Dehomogenize this point to affine coordinates.
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///
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/// # Return
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///
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/// * \\( u = U / W \\) if \\( W \neq 0 \\);
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/// * \\( 0 \\) if \\( W \eq 0 \\);
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pub fn as_affine(&self) -> MontgomeryPoint {
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let u = &self.U * &self.W.invert();
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MontgomeryPoint(u.as_bytes())
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}
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}
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/// Perform the double-and-add step of the Montgomery ladder.
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///
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/// Given projective points
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/// \\( (U\_P : W\_P) = u(P) \\),
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/// \\( (U\_Q : W\_Q) = u(Q) \\),
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/// and the affine difference
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/// \\( u\_{P-Q} = u(P-Q) \\), set
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/// $$
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/// (U\_P : W\_P) \gets u(\[2\]P)
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/// $$
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/// and
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/// $$
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/// (U\_Q : W\_Q) \gets u(P + Q).
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/// $$
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#[rustfmt::skip] // keep alignment of explanatory comments
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fn differential_add_and_double(
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P: &mut ProjectivePoint,
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Q: &mut ProjectivePoint,
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affine_PmQ: &FieldElement,
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) {
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let t0 = &P.U + &P.W;
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let t1 = &P.U - &P.W;
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let t2 = &Q.U + &Q.W;
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let t3 = &Q.U - &Q.W;
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let t4 = t0.square(); // (U_P + W_P)^2 = U_P^2 + 2 U_P W_P + W_P^2
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let t5 = t1.square(); // (U_P - W_P)^2 = U_P^2 - 2 U_P W_P + W_P^2
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let t6 = &t4 - &t5; // 4 U_P W_P
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let t7 = &t0 * &t3; // (U_P + W_P) (U_Q - W_Q) = U_P U_Q + W_P U_Q - U_P W_Q - W_P W_Q
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let t8 = &t1 * &t2; // (U_P - W_P) (U_Q + W_Q) = U_P U_Q - W_P U_Q + U_P W_Q - W_P W_Q
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let t9 = &t7 + &t8; // 2 (U_P U_Q - W_P W_Q)
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let t10 = &t7 - &t8; // 2 (W_P U_Q - U_P W_Q)
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let t11 = t9.square(); // 4 (U_P U_Q - W_P W_Q)^2
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let t12 = t10.square(); // 4 (W_P U_Q - U_P W_Q)^2
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let t13 = &APLUS2_OVER_FOUR * &t6; // (A + 2) U_P U_Q
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let t14 = &t4 * &t5; // ((U_P + W_P)(U_P - W_P))^2 = (U_P^2 - W_P^2)^2
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let t15 = &t13 + &t5; // (U_P - W_P)^2 + (A + 2) U_P W_P
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let t16 = &t6 * &t15; // 4 (U_P W_P) ((U_P - W_P)^2 + (A + 2) U_P W_P)
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let t17 = affine_PmQ * &t12; // U_D * 4 (W_P U_Q - U_P W_Q)^2
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let t18 = t11; // W_D * 4 (U_P U_Q - W_P W_Q)^2
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P.U = t14; // U_{P'} = (U_P + W_P)^2 (U_P - W_P)^2
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P.W = t16; // W_{P'} = (4 U_P W_P) ((U_P - W_P)^2 + ((A + 2)/4) 4 U_P W_P)
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Q.U = t18; // U_{Q'} = W_D * 4 (U_P U_Q - W_P W_Q)^2
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Q.W = t17; // W_{Q'} = U_D * 4 (W_P U_Q - U_P W_Q)^2
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}
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define_mul_assign_variants!(LHS = MontgomeryPoint, RHS = Scalar);
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define_mul_variants!(
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LHS = MontgomeryPoint,
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RHS = Scalar,
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Output = MontgomeryPoint
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);
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define_mul_variants!(
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LHS = Scalar,
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RHS = MontgomeryPoint,
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Output = MontgomeryPoint
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);
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/// Multiply this `MontgomeryPoint` by a `Scalar`.
