4777 lines
211 KiB
Rust
4777 lines
211 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 various constants (such as curve parameters
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//! and useful field elements like `sqrt(-1)`), as well as
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//! lookup tables of pre-computed points.
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use backend::serial::curve_models::AffineNielsPoint;
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use backend::serial::u32::field::FieldElement2625;
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use backend::serial::u32::scalar::Scalar29;
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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: FieldElement2625 = FieldElement2625([
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67108844, 33554431, 67108863, 33554431, 67108863, 33554431, 67108863, 33554431, 67108863, 33554431
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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: FieldElement2625 = FieldElement2625([
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56195235, 13857412, 51736253, 6949390, 114729, 24766616, 60832955, 30306712, 48412415, 21499315,
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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: FieldElement2625 = FieldElement2625([
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45281625, 27714825, 36363642, 13898781, 229458, 15978800, 54557047, 27058993, 29715967, 9444199,
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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: FieldElement2625 = FieldElement2625([
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6275446, 16937061, 44170319, 29780721, 11667076, 7397348, 39186143, 1766194, 42675006, 672202
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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: FieldElement2625 = FieldElement2625([
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15551776, 22456977, 53683765, 23429360, 55212328, 10178283, 40474537, 4729243, 61826754, 23438029
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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: FieldElement2625 = FieldElement2625([
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24849947, 33400850, 43495378, 6347714, 46036536, 32887293, 41837720, 18186727, 66238516,
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14525638,
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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: FieldElement2625 = FieldElement2625([
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6111466, 4156064, 39310137, 12243467, 41204824, 120896, 20826367, 26493656, 6093567, 31568420,
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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: FieldElement2625 = FieldElement2625([
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34513072, 25610706, 9377949, 3500415, 12389472, 33281959, 41962654, 31548777, 326685, 11406482,
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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: FieldElement2625 =
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FieldElement2625([121666, 0, 0, 0, 0, 0, 0, 0, 0, 0]);
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/// `L` is the order of base point, i.e. 2^252 +
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/// 27742317777372353535851937790883648493
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pub(crate) const L: Scalar29 = Scalar29([
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0x1cf5d3ed, 0x009318d2, 0x1de73596, 0x1df3bd45, 0x0000014d, 0x00000000, 0x00000000, 0x00000000,
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0x00100000,
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]);
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/// `L` * `LFACTOR` = -1 (mod 2^29)
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pub(crate) const LFACTOR: u32 = 0x12547e1b;
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/// `R` = R % L where R = 2^261
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pub(crate) const R: Scalar29 = Scalar29([
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0x114df9ed, 0x1a617303, 0x0f7c098c, 0x16793167, 0x1ffd656e, 0x1fffffff, 0x1fffffff, 0x1fffffff,
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0x000fffff,
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]);
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/// `RR` = (R^2) % L where R = 2^261
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pub(crate) const RR: Scalar29 = Scalar29([
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0x0b5f9d12, 0x1e141b17, 0x158d7f3d, 0x143f3757, 0x1972d781, 0x042feb7c, 0x1ceec73d, 0x1e184d1e,
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0x0005046d,
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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: FieldElement2625([
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52811034, 25909283, 16144682, 17082669, 27570973, 30858332, 40966398, 8378388, 20764389,
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8758491,
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]),
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Y: FieldElement2625([
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40265304, 26843545, 13421772, 20132659, 26843545, 6710886, 53687091, 13421772, 40265318,
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26843545,
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]),
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Z: FieldElement2625([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
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T: FieldElement2625([
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28827043, 27438313, 39759291, 244362, 8635006, 11264893, 19351346, 13413597, 16611511,
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27139452,
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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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/// The Ed25519 basepoint has y = 4/5. This is called `_POINT` to
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/// distinguish it from `_TABLE`, which should be used for scalar
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/// multiplication (it's much faster).
