7744 lines
253 KiB
Rust
7744 lines
253 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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//! This module contains backend-specific constant values, such as the 64-bit limbs of curve constants.
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use backend::serial::curve_models::AffineNielsPoint;
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use backend::serial::u64::field::FieldElement51;
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use backend::serial::u64::scalar::Scalar52;
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use edwards::{EdwardsBasepointTable, EdwardsPoint};
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use window::{LookupTable, NafLookupTable8};
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/// The value of minus one, equal to `-&FieldElement::one()`
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pub(crate) const MINUS_ONE: FieldElement51 = 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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/// Edwards `d` value, equal to `-121665/121666 mod p`.
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pub(crate) const EDWARDS_D: FieldElement51 = FieldElement51([
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929955233495203,
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466365720129213,
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1662059464998953,
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2033849074728123,
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1442794654840575,
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]);
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/// Edwards `2*d` value, equal to `2*(-121665/121666) mod p`.
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pub(crate) const EDWARDS_D2: FieldElement51 = FieldElement51([
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1859910466990425,
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932731440258426,
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1072319116312658,
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1815898335770999,
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633789495995903,
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]);
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/// One minus edwards `d` value squared, equal to `(1 - (-121665/121666) mod p) pow 2`
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pub(crate) const ONE_MINUS_EDWARDS_D_SQUARED: FieldElement51 = FieldElement51([
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1136626929484150,
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1998550399581263,
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496427632559748,
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118527312129759,
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45110755273534
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]);
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/// Edwards `d` value minus one squared, equal to `(((-121665/121666) mod p) - 1) pow 2`
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pub(crate) const EDWARDS_D_MINUS_ONE_SQUARED: FieldElement51 = FieldElement51([
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1507062230895904,
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1572317787530805,
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683053064812840,
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317374165784489,
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1572899562415810
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]);
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/// `= sqrt(a*d - 1)`, where `a = -1 (mod p)`, `d` are the Edwards curve parameters.
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pub(crate) const SQRT_AD_MINUS_ONE: FieldElement51 = FieldElement51([
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2241493124984347,
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425987919032274,
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2207028919301688,
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1220490630685848,
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974799131293748,
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]);
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/// `= 1/sqrt(a-d)`, where `a = -1 (mod p)`, `d` are the Edwards curve parameters.
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pub(crate) const INVSQRT_A_MINUS_D: FieldElement51 = FieldElement51([
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278908739862762,
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821645201101625,
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8113234426968,
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1777959178193151,
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2118520810568447,
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]);
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/// Precomputed value of one of the square roots of -1 (mod p)
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pub(crate) const SQRT_M1: FieldElement51 = FieldElement51([
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1718705420411056,
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234908883556509,
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2233514472574048,
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2117202627021982,
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765476049583133,
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]);
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/// `APLUS2_OVER_FOUR` is (A+2)/4. (This is used internally within the Montgomery ladder.)
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pub(crate) const APLUS2_OVER_FOUR: FieldElement51 = FieldElement51([121666, 0, 0, 0, 0]);
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/// `L` is the order of base point, i.e. 2^252 + 27742317777372353535851937790883648493
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pub(crate) const L: Scalar52 = Scalar52([
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0x0002631a5cf5d3ed,
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0x000dea2f79cd6581,
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0x000000000014def9,
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0x0000000000000000,
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0x0000100000000000,
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]);
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/// `L` * `LFACTOR` = -1 (mod 2^52)
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pub(crate) const LFACTOR: u64 = 0x51da312547e1b;
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/// `R` = R % L where R = 2^260
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pub(crate) const R: Scalar52 = Scalar52([
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0x000f48bd6721e6ed,
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0x0003bab5ac67e45a,
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0x000fffffeb35e51b,
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0x000fffffffffffff,
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0x00000fffffffffff,
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]);
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/// `RR` = (R^2) % L where R = 2^260
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pub(crate) const RR: Scalar52 = Scalar52([
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0x0009d265e952d13b,
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0x000d63c715bea69f,
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0x0005be65cb687604,
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0x0003dceec73d217f,
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0x000009411b7c309a,
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]);
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/// The Ed25519 basepoint, as an `EdwardsPoint`.