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impl Mul<&Scalar> for &MontgomeryPoint {
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type Output = MontgomeryPoint;
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/// Given `self` \\( = u\_0(P) \\), and a `Scalar` \\(n\\), return \\( u\_0(\[n\]P) \\)
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fn mul(self, scalar: &Scalar) -> MontgomeryPoint {
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// We multiply by the integer representation of the given Scalar. By scalar invariant #1,
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// the MSB is 0, so we can skip it.
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self.mul_bits_be(scalar.bits_le().rev().skip(1))
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}
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}
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impl MulAssign<&Scalar> for MontgomeryPoint {
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fn mul_assign(&mut self, scalar: &Scalar) {
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*self = (self as &MontgomeryPoint) * scalar;
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}
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}
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impl Mul<&MontgomeryPoint> for &Scalar {
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type Output = MontgomeryPoint;
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fn mul(self, point: &MontgomeryPoint) -> MontgomeryPoint {
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point * self
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}
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}
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// ------------------------------------------------------------------------
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// Tests
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// ------------------------------------------------------------------------
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#[cfg(test)]
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mod test {
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use super::*;
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use crate::constants;
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#[cfg(feature = "alloc")]
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use alloc::vec::Vec;
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use rand_core::{CryptoRng, RngCore};
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#[test]
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fn identity_in_different_coordinates() {
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let id_projective = ProjectivePoint::identity();
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let id_montgomery = id_projective.as_affine();
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assert!(id_montgomery == MontgomeryPoint::identity());
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}
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#[test]
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fn identity_in_different_models() {
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assert!(EdwardsPoint::identity().to_montgomery() == MontgomeryPoint::identity());
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}
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#[test]
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#[cfg(feature = "serde")]
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fn serde_bincode_basepoint_roundtrip() {
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use bincode;
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let encoded = bincode::serialize(&constants::X25519_BASEPOINT).unwrap();
|
|
let decoded: MontgomeryPoint = bincode::deserialize(&encoded).unwrap();
|
|
|
|
assert_eq!(encoded.len(), 32);
|
|
assert_eq!(decoded, constants::X25519_BASEPOINT);
|
|
|
|
let raw_bytes = constants::X25519_BASEPOINT.as_bytes();
|
|
let bp: MontgomeryPoint = bincode::deserialize(raw_bytes).unwrap();
|
|
assert_eq!(bp, constants::X25519_BASEPOINT);
|
|
}
|
|
|
|
/// Test Montgomery -> Edwards on the X/Ed25519 basepoint
|
|
#[test]
|
|
fn basepoint_montgomery_to_edwards() {
|
|
// sign bit = 0 => basepoint
|
|
assert_eq!(
|
|
constants::ED25519_BASEPOINT_POINT,
|
|
constants::X25519_BASEPOINT.to_edwards(0).unwrap()
|
|
);
|
|
// sign bit = 1 => minus basepoint
|
|
assert_eq!(
|
|
-constants::ED25519_BASEPOINT_POINT,
|
|
constants::X25519_BASEPOINT.to_edwards(1).unwrap()
|
|
);
|
|
}
|
|
|
|
/// Test Edwards -> Montgomery on the X/Ed25519 basepoint
|
|
#[test]
|
|
fn basepoint_edwards_to_montgomery() {
|
|
assert_eq!(
|
|
constants::ED25519_BASEPOINT_POINT.to_montgomery(),
|
|
constants::X25519_BASEPOINT
|
|
);
|
|
}
|
|
|
|
/// Check that Montgomery -> Edwards fails for points on the twist.
|
|
#[test]
|
|
fn montgomery_to_edwards_rejects_twist() {
|
|
let one = FieldElement::ONE;
|
|
|
|
// u = 2 corresponds to a point on the twist.
|
|
let two = MontgomeryPoint((&one + &one).as_bytes());
|
|
|
|
assert!(two.to_edwards(0).is_none());
|
|
|
|
// u = -1 corresponds to a point on the twist, but should be
|
|
// checked explicitly because it's an exceptional point for the
|
|
// birational map. For instance, libsignal will accept it.