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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: FieldElement2625([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
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Y: FieldElement2625([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
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Z: FieldElement2625([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
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T: FieldElement2625([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
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},
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EdwardsPoint {
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X: FieldElement2625([
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21352778, 5345713, 4660180, 25206575, 24143089, 14568123, 30185756, 21306662, 33579924,
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8345318,
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]),
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Y: FieldElement2625([
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6952903, 1265500, 60246523, 7057497, 4037696, 5447722, 35427965, 15325401, 19365852,
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31985330,
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]),
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Z: FieldElement2625([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
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T: FieldElement2625([
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41846657, 21581751, 11716001, 27684820, 48915701, 16297738, 20670665, 24995334,
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3541542, 28543251,
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]),
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},
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EdwardsPoint {
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X: FieldElement2625([
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32595773, 7943725, 57730914, 30054016, 54719391, 272472, 25146209, 2005654, 66782178,
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22147949,
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]),
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Y: FieldElement2625([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
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Z: FieldElement2625([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
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T: FieldElement2625([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
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},
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EdwardsPoint {
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X: FieldElement2625([
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21352778, 5345713, 4660180, 25206575, 24143089, 14568123, 30185756, 21306662, 33579924,
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8345318,
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]),
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Y: FieldElement2625([
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60155942, 32288931, 6862340, 26496934, 63071167, 28106709, 31680898, 18229030,
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47743011, 1569101,
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]),
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Z: FieldElement2625([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
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T: FieldElement2625([
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25262188, 11972680, 55392862, 5869611, 18193162, 17256693, 46438198, 8559097, 63567321,
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5011180,
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]),
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},
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EdwardsPoint {
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X: FieldElement2625([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
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Y: FieldElement2625([
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67108844, 33554431, 67108863, 33554431, 67108863, 33554431, 67108863, 33554431,
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67108863, 33554431,
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]),
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Z: FieldElement2625([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
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T: FieldElement2625([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
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},
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EdwardsPoint {
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X: FieldElement2625([
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45756067, 28208718, 62448683, 8347856, 42965774, 18986308, 36923107, 12247769,
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33528939, 25209113,
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]),
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Y: FieldElement2625([
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60155942, 32288931, 6862340, 26496934, 63071167, 28106709, 31680898, 18229030,
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47743011, 1569101,
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]),
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Z: FieldElement2625([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
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T: FieldElement2625([
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41846657, 21581751, 11716001, 27684820, 48915701, 16297738, 20670665, 24995334,
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3541542, 28543251,
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]),
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},
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EdwardsPoint {
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X: FieldElement2625([
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34513072, 25610706, 9377949, 3500415, 12389472, 33281959, 41962654, 31548777, 326685,
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11406482,
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]),
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Y: FieldElement2625([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
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Z: FieldElement2625([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
