curve25519-dalek 4.0.0-rc.0

// -*- mode: rust; -*-
//
// This file is part of curve25519-dalek.
// Copyright (c) 2016-2021 isis lovecruft
// Copyright (c) 2016-2019 Henry de Valence
// See LICENSE for licensing information.
//
// Authors:
// - isis agora lovecruft <isis@patternsinthevoid.net>
// - Henry de Valence <hdevalence@hdevalence.ca>

//! This module contains backend-specific constant values, such as the 64-bit limbs of curve constants.

use super::field::FieldElement51;
use super::scalar::Scalar52;
use crate::edwards::EdwardsPoint;

#[cfg(feature = "precomputed-tables")]
use crate::{
    backend::serial::curve_models::AffineNielsPoint,
    edwards::EdwardsBasepointTable,
    window::{LookupTable, NafLookupTable8},
};

/// The value of minus one, equal to `-&FieldElement::ONE`
pub(crate) const MINUS_ONE: FieldElement51 = FieldElement51([
    2251799813685228,
    2251799813685247,
    2251799813685247,
    2251799813685247,
    2251799813685247,
]);

/// Edwards `d` value, equal to `-121665/121666 mod p`.
pub(crate) const EDWARDS_D: FieldElement51 = FieldElement51([
    929955233495203,
    466365720129213,
    1662059464998953,
    2033849074728123,
    1442794654840575,
]);

/// Edwards `2*d` value, equal to `2*(-121665/121666) mod p`.
pub(crate) const EDWARDS_D2: FieldElement51 = FieldElement51([
    1859910466990425,
    932731440258426,
    1072319116312658,
    1815898335770999,
    633789495995903,
]);

/// One minus edwards `d` value squared, equal to `(1 - (-121665/121666) mod p) pow 2`
pub(crate) const ONE_MINUS_EDWARDS_D_SQUARED: FieldElement51 = FieldElement51([
    1136626929484150,
    1998550399581263,
    496427632559748,
    118527312129759,
    45110755273534,
]);

/// Edwards `d` value minus one squared, equal to `(((-121665/121666) mod p) - 1) pow 2`
pub(crate) const EDWARDS_D_MINUS_ONE_SQUARED: FieldElement51 = FieldElement51([
    1507062230895904,
    1572317787530805,
    683053064812840,
    317374165784489,
    1572899562415810,
]);

/// `= sqrt(a*d - 1)`, where `a = -1 (mod p)`, `d` are the Edwards curve parameters.
pub(crate) const SQRT_AD_MINUS_ONE: FieldElement51 = FieldElement51([
    2241493124984347,
    425987919032274,
    2207028919301688,
    1220490630685848,
    974799131293748,
]);

/// `= 1/sqrt(a-d)`, where `a = -1 (mod p)`, `d` are the Edwards curve parameters.
pub(crate) const INVSQRT_A_MINUS_D: FieldElement51 = FieldElement51([
    278908739862762,
    821645201101625,
    8113234426968,
    1777959178193151,
    2118520810568447,
]);

/// Precomputed value of one of the square roots of -1 (mod p)
pub(crate) const SQRT_M1: FieldElement51 = FieldElement51([
    1718705420411056,
    234908883556509,
    2233514472574048,
    2117202627021982,
    765476049583133,
]);

/// `APLUS2_OVER_FOUR` is (A+2)/4. (This is used internally within the Montgomery ladder.)
pub(crate) const APLUS2_OVER_FOUR: FieldElement51 = FieldElement51([121666, 0, 0, 0, 0]);

/// `MONTGOMERY_A` is equal to 486662, which is a constant of the curve equation
/// for Curve25519 in its Montgomery form. (This is used internally within the
/// Elligator map.)
pub(crate) const MONTGOMERY_A: FieldElement51 = FieldElement51([486662, 0, 0, 0, 0]);

/// `MONTGOMERY_A_NEG` is equal to -486662. (This is used internally within the
/// Elligator map.)
pub(crate) const MONTGOMERY_A_NEG: FieldElement51 = FieldElement51([
    2251799813198567,
    2251799813685247,
    2251799813685247,
    2251799813685247,
    2251799813685247,
]);

/// `L` is the order of base point, i.e. 2^252 + 27742317777372353535851937790883648493
pub(crate) const L: Scalar52 = Scalar52([
    0x0002631a5cf5d3ed,
    0x000dea2f79cd6581,
    0x000000000014def9,
    0x0000000000000000,
    0x0000100000000000,
]);