|
|
let minus_one = MontgomeryPoint((-&one).as_bytes());
|
|
|
|
assert!(minus_one.to_edwards(0).is_none());
|
|
}
|
|
|
|
#[test]
|
|
fn eq_defined_mod_p() {
|
|
let mut u18_bytes = [0u8; 32];
|
|
u18_bytes[0] = 18;
|
|
let u18 = MontgomeryPoint(u18_bytes);
|
|
let u18_unred = MontgomeryPoint([255; 32]);
|
|
|
|
assert_eq!(u18, u18_unred);
|
|
}
|
|
|
|
/// Returns a random point on the prime-order subgroup
|
|
fn rand_prime_order_point(mut rng: impl RngCore + CryptoRng) -> EdwardsPoint {
|
|
let s: Scalar = Scalar::random(&mut rng);
|
|
EdwardsPoint::mul_base(&s)
|
|
}
|
|
|
|
/// Given a bytestring that's little-endian at the byte level, return an iterator over all the
|
|
/// bits, in little-endian order.
|
|
fn bytestring_bits_le(x: &[u8]) -> impl DoubleEndedIterator<Item = bool> + Clone + '_ {
|
|
let bitlen = x.len() * 8;
|
|
(0..bitlen).map(|i| {
|
|
// As i runs from 0..256, the bottom 3 bits index the bit, while the upper bits index
|
|
// the byte. Since self.bytes is little-endian at the byte level, this iterator is
|
|
// little-endian on the bit level
|
|
((x[i >> 3] >> (i & 7)) & 1u8) == 1
|
|
})
|
|
}
|
|
|
|
#[test]
|
|
fn montgomery_ladder_matches_edwards_scalarmult() {
|
|
let mut csprng = rand_core::OsRng;
|
|
|
|
for _ in 0..100 {
|
|
let p_edwards = rand_prime_order_point(&mut csprng);
|
|
let p_montgomery: MontgomeryPoint = p_edwards.to_montgomery();
|
|
|
|
let s: Scalar = Scalar::random(&mut csprng);
|
|
let expected = s * p_edwards;
|
|
let result = s * p_montgomery;
|
|
|
|
assert_eq!(result, expected.to_montgomery())
|
|
}
|
|
}
|
|
|
|
// Tests that, on the prime-order subgroup, MontgomeryPoint::mul_bits_be is the same as
|
|
// multiplying by the Scalar representation of the same bits
|
|
#[test]
|
|
fn montgomery_mul_bits_be() {
|
|
let mut csprng = rand_core::OsRng;
|
|
|
|
for _ in 0..100 {
|
|
// Make a random prime-order point P
|
|
let p_edwards = rand_prime_order_point(&mut csprng);
|
|
let p_montgomery: MontgomeryPoint = p_edwards.to_montgomery();
|
|
|
|
// Make a random integer b
|
|
let mut bigint = [0u8; 64];
|
|
csprng.fill_bytes(&mut bigint[..]);
|
|
let bigint_bits_be = bytestring_bits_le(&bigint).rev();
|
|
|
|
// Check that bP is the same whether calculated as scalar-times-edwards or
|
|
// integer-times-montgomery.
|
|
let expected = Scalar::from_bytes_mod_order_wide(&bigint) * p_edwards;
|
|
let result = p_montgomery.mul_bits_be(bigint_bits_be);
|
|
assert_eq!(result, expected.to_montgomery())
|
|
}
|
|
}
|
|
|
|
// Tests that MontgomeryPoint::mul_bits_be is consistent on any point, even ones that might be
|
|
// on the curve's twist. Specifically, this tests that b₁(b₂P) == b₂(b₁P) for random
|
|
// integers b₁, b₂ and random (curve or twist) point P.