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T: FieldElement2625([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
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},
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EdwardsPoint {
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X: FieldElement2625([
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45756067, 28208718, 62448683, 8347856, 42965774, 18986308, 36923107, 12247769,
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33528939, 25209113,
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]),
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Y: FieldElement2625([
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6952903, 1265500, 60246523, 7057497, 4037696, 5447722, 35427965, 15325401, 19365852,
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31985330,
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]),
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Z: FieldElement2625([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
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T: FieldElement2625([
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25262188, 11972680, 55392862, 5869611, 18193162, 17256693, 46438198, 8559097, 63567321,
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5011180,
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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: FieldElement2625([
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93076338, 52752828, 29566454, 37215328, 54414518, 37569218, 94653489, 21800160,
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61029707, 35602036,
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]),
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y_minus_x: FieldElement2625([
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54563134, 934261, 64385954, 3049989, 66381436, 9406985, 12720692, 5043384,
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19500929, 18085054,
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]),
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xy2d: FieldElement2625([
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58370664, 4489569, 9688441, 18769238, 10184608, 21191052, 29287918, 11864899,
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42594502, 29115885,
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]),
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},
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AffineNielsPoint {
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y_plus_x: FieldElement2625([
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54292951, 54132516, 45527619, 11784319, 41753206, 30803714, 55390960, 29739860,
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66750418, 23343128,
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]),
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y_minus_x: FieldElement2625([
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45405608, 6903824, 27185491, 6451973, 37531140, 24000426, 51492312, 11189267,
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40279186, 28235350,
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]),
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xy2d: FieldElement2625([
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26966623, 11152617, 32442495, 15396054, 14353839, 20802097, 63980037, 24013313,
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51636816, 29387734,
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]),
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},
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AffineNielsPoint {
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y_plus_x: FieldElement2625([
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82745136, 23865874, 24204772, 25642034, 67725840, 16869169, 94896463, 52336674,
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28944398, 32004408,
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]),
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y_minus_x: FieldElement2625([
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16568933, 4717097, 55552716, 32452109, 15682895, 21747389, 16354576, 21778470,
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7689661, 11199574,
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]),
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xy2d: FieldElement2625([
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30464137, 27578307, 55329429, 17883566, 23220364, 15915852, 7512774, 10017326,
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49359771, 23634074,
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]),
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},
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AffineNielsPoint {
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y_plus_x: FieldElement2625([
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50071967, 13921891, 78054670, 27521000, 27105051, 17470053, 105291517,
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15006021, 70393432, 27277891,
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]),
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y_minus_x: FieldElement2625([
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23599295, 25248385, 55915199, 25867015, 13236773, 10506355, 7464579, 9656445,
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13059162, 10374397,
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]),
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xy2d: FieldElement2625([
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7798537, 16710257, 3033922, 2874086, 28997861, 2835604, 32406664, 29715387,
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66467155, 33453106,
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]),
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},
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AffineNielsPoint {
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y_plus_x: FieldElement2625([
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|
77970208, 11473153, 27284546, 35535607, 37044514, 46132292, 99976748, 48069538,
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118779423, 44373810,
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]),
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y_minus_x: FieldElement2625([
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4708026, 6336745, 20377586, 9066809, 55836755, 6594695, 41455196, 12483687,
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54440373, 5581305,
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]),
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|
xy2d: FieldElement2625([
|
|
19563141, 16186464, 37722007, 4097518, 10237984, 29206317, 28542349, 13850243,
