250 lines
7.9 KiB
Rust
250 lines
7.9 KiB
Rust
// -*- mode: rust; coding: utf-8; -*-
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//
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// This file is part of curve25519-dalek.
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// Copyright (c) 2016-2018 Isis Lovecruft, 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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//! Field arithmetic modulo \\(p = 2\^{255} - 19\\), using \\(64\\)-bit
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//! limbs with \\(128\\)-bit products.
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//!
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//! This uses the formally-verified field arithmetic generated by the
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//! [fiat-crypto project](https://github.com/mit-plv/fiat-crypto)
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use core::fmt::Debug;
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use core::ops::Neg;
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use core::ops::{Add, AddAssign};
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use core::ops::{Mul, MulAssign};
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use core::ops::{Sub, SubAssign};
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use subtle::Choice;
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use subtle::ConditionallySelectable;
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use zeroize::Zeroize;
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use fiat_crypto::curve25519_64::*;
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/// A `FieldElement51` represents an element of the field
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/// \\( \mathbb Z / (2\^{255} - 19)\\).
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///
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/// In the 64-bit implementation, a `FieldElement` is represented in
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/// radix \\(2\^{51}\\) as five `u64`s; the coefficients are allowed to
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/// grow up to \\(2\^{54}\\) between reductions modulo \\(p\\).
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///
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/// # Note
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///
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/// The `curve25519_dalek::field` module provides a type alias
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/// `curve25519_dalek::field::FieldElement` to either `FieldElement51`
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/// or `FieldElement2625`.
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///
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/// The backend-specific type `FieldElement51` should not be used
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/// outside of the `curve25519_dalek::field` module.
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#[derive(Copy, Clone)]
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pub struct FieldElement51(pub(crate) [u64; 5]);
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impl Debug for FieldElement51 {
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fn fmt(&self, f: &mut ::core::fmt::Formatter) -> ::core::fmt::Result {
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write!(f, "FieldElement51({:?})", &self.0[..])
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}
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}
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impl Zeroize for FieldElement51 {
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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<'b> AddAssign<&'b FieldElement51> for FieldElement51 {
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fn add_assign(&mut self, _rhs: &'b FieldElement51) {
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let input = self.0;
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fiat_25519_add(&mut self.0, &input, &_rhs.0);
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let input = self.0;
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fiat_25519_carry(&mut self.0, &input);
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}
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}
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impl<'a, 'b> Add<&'b FieldElement51> for &'a FieldElement51 {
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type Output = FieldElement51;
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fn add(self, _rhs: &'b FieldElement51) -> FieldElement51 {
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let mut output = *self;
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fiat_25519_add(&mut output.0, &self.0, &_rhs.0);
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let input = output.0;
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fiat_25519_carry(&mut output.0, &input);
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output
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}
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}
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impl<'b> SubAssign<&'b FieldElement51> for FieldElement51 {
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fn sub_assign(&mut self, _rhs: &'b FieldElement51) {
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let input = self.0;
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fiat_25519_sub(&mut self.0, &input, &_rhs.0);
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let input = self.0;
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fiat_25519_carry(&mut self.0, &input);
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}
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}
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impl<'a, 'b> Sub<&'b FieldElement51> for &'a FieldElement51 {
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type Output = FieldElement51;
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fn sub(self, _rhs: &'b FieldElement51) -> FieldElement51 {
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let mut output = *self;
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fiat_25519_sub(&mut output.0, &self.0, &_rhs.0);
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let input = output.0;
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fiat_25519_carry(&mut output.0, &input);
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output
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}
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}
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impl<'b> MulAssign<&'b FieldElement51> for FieldElement51 {
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fn mul_assign(&mut self, _rhs: &'b FieldElement51) {
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let input = self.0;
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fiat_25519_carry_mul(&mut self.0, &input, &_rhs.0);
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}
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}
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impl<'a, 'b> Mul<&'b FieldElement51> for &'a FieldElement51 {
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type Output = FieldElement51;
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fn mul(self, _rhs: &'b FieldElement51) -> FieldElement51 {
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let mut output = *self;
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fiat_25519_carry_mul(&mut output.0, &self.0, &_rhs.0);
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output
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}
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}
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impl<'a> Neg for &'a FieldElement51 {
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type Output = FieldElement51;
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fn neg(self) -> FieldElement51 {
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let mut output = *self;
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fiat_25519_opp(&mut output.0, &self.0);
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let input = output.0;
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fiat_25519_carry(&mut output.0, &input);
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output
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}
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}
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impl ConditionallySelectable for FieldElement51 {
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fn conditional_select(
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a: &FieldElement51,
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b: &FieldElement51,
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choice: Choice,