/// `L` * `LFACTOR` = -1 (mod 2^52)
pub(crate) const LFACTOR: u64 = 0x51da312547e1b;

/// `R` = R % L where R = 2^260
pub(crate) const R: Scalar52 = Scalar52([
    0x000f48bd6721e6ed,
    0x0003bab5ac67e45a,
    0x000fffffeb35e51b,
    0x000fffffffffffff,
    0x00000fffffffffff,
]);

/// `RR` = (R^2) % L where R = 2^260
pub(crate) const RR: Scalar52 = Scalar52([
    0x0009d265e952d13b,
    0x000d63c715bea69f,
    0x0005be65cb687604,
    0x0003dceec73d217f,
    0x000009411b7c309a,
]);

/// The Ed25519 basepoint, as an `EdwardsPoint`.
///
/// This is called `_POINT` to distinguish it from
/// `ED25519_BASEPOINT_TABLE`, which should be used for scalar
/// multiplication (it's much faster).
pub const ED25519_BASEPOINT_POINT: EdwardsPoint = EdwardsPoint {
    X: FieldElement51([
        1738742601995546,
        1146398526822698,
        2070867633025821,
        562264141797630,
        587772402128613,
    ]),
    Y: FieldElement51([
        1801439850948184,
        1351079888211148,
        450359962737049,
        900719925474099,
        1801439850948198,
    ]),
    Z: FieldElement51([1, 0, 0, 0, 0]),
    T: FieldElement51([
        1841354044333475,
        16398895984059,
        755974180946558,
        900171276175154,
        1821297809914039,
    ]),
};

/// The 8-torsion subgroup \\(\mathcal E \[8\]\\).
///
/// In the case of Curve25519, it is cyclic; the \\(i\\)-th element of
/// the array is \\(\[i\]P\\), where \\(P\\) is a point of order \\(8\\)
/// generating \\(\mathcal E\[8\]\\).
///
/// Thus \\(\mathcal E\[4\]\\) is the points indexed by `0,2,4,6`, and
/// \\(\mathcal E\[2\]\\) is the points indexed by `0,4`.
pub const EIGHT_TORSION: [EdwardsPoint; 8] = EIGHT_TORSION_INNER_DOC_HIDDEN;

/// Inner item used to hide limb constants from cargo doc output.
#[doc(hidden)]
pub const EIGHT_TORSION_INNER_DOC_HIDDEN: [EdwardsPoint; 8] = [
    EdwardsPoint {
        X: FieldElement51([0, 0, 0, 0, 0]),
        Y: FieldElement51([1, 0, 0, 0, 0]),
        Z: FieldElement51([1, 0, 0, 0, 0]),
        T: FieldElement51([0, 0, 0, 0, 0]),
    },
    EdwardsPoint {
        X: FieldElement51([
            358744748052810,
            1691584618240980,
            977650209285361,
            1429865912637724,
            560044844278676,
        ]),
        Y: FieldElement51([
            84926274344903,
            473620666599931,
            365590438845504,
            1028470286882429,
            2146499180330972,
        ]),
        Z: FieldElement51([1, 0, 0, 0, 0]),
        T: FieldElement51([
            1448326834587521,
            1857896831960481,
            1093722731865333,
            1677408490711241,
            1915505153018406,
        ]),
    },
    EdwardsPoint {
        X: FieldElement51([
            533094393274173,
            2016890930128738,
            18285341111199,
            134597186663265,
            1486323764102114,
        ]),
        Y: FieldElement51([0, 0, 0, 0, 0]),
        Z: FieldElement51([1, 0, 0, 0, 0]),
        T: FieldElement51([0, 0, 0, 0, 0]),
    },
    EdwardsPoint {
        X: FieldElement51([
            358744748052810,
            1691584618240980,
            977650209285361,
            1429865912637724,
            560044844278676,
        ]),
        Y: FieldElement51([
            2166873539340326,
            1778179147085316,
            1886209374839743,
            1223329526802818,
            105300633354275,
        ]),
        Z: FieldElement51([1, 0, 0, 0, 0]),
        T: FieldElement51([
            803472979097708,
            393902981724766,
            1158077081819914,
            574391322974006,
            336294660666841,
        ]),
    },
    EdwardsPoint {
        X: FieldElement51([0, 0, 0, 0, 0]),
        Y: FieldElement51([
            2251799813685228,
            2251799813685247,
            2251799813685247,
            2251799813685247,
            2251799813685247,
        ]),
        Z: FieldElement51([1, 0, 0, 0, 0]),
        T: FieldElement51([0, 0, 0, 0, 0]),
    },
    EdwardsPoint {
        X: FieldElement51([
            1893055065632419,
            560215195444267,
            1274149604399886,
            821933901047523,
            1691754969406571,
        ]),
        Y: FieldElement51([
            2166873539340326,
            1778179147085316,
            1886209374839743,
            1223329526802818,
            105300633354275,
        ]),
        Z: FieldElement51([1, 0, 0, 0, 0]),
        T: FieldElement51([
            1448326834587521,
            1857896831960481,
            1093722731865333,
            1677408490711241,
            1915505153018406,
        ]),
    },
    EdwardsPoint {
        X: FieldElement51([
            1718705420411056,
            234908883556509,
            2233514472574048,
            2117202627021982,
            765476049583133,
        ]),
        Y: FieldElement51([0, 0, 0, 0, 0]),
        Z: FieldElement51([1, 0, 0, 0, 0]),
        T: FieldElement51([0, 0, 0, 0, 0]),
    },
    EdwardsPoint {
        X: FieldElement51([
            1893055065632419,
            560215195444267,
            1274149604399886,
            821933901047523,
            1691754969406571,
        ]),
        Y: FieldElement51([
            84926274344903,
            473620666599931,
            365590438845504,
            1028470286882429,
            2146499180330972,
        ]),
        Z: FieldElement51([1, 0, 0, 0, 0]),
        T: FieldElement51([
            803472979097708,
            393902981724766,
            1158077081819914,
            574391322974006,
            336294660666841,
        ]),
    },
];