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|
43430843, 17738489,
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]),
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},
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|
AffineNielsPoint {
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|
y_plus_x: FieldElement2625([
|
|
51736881, 20691677, 32573249, 4720197, 107781206, 39429941, 115029100,
|
|
18329611, 124398787, 21468653,
|
|
]),
|
|
y_minus_x: FieldElement2625([
|
|
58559652, 109982, 15149363, 2178705, 22900618, 4543417, 3044240, 17864545,
|
|
1762327, 14866737,
|
|
]),
|
|
xy2d: FieldElement2625([
|
|
48909169, 17603008, 56635573, 1707277, 49922944, 3916100, 38872452, 3959420,
|
|
27914454, 4383652,
|
|
]),
|
|
},
|
|
AffineNielsPoint {
|
|
y_plus_x: FieldElement2625([
|
|
72262591, 43463716, 68832610, 30776557, 97632468, 39071304, 86589715, 38784565,
|
|
43156424, 18378665,
|
|
]),
|
|
y_minus_x: FieldElement2625([
|
|
36839857, 30090922, 7665485, 10083793, 28475525, 1649722, 20654025, 16520125,
|
|
30598449, 7715701,
|
|
]),
|
|
xy2d: FieldElement2625([
|
|
28881826, 14381568, 9657904, 3680757, 46927229, 7843315, 35708204, 1370707,
|
|
29794553, 32145132,
|
|
]),
|
|
},
|
|
AffineNielsPoint {
|
|
y_plus_x: FieldElement2625([
|
|
14499452, 64379265, 33917749, 62854211, 95603724, 14271266, 97399599, 10876453,
|
|
33954766, 35936157,
|
|
]),
|
|
y_minus_x: FieldElement2625([
|
|
59913433, 30899068, 52378708, 462250, 39384538, 3941371, 60872247, 3696004,
|
|
34808032, 15351954,
|
|
]),
|
|
xy2d: FieldElement2625([
|
|
27431194, 8222322, 16448760, 29646437, 48401861, 11938354, 34147463, 30583916,
|
|
29551812, 10109425,
|
|
]),
|
|
},
|
|
]),
|
|
LookupTable([
|
|
AffineNielsPoint {
|
|
y_plus_x: FieldElement2625([
|
|
53451805, 20399000, 102933977, 45331528, 88556249, 40073815, 64730579,
|
|
31926875, 77201646, 28790260,
|
|
]),
|
|
y_minus_x: FieldElement2625([
|
|
27939166, 14210322, 4677035, 16277044, 44144402, 21156292, 34600109, 12005537,
|
|
49298737, 12803509,
|
|
]),
|
|
xy2d: FieldElement2625([
|
|
17228999, 17892808, 65875336, 300139, 65883994, 21839654, 30364212, 24516238,
|
|
18016356, 4397660,
|
|
]),
|
|
},
|
|
AffineNielsPoint {
|
|
y_plus_x: FieldElement2625([
|
|
56150002, 25864224, 4776340, 18600194, 27850027, 17952220, 40489757, 14544524,
|
|
49631360, 34537070,
|
|
]),
|
|
y_minus_x: FieldElement2625([
|
|
29253598, 15796703, 64244882, 23645547, 10057022, 3163536, 7332899, 29434304,
|
|
46061167, 9934962,
|
|
]),
|
|
xy2d: FieldElement2625([
|
|
5793284, 16271923, 42977250, 23438027, 29188559, 1206517, 52360934, 4559894,
|
|
36984942, 22656481,
|
|
]),
|
|
},
|
|
AffineNielsPoint {
|
|
y_plus_x: FieldElement2625([
|
|
39464893, 55615857, 83391519, 22517938, 28414020, 52096600, 24191032, 38096129,
|
|
53770554, 39054999,
|
|
]),
|
|
y_minus_x: FieldElement2625([
|
|
12650548, 32057319, 9052870, 11355358, 49428827, 25154267, 49678271, 12264342,
|
|
10874051, 13524335,
|
|
]),
|
|
xy2d: FieldElement2625([
|
|
25556948, 30508442, 714650, 2510400, 23394682, 23139102, 33119037, 5080568,
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y_minus_x: FieldElement2625([
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LookupTable([
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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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]),
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},
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AffineNielsPoint {
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y_plus_x: FieldElement2625([
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xy2d: FieldElement2625([
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AffineNielsPoint {
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y_minus_x: FieldElement2625([
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xy2d: FieldElement2625([
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]),
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},
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AffineNielsPoint {
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y_plus_x: FieldElement2625([
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y_minus_x: FieldElement2625([
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]),
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xy2d: FieldElement2625([
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]),
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},
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AffineNielsPoint {
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y_plus_x: FieldElement2625([
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]),
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y_minus_x: FieldElement2625([
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},
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AffineNielsPoint {
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y_plus_x: FieldElement2625([
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y_minus_x: FieldElement2625([
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]),
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xy2d: FieldElement2625([
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]),
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},
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AffineNielsPoint {
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y_plus_x: FieldElement2625([
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]),
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y_minus_x: FieldElement2625([
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]),
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xy2d: FieldElement2625([
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]),
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},
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AffineNielsPoint {
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y_plus_x: FieldElement2625([
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]),
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y_minus_x: FieldElement2625([
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]),
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xy2d: FieldElement2625([
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]),
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},
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AffineNielsPoint {
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y_plus_x: FieldElement2625([
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]),
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y_minus_x: FieldElement2625([
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