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) -> FieldElement51 {
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let mut output = [0u64; 5];
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fiat_25519_selectznz(&mut output, choice.unwrap_u8() as fiat_25519_u1, &a.0, &b.0);
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FieldElement51(output)
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}
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fn conditional_swap(a: &mut FieldElement51, b: &mut FieldElement51, choice: Choice) {
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u64::conditional_swap(&mut a.0[0], &mut b.0[0], choice);
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u64::conditional_swap(&mut a.0[1], &mut b.0[1], choice);
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u64::conditional_swap(&mut a.0[2], &mut b.0[2], choice);
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u64::conditional_swap(&mut a.0[3], &mut b.0[3], choice);
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u64::conditional_swap(&mut a.0[4], &mut b.0[4], choice);
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}
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fn conditional_assign(&mut self, _rhs: &FieldElement51, choice: Choice) {
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let mut output = [0u64; 5];
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let choicebit = choice.unwrap_u8() as fiat_25519_u1;
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fiat_25519_cmovznz_u64(&mut output[0], choicebit, self.0[0], _rhs.0[0]);
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fiat_25519_cmovznz_u64(&mut output[1], choicebit, self.0[1], _rhs.0[1]);
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fiat_25519_cmovznz_u64(&mut output[2], choicebit, self.0[2], _rhs.0[2]);
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fiat_25519_cmovznz_u64(&mut output[3], choicebit, self.0[3], _rhs.0[3]);
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fiat_25519_cmovznz_u64(&mut output[4], choicebit, self.0[4], _rhs.0[4]);
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*self = FieldElement51(output);
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}
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}
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impl FieldElement51 {
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/// Construct zero.
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pub fn zero() -> FieldElement51 {
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FieldElement51([0, 0, 0, 0, 0])
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}
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/// Construct one.
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pub fn one() -> FieldElement51 {
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FieldElement51([1, 0, 0, 0, 0])
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}
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/// Construct -1.
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pub fn minus_one() -> FieldElement51 {
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FieldElement51([
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2251799813685228,
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2251799813685247,
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2251799813685247,
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2251799813685247,
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2251799813685247,
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])
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}
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/// Given 64-bit input limbs, reduce to enforce the bound 2^(51 + epsilon).
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#[inline(always)]
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#[allow(dead_code)] // Need this to not complain about reduce not being used
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fn reduce(mut limbs: [u64; 5]) -> FieldElement51 {
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let input = limbs;
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fiat_25519_carry(&mut limbs, &input);
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FieldElement51(limbs)
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}
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/// Load a `FieldElement51` from the low 255 bits of a 256-bit
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/// input.
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///
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/// # Warning
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///
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/// This function does not check that the input used the canonical
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/// representative. It masks the high bit, but it will happily
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/// decode 2^255 - 18 to 1. Applications that require a canonical
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/// encoding of every field element should decode, re-encode to
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/// the canonical encoding, and check that the input was
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/// canonical.
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///
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pub fn from_bytes(bytes: &[u8; 32]) -> FieldElement51 {
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let mut temp = [0u8; 32];
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temp.copy_from_slice(bytes);
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temp[31] &= 127u8;
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let mut output = [0u64; 5];
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fiat_25519_from_bytes(&mut output, &temp);
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FieldElement51(output)
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}
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/// Serialize this `FieldElement51` to a 32-byte array. The
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/// encoding is canonical.
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pub fn to_bytes(&self) -> [u8; 32] {
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let mut bytes = [0u8; 32];
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fiat_25519_to_bytes(&mut bytes, &self.0);
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return bytes;
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}
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/// Given `k > 0`, return `self^(2^k)`.
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pub fn pow2k(&self, mut k: u32) -> FieldElement51 {
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let mut output = *self;
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loop {
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let input = output.0;
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fiat_25519_carry_square(&mut output.0, &input);
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k -= 1;
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if k == 0 {
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return output;
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}
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}
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}
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/// Returns the square of this field element.
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pub fn square(&self) -> FieldElement51 {
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let mut output = *self;
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fiat_25519_carry_square(&mut output.0, &self.0);
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output
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}
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/// Returns 2 times the square of this field element.
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pub fn square2(&self) -> FieldElement51 {
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let mut output = *self;
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let mut temp = *self;
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// Void vs return type, measure cost of copying self
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fiat_25519_carry_square(&mut temp.0, &self.0);
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fiat_25519_add(&mut output.0, &temp.0, &temp.0);
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let input = output.0;
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fiat_25519_carry(&mut output.0, &input);
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output
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}
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}
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