/// Table containing precomputed multiples of the Ed25519 basepoint \\(B = (x, 4/5)\\).
#[cfg(feature = "precomputed-tables")]
pub static ED25519_BASEPOINT_TABLE: &'static EdwardsBasepointTable =
    &ED25519_BASEPOINT_TABLE_INNER_DOC_HIDDEN;

/// Inner constant, used to avoid filling the docs with precomputed points.
#[doc(hidden)]
#[cfg(feature = "precomputed-tables")]
static ED25519_BASEPOINT_TABLE_INNER_DOC_HIDDEN: EdwardsBasepointTable = EdwardsBasepointTable([
    LookupTable([
        AffineNielsPoint {
            y_plus_x: FieldElement51([
                3540182452943730,
                2497478415033846,
                2521227595762870,
                1462984067271729,
                2389212253076811,
            ]),
            y_minus_x: FieldElement51([
                62697248952638,
                204681361388450,
                631292143396476,
                338455783676468,
                1213667448819585,
            ]),
            xy2d: FieldElement51([
                301289933810280,
                1259582250014073,
                1422107436869536,
                796239922652654,
                1953934009299142,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement51([
                3632771708514775,
                790832306631235,
                2067202295274102,
                1995808275510000,
                1566530869037010,
            ]),
            y_minus_x: FieldElement51([
                463307831301544,
                432984605774163,
                1610641361907204,
                750899048855000,
                1894842303421586,
            ]),
            xy2d: FieldElement51([
                748439484463711,
                1033211726465151,
                1396005112841647,
                1611506220286469,
                1972177495910992,
            ]),
        },
        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,
                805677984380077,
                859228993502513,
            ]),
            xy2d: FieldElement51([
                1200766035879111,
                20142053207432,
                1465634435977050,
                1645256912097844,
                295121984874596,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement51([
                1735718747031538,
                1248237894295956,
                1204753118328107,
                976066523550493,
                2317743583219840,
            ]),
            y_minus_x: FieldElement51([
                1060098822528990,
                1586825862073490,
                212301317240126,
                1975302711403555,
                666724059764335,
            ]),
            xy2d: FieldElement51([
                1091990273418756,
                1572899409348578,
                80968014455247,
                306009358661350,
                1520450739132526,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement51([
                3732317023121341,
                1511153322193951,
                3496143672676420,
                2556587964178488,
                2620936670181690,
            ]),
            y_minus_x: FieldElement51([
                2151330273626164,
                762045184746182,
                1688074332551515,
                823046109005759,
                907602769079491,
            ]),
            xy2d: FieldElement51([
                2047386910586836,
                168470092900250,
                1552838872594810,
                340951180073789,
                360819374702533,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement51([
                1982622644432037,
                2014393600336956,
                2380709022489462,
                3869592437614438,
                2357094095599062,
            ]),
            y_minus_x: FieldElement51([
                980234343912898,
                1712256739246056,
                588935272190264,
                204298813091998,
                841798321043288,
            ]),
            xy2d: FieldElement51([
                197561292938973,
                454817274782871,
                1963754960082318,
                2113372252160468,
                971377527342673,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement51([
                2416499262514576,
                2254927265442919,
                3451304785234000,
                1766155447043651,
                1899238924683527,
            ]),
            y_minus_x: FieldElement51([
                732262946680281,
                1674412764227063,
                2182456405662809,
                1350894754474250,
                558458873295247,
            ]),
            xy2d: FieldElement51([
                2103305098582922,
                1960809151316468,
                715134605001343,
                1454892949167181,