|
|
#[test]
|
|
fn montgomery_mul_bits_be_twist() {
|
|
let mut csprng = rand_core::OsRng;
|
|
|
|
for _ in 0..100 {
|
|
// Make a random point P on the curve or its twist
|
|
let p_montgomery = {
|
|
let mut buf = [0u8; 32];
|
|
csprng.fill_bytes(&mut buf);
|
|
MontgomeryPoint(buf)
|
|
};
|
|
|
|
// Compute two big integers b₁ and b₂
|
|
let mut bigint1 = [0u8; 64];
|
|
let mut bigint2 = [0u8; 64];
|
|
csprng.fill_bytes(&mut bigint1[..]);
|
|
csprng.fill_bytes(&mut bigint2[..]);
|
|
|
|
// Compute b₁P and b₂P
|
|
let bigint1_bits_be = bytestring_bits_le(&bigint1).rev();
|
|
let bigint2_bits_be = bytestring_bits_le(&bigint2).rev();
|
|
let prod1 = p_montgomery.mul_bits_be(bigint1_bits_be.clone());
|
|
let prod2 = p_montgomery.mul_bits_be(bigint2_bits_be.clone());
|
|
|
|
// Check that b₁(b₂P) == b₂(b₁P)
|
|
assert_eq!(
|
|
prod1.mul_bits_be(bigint2_bits_be),
|
|
prod2.mul_bits_be(bigint1_bits_be)
|
|
);
|
|
}
|
|
}
|
|
|
|
/// Check that mul_base_clamped and mul_clamped agree
|
|
#[test]
|
|
fn mul_base_clamped() {
|
|
let mut csprng = rand_core::OsRng;
|
|
|
|
// Test agreement on a large integer. Even after clamping, this is not reduced mod l.
|
|
let a_bytes = [0xff; 32];
|
|
assert_eq!(
|
|
MontgomeryPoint::mul_base_clamped(a_bytes),
|
|
constants::X25519_BASEPOINT.mul_clamped(a_bytes)
|
|
);
|
|
|
|
// Test agreement on random integers
|
|
for _ in 0..100 {
|
|
// This will be reduced mod l with probability l / 2^256 ≈ 6.25%
|
|
let mut a_bytes = [0u8; 32];
|
|
csprng.fill_bytes(&mut a_bytes);
|
|
|
|
assert_eq!(
|
|
MontgomeryPoint::mul_base_clamped(a_bytes),
|
|
constants::X25519_BASEPOINT.mul_clamped(a_bytes)
|
|
);
|
|
}
|
|
}
|
|
|
|
#[cfg(feature = "alloc")]
|
|
const ELLIGATOR_CORRECT_OUTPUT: [u8; 32] = [
|
|
0x5f, 0x35, 0x20, 0x00, 0x1c, 0x6c, 0x99, 0x36, 0xa3, 0x12, 0x06, 0xaf, 0xe7, 0xc7, 0xac,
|
|
0x22, 0x4e, 0x88, 0x61, 0x61, 0x9b, 0xf9, 0x88, 0x72, 0x44, 0x49, 0x15, 0x89, 0x9d, 0x95,
|
|
0xf4, 0x6e,
|
|
];
|
|
|
|
#[test]
|
|
#[cfg(feature = "alloc")]
|
|
fn montgomery_elligator_correct() {
|
|
let bytes: Vec<u8> = (0u8..32u8).collect();
|
|
let bits_in: [u8; 32] = (&bytes[..]).try_into().expect("Range invariant broken");
|
|
|
|
let fe = FieldElement::from_bytes(&bits_in);
|
|
let eg = elligator_encode(&fe);
|
|
assert_eq!(eg.to_bytes(), ELLIGATOR_CORRECT_OUTPUT);
|
|
}
|
|
|
|
#[test]
|
|
fn montgomery_elligator_zero_zero() {
|
|
let zero = [0u8; 32];
|
|
let fe = FieldElement::from_bytes(&zero);
|
|
let eg = elligator_encode(&fe);
|
|
assert_eq!(eg.to_bytes(), zero);
|
|
}
|
|
}
|