177 lines
6.0 KiB
Rust
177 lines
6.0 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) 2016-2019 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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//! Various constants, such as the Ristretto and Ed25519 basepoints.
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//!
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//! Most of the constants are given with
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//! `LONG_DESCRIPTIVE_UPPER_CASE_NAMES`, but they can be brought into
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//! scope using a `let` binding:
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//!
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//! ```
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//! use curve25519_dalek::constants;
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//! use curve25519_dalek::traits::IsIdentity;
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//!
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//! let B = &constants::RISTRETTO_BASEPOINT_TABLE;
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//! let l = &constants::BASEPOINT_ORDER;
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//!
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//! let A = l * B;
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//! assert!(A.is_identity());
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//! ```
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#![allow(non_snake_case)]
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use edwards::CompressedEdwardsY;
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use ristretto::RistrettoPoint;
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use ristretto::CompressedRistretto;
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use montgomery::MontgomeryPoint;
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use scalar::Scalar;
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#[cfg(feature = "u64_backend")]
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pub use backend::serial::u64::constants::*;
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#[cfg(feature = "u32_backend")]
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pub use backend::serial::u32::constants::*;
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/// The Ed25519 basepoint, in `CompressedEdwardsY` format.
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///
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/// This is the little-endian byte encoding of \\( 4/5 \pmod p \\),
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/// which is the \\(y\\)-coordinate of the Ed25519 basepoint.
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///
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/// The sign bit is 0 since the basepoint has \\(x\\) chosen to be positive.
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pub const ED25519_BASEPOINT_COMPRESSED: CompressedEdwardsY =
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CompressedEdwardsY([0x58, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66,
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0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66,
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0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66,
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0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66]);
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/// The X25519 basepoint, in `MontgomeryPoint` format.
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pub const X25519_BASEPOINT: MontgomeryPoint =
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MontgomeryPoint([0x09, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
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0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
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0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
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0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]);
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/// The Ristretto basepoint, in `CompressedRistretto` format.
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pub const RISTRETTO_BASEPOINT_COMPRESSED: CompressedRistretto =
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CompressedRistretto([0xe2, 0xf2, 0xae, 0x0a, 0x6a, 0xbc, 0x4e, 0x71,
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0xa8, 0x84, 0xa9, 0x61, 0xc5, 0x00, 0x51, 0x5f,
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0x58, 0xe3, 0x0b, 0x6a, 0xa5, 0x82, 0xdd, 0x8d,
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0xb6, 0xa6, 0x59, 0x45, 0xe0, 0x8d, 0x2d, 0x76]);
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/// The Ristretto basepoint, as a `RistrettoPoint`.
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///
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/// This is called `_POINT` to distinguish it from `_TABLE`, which
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/// provides fast scalar multiplication.
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pub const RISTRETTO_BASEPOINT_POINT: RistrettoPoint = RistrettoPoint(ED25519_BASEPOINT_POINT);
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/// `BASEPOINT_ORDER` is the order of the Ristretto group and of the Ed25519 basepoint, i.e.,
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/// $$
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/// \ell = 2^\{252\} + 27742317777372353535851937790883648493.
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/// $$
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pub const BASEPOINT_ORDER: Scalar = Scalar{
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bytes: [
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0xed, 0xd3, 0xf5, 0x5c, 0x1a, 0x63, 0x12, 0x58,
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0xd6, 0x9c, 0xf7, 0xa2, 0xde, 0xf9, 0xde, 0x14,
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0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
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0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x10,
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],
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};
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use ristretto::RistrettoBasepointTable;
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/// The Ristretto basepoint, as a `RistrettoBasepointTable` for scalar multiplication.
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pub const RISTRETTO_BASEPOINT_TABLE: RistrettoBasepointTable
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= RistrettoBasepointTable(ED25519_BASEPOINT_TABLE);
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#[cfg(test)]
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mod test {
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use field::FieldElement;
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use traits::{IsIdentity, ValidityCheck};
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use constants;
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#[test]
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fn test_eight_torsion() {
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for i in 0..8 {
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let Q = constants::EIGHT_TORSION[i].mul_by_pow_2(3);
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assert!(Q.is_valid());
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assert!(Q.is_identity());
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}
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}
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#[test]
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fn test_four_torsion() {
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for i in (0..8).filter(|i| i % 2 == 0) {
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let Q = constants::EIGHT_TORSION[i].mul_by_pow_2(2);
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assert!(Q.is_valid());
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assert!(Q.is_identity());
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}
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}
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#[test]
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fn test_two_torsion() {
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for i in (0..8).filter(|i| i % 4 == 0) {
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let Q = constants::EIGHT_TORSION[i].mul_by_pow_2(1);
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assert!(Q.is_valid());
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assert!(Q.is_identity());
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}
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}
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/// Test that SQRT_M1 is the positive square root of -1
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#[test]
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fn test_sqrt_minus_one() {
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let minus_one = FieldElement::minus_one();
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let sqrt_m1_sq = &constants::SQRT_M1 * &constants::SQRT_M1;
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assert_eq!(minus_one, sqrt_m1_sq);
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assert_eq!(constants::SQRT_M1.is_negative().unwrap_u8(), 0);
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}
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#[test]
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fn test_sqrt_constants_sign() {
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let minus_one = FieldElement::minus_one();
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let (was_nonzero_square, invsqrt_m1) = minus_one.invsqrt();
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assert_eq!(was_nonzero_square.unwrap_u8(), 1u8);
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let sign_test_sqrt = &invsqrt_m1 * &constants::SQRT_M1;
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assert_eq!(sign_test_sqrt, minus_one);
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}
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/// Test that d = -121665/121666
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#[test]
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#[cfg(feature = "u32_backend")]
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fn test_d_vs_ratio() {
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use backend::serial::u32::field::FieldElement2625;
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let a = -&FieldElement2625([121665,0,0,0,0,0,0,0,0,0]);
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let b = FieldElement2625([121666,0,0,0,0,0,0,0,0,0]);
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let d = &a * &b.invert();
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let d2 = &d + &d;
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assert_eq!(d, constants::EDWARDS_D);
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assert_eq!(d2, constants::EDWARDS_D2);
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}
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/// Test that d = -121665/121666
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#[test]
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#[cfg(feature = "u64_backend")]
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fn test_d_vs_ratio() {
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use backend::serial::u64::field::FieldElement51;
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let a = -&FieldElement51([121665,0,0,0,0]);
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let b = FieldElement51([121666,0,0,0,0]);
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let d = &a * &b.invert();
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let d2 = &d + &d;
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assert_eq!(d, constants::EDWARDS_D);
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assert_eq!(d2, constants::EDWARDS_D2);
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}
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#[test]
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fn test_sqrt_ad_minus_one() {
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let a = FieldElement::minus_one();
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let ad_minus_one = &(&a * &constants::EDWARDS_D) + &a;
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let should_be_ad_minus_one = constants::SQRT_AD_MINUS_ONE.square();
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assert_eq!(should_be_ad_minus_one, ad_minus_one);
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}
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}
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