                40827143824949,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement51([
                1239289043050193,
                1744654158124578,
                758702410031698,
                4048562808759936,
                2253402870349013,
            ]),
            y_minus_x: FieldElement51([
                2232056027107988,
                987343914584615,
                2115594492994461,
                1819598072792159,
                1119305654014850,
            ]),
            xy2d: FieldElement51([
                320153677847348,
                939613871605645,
                641883205761567,
                1930009789398224,
                329165806634126,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement51([
                3232730304159378,
                1242488692177892,
                1251446316964684,
                1086618677993530,
                1961430968465772,
            ]),
            y_minus_x: FieldElement51([
                276821765317453,
                1536835591188030,
                1305212741412361,
                61473904210175,
                2051377036983058,
            ]),
            xy2d: FieldElement51([
                833449923882501,
                1750270368490475,
                1123347002068295,
                185477424765687,
                278090826653186,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement51([
                794524995833413,
                1849907304548286,
                2305148486158393,
                1272368559505216,
                1147304168324779,
            ]),
            y_minus_x: FieldElement51([
                1504846112759364,
                1203096289004681,
                562139421471418,
                274333017451844,
                1284344053775441,
            ]),
            xy2d: FieldElement51([
                483048732424432,
                2116063063343382,
                30120189902313,
                292451576741007,
                1156379271702225,
            ]),
        },
    ]),
    LookupTable([
        AffineNielsPoint {
            y_plus_x: FieldElement51([
                3180171966714267,
                2147692869914563,
                1455665844462196,
                1986737809425946,
                2437006863943337,
            ]),
            y_minus_x: FieldElement51([
                137732961814206,
                706670923917341,
                1387038086865771,
                1965643813686352,
                1384777115696347,
            ]),
            xy2d: FieldElement51([
                481144981981577,
                2053319313589856,
                2065402289827512,
                617954271490316,
                1106602634668125,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement51([
                2948097833334040,
                3145099472726142,
                1148636718636008,
                2278533891034865,
                2203955659340680,
            ]),
            y_minus_x: FieldElement51([
                657390353372855,
                998499966885562,
                991893336905797,
                810470207106761,
                343139804608786,
            ]),
            xy2d: FieldElement51([
                791736669492960,
                934767652997115,
                824656780392914,
                1759463253018643,
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            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement51([
                2022541353055578,
                4346500076272714,
                3802807888710933,
                2494585331103411,
                2947785218648809,
            ]),
            y_minus_x: FieldElement51([
                1287487199965223,
                2215311941380308,
                1552928390931986,
                1664859529680196,
                1125004975265243,
            ]),
            xy2d: FieldElement51([
                677434665154918,
                989582503122485,
                1817429540898386,
                1052904935475344,
                1143826298169798,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement51([
                2619066141993637,
                2570231002607651,
                2947429167440602,
                2885885471266079,
                2276381426249673,
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    LookupTable([
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    LookupTable([
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]);

/// Odd multiples of the basepoint `[B, 3B, 5B, 7B, 9B, 11B, 13B, 15B, ..., 127B]`.
#[cfg(feature = "precomputed-tables")]
#[allow(dead_code)]
pub(crate) const AFFINE_ODD_MULTIPLES_OF_BASEPOINT: NafLookupTable8<AffineNielsPoint> =
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