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///
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/// This is called `_POINT` to distinguish it from
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/// `ED25519_BASEPOINT_TABLE`, which should be used for scalar
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/// multiplication (it's much faster).
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pub const ED25519_BASEPOINT_POINT: EdwardsPoint = EdwardsPoint {
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X: FieldElement51([
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1738742601995546,
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1146398526822698,
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2070867633025821,
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562264141797630,
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587772402128613,
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]),
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Y: FieldElement51([
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1801439850948184,
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1351079888211148,
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450359962737049,
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900719925474099,
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1801439850948198,
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]),
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Z: FieldElement51([1, 0, 0, 0, 0]),
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T: FieldElement51([
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1841354044333475,
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16398895984059,
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755974180946558,
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900171276175154,
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1821297809914039,
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]),
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};
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/// The 8-torsion subgroup \\(\mathcal E [8]\\).
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///
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/// In the case of Curve25519, it is cyclic; the \\(i\\)-th element of
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/// the array is \\([i]P\\), where \\(P\\) is a point of order \\(8\\)
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/// generating \\(\mathcal E[8]\\).
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///
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/// Thus \\(\mathcal E[4]\\) is the points indexed by `0,2,4,6`, and
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/// \\(\mathcal E[2]\\) is the points indexed by `0,4`.
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pub const EIGHT_TORSION: [EdwardsPoint; 8] = EIGHT_TORSION_INNER_DOC_HIDDEN;
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/// Inner item used to hide limb constants from cargo doc output.
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#[doc(hidden)]
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pub const EIGHT_TORSION_INNER_DOC_HIDDEN: [EdwardsPoint; 8] = [
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EdwardsPoint {
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X: FieldElement51([0, 0, 0, 0, 0]),
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Y: FieldElement51([1, 0, 0, 0, 0]),
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Z: FieldElement51([1, 0, 0, 0, 0]),
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T: FieldElement51([0, 0, 0, 0, 0]),
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},
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EdwardsPoint {
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X: FieldElement51([
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358744748052810,
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1691584618240980,
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977650209285361,
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1429865912637724,
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560044844278676,
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]),
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Y: FieldElement51([
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84926274344903,
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473620666599931,
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365590438845504,
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1028470286882429,
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2146499180330972,
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]),
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Z: FieldElement51([1, 0, 0, 0, 0]),
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T: FieldElement51([
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1448326834587521,
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1857896831960481,
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1093722731865333,
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1677408490711241,
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1915505153018406,
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]),
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},
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EdwardsPoint {
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X: FieldElement51([
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533094393274173,
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2016890930128738,
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18285341111199,
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134597186663265,
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1486323764102114,
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]),
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Y: FieldElement51([0, 0, 0, 0, 0]),
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Z: FieldElement51([1, 0, 0, 0, 0]),
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T: FieldElement51([0, 0, 0, 0, 0]),
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},
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EdwardsPoint {
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X: FieldElement51([
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358744748052810,
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1691584618240980,
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977650209285361,
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1429865912637724,
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560044844278676,
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]),
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Y: FieldElement51([
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2166873539340326,
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1778179147085316,
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1886209374839743,
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1223329526802818,
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105300633354275,
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]),
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Z: FieldElement51([1, 0, 0, 0, 0]),
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T: FieldElement51([
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803472979097708,
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393902981724766,
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1158077081819914,
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574391322974006,
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336294660666841,
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]),
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},
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EdwardsPoint {
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X: FieldElement51([0, 0, 0, 0, 0]),
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Y: 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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Z: FieldElement51([1, 0, 0, 0, 0]),
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T: FieldElement51([0, 0, 0, 0, 0]),
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},
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EdwardsPoint {
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X: FieldElement51([
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1893055065632419,
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560215195444267,
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1274149604399886,
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821933901047523,
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1691754969406571,
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]),
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Y: FieldElement51([
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2166873539340326,
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1778179147085316,
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1886209374839743,
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1223329526802818,
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105300633354275,
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]),
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Z: FieldElement51([1, 0, 0, 0, 0]),
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T: FieldElement51([
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1448326834587521,
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1857896831960481,
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1093722731865333,
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1677408490711241,
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1915505153018406,
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]),
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},
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EdwardsPoint {
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X: FieldElement51([
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1718705420411056,
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234908883556509,
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2233514472574048,
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2117202627021982,
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765476049583133,
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]),
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Y: FieldElement51([0, 0, 0, 0, 0]),
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Z: FieldElement51([1, 0, 0, 0, 0]),
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T: FieldElement51([0, 0, 0, 0, 0]),
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},
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EdwardsPoint {
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X: FieldElement51([
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1893055065632419,
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560215195444267,
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1274149604399886,
|
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821933901047523,
|
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1691754969406571,
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]),
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Y: FieldElement51([
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84926274344903,
|
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473620666599931,
|
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365590438845504,
|
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1028470286882429,
|
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2146499180330972,
|
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]),
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Z: FieldElement51([1, 0, 0, 0, 0]),
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T: FieldElement51([
|
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803472979097708,
|
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393902981724766,
|
|
1158077081819914,
|
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574391322974006,
|
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336294660666841,
|
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]),
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},
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];
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/// Table containing precomputed multiples of the Ed25519 basepoint \\(B = (x, 4/5)\\).
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pub const ED25519_BASEPOINT_TABLE: EdwardsBasepointTable = ED25519_BASEPOINT_TABLE_INNER_DOC_HIDDEN;
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/// Inner constant, used to avoid filling the docs with precomputed points.
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#[doc(hidden)]
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pub const ED25519_BASEPOINT_TABLE_INNER_DOC_HIDDEN: EdwardsBasepointTable =
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EdwardsBasepointTable([
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LookupTable([
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AffineNielsPoint {
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y_plus_x: FieldElement51([
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3540182452943730,
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2497478415033846,
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2521227595762870,
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1462984067271729,
|
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2389212253076811,
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]),
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y_minus_x: FieldElement51([
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62697248952638,
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204681361388450,
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631292143396476,
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338455783676468,
|
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1213667448819585,
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]),
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xy2d: FieldElement51([
|
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301289933810280,
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1259582250014073,
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1422107436869536,
|
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796239922652654,
|
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1953934009299142,
|
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]),
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},
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AffineNielsPoint {
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y_plus_x: FieldElement51([
|
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3632771708514775,
|
|
790832306631235,
|
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2067202295274102,
|
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1995808275510000,
|
|
1566530869037010,
|
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]),
|
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y_minus_x: FieldElement51([
|
|
463307831301544,
|
|
432984605774163,
|
|
1610641361907204,
|
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750899048855000,
|
|
1894842303421586,
|
|
]),
|
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xy2d: FieldElement51([
|
|
748439484463711,
|
|
1033211726465151,
|
|
1396005112841647,
|
|
1611506220286469,
|
|
1972177495910992,
|
|
]),
|
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},
|
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AffineNielsPoint {
|
|
y_plus_x: FieldElement51([
|
|
1601611775252272,
|
|
1720807796594148,
|
|
1132070835939856,
|
|
3512254832574799,
|
|
2147779492816910,
|
|
]),
|
|
y_minus_x: FieldElement51([
|
|
316559037616741,
|
|
2177824224946892,
|
|
1459442586438991,
|
|
1461528397712656,
|
|
751590696113597,
|
|
]),
|
|
xy2d: FieldElement51([
|
|
1850748884277385,
|
|
1200145853858453,
|
|
1068094770532492,
|
|
672251375690438,
|
|
1586055907191707,
|
|
]),
|
|
},
|
|
AffineNielsPoint {
|
|
y_plus_x: FieldElement51([
|
|
934282339813791,
|
|
1846903124198670,
|
|
1172395437954843,
|
|
1007037127761661,
|
|
1830588347719256,
|
|
]),
|
|
y_minus_x: FieldElement51([
|
|
1694390458783935,
|
|
1735906047636159,
|
|
705069562067493,
|
|
648033061693059,
|
|
696214010414170,
|
|
]),
|
|
xy2d: FieldElement51([
|
|
1121406372216585,
|
|
192876649532226,
|
|
190294192191717,
|
|
1994165897297032,
|
|
2245000007398739,
|
|
]),
|
|
},
|
|
AffineNielsPoint {
|
|
y_plus_x: FieldElement51([
|
|
769950342298400,
|
|
2384754244604994,
|
|
3095885746880802,
|
|
3225892188161580,
|
|
2977876099231263,
|
|
]),
|
|
y_minus_x: FieldElement51([
|
|
425251763115706,
|
|
608463272472562,
|
|
442562545713235,
|
|
837766094556764,
|
|
374555092627893,
|
|
]),
|
|
xy2d: FieldElement51([
|
|
1086255230780037,
|
|
274979815921559,
|
|
1960002765731872,
|
|
929474102396301,
|
|
1190409889297339,
|
|
]),
|
|
},
|
|
AffineNielsPoint {
|
|
y_plus_x: FieldElement51([
|
|
1388594989461809,
|
|
316767091099457,
|
|
2646098655878230,
|
|
1230079486801004,
|
|
1440737038838979,
|
|
]),
|
|
y_minus_x: FieldElement51([
|
|
7380825640100,
|
|
146210432690483,
|
|
304903576448906,
|
|
1198869323871120,
|
|
997689833219095,
|
|
]),
|
|
xy2d: FieldElement51([
|
|
1181317918772081,
|
|
114573476638901,
|
|
262805072233344,
|
|
265712217171332,
|
|
294181933805782,
|
|
]),
|
|
},
|
|
AffineNielsPoint {
|
|
y_plus_x: FieldElement51([
|
|
2916800678241215,
|
|
2065379846933858,
|
|
2622030924071124,
|
|
2602788184473875,
|
|
1233371373142984,
|
|
]),
|
|
y_minus_x: FieldElement51([
|
|
2019367628972465,
|
|
676711900706637,
|
|
110710997811333,
|
|
1108646842542025,
|
|
517791959672113,
|
|
]),
|
|
xy2d: FieldElement51([
|
|
965130719900578,
|
|
247011430587952,
|
|
526356006571389,
|
|
91986625355052,
|
|
2157223321444601,
|
|
]),
|
|
},
|
|
AffineNielsPoint {
|
|
y_plus_x: FieldElement51([
|
|
4320419353804412,
|
|
4218074731744053,
|
|
957728544705548,
|
|
729906502578991,
|
|
2411634706750414,
|
|
]),
|
|
y_minus_x: FieldElement51([
|
|
2073601412052185,
|
|
31021124762708,
|
|
264500969797082,
|
|
248034690651703,
|
|
1030252227928288,
|
|
]),
|
|
xy2d: FieldElement51([
|
|
551790716293402,
|
|
1989538725166328,
|
|
801169423371717,
|
|
2052451893578887,
|
|
678432056995012,
|
|
]),
|
|
},
|
|
]),
|
|
LookupTable([
|
|
AffineNielsPoint {
|
|
y_plus_x: FieldElement51([
|
|
1368953770187805,
|
|
3042147450398169,
|
|
2689308289352409,
|
|
2142576377050579,
|
|
1932081720066286,
|
|
]),
|
|
y_minus_x: FieldElement51([
|
|
953638594433374,
|
|
1092333936795051,
|
|
1419774766716690,
|
|
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|
|
/// Odd multiples of the basepoint `[B, 3B, 5B, 7B, 9B, 11B, 13B, 15B, ..., 127B]`.
|
|
pub(crate) const AFFINE_ODD_MULTIPLES_OF_BASEPOINT: NafLookupTable8<AffineNielsPoint> =
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NafLookupTable8([
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AffineNielsPoint {
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AffineNielsPoint {
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AffineNielsPoint {
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AffineNielsPoint {
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