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Precomputed MDS matrix for CrandallField

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This commit is contained in:
Daniel Lubarov 2021-04-28 14:42:21 -07:00
parent 5913fd71b9
commit 6db30c6db3
2 changed files with 96 additions and 1 deletions
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95
src/field/crandall_field.rs
View File

@ -11,6 +11,90 @@ use std::iter::{Product, Sum};
/// EPSILON = 9 * 2**28 - 1
const EPSILON: u64 = 2415919103;
/// A precomputed 8*8 Cauchy matrix, generated with `Field::mds_8`.
const CAUCHY_MDS_8: [[CrandallField; 8]; 8] = [
[
CrandallField(16140901062381928449),
CrandallField(2635249153041947502),
CrandallField(3074457345215605419),
CrandallField(11068046442776179508),
CrandallField(13835058053470224385),
CrandallField(6148914690431210838),
CrandallField(9223372035646816257),
CrandallField(1),
],
[
CrandallField(2049638230143736946),
CrandallField(16140901062381928449),
CrandallField(2635249153041947502),
CrandallField(3074457345215605419),
CrandallField(11068046442776179508),
CrandallField(13835058053470224385),
CrandallField(6148914690431210838),
CrandallField(9223372035646816257),
],
[
CrandallField(5534023221388089754),
CrandallField(2049638230143736946),
CrandallField(16140901062381928449),
CrandallField(2635249153041947502),
CrandallField(3074457345215605419),
CrandallField(11068046442776179508),
CrandallField(13835058053470224385),
CrandallField(6148914690431210838),
],
[
CrandallField(16769767337539665921),
CrandallField(5534023221388089754),
CrandallField(2049638230143736946),
CrandallField(16140901062381928449),
CrandallField(2635249153041947502),
CrandallField(3074457345215605419),
CrandallField(11068046442776179508),
CrandallField(13835058053470224385),
],
[
CrandallField(10760600708254618966),
CrandallField(16769767337539665921),
CrandallField(5534023221388089754),
CrandallField(2049638230143736946),
CrandallField(16140901062381928449),
CrandallField(2635249153041947502),
CrandallField(3074457345215605419),
CrandallField(11068046442776179508),
],
[
CrandallField(5675921252705733081),
CrandallField(10760600708254618966),
CrandallField(16769767337539665921),
CrandallField(5534023221388089754),
CrandallField(2049638230143736946),
CrandallField(16140901062381928449),
CrandallField(2635249153041947502),
CrandallField(3074457345215605419),
],
[
CrandallField(1317624576520973751),
CrandallField(5675921252705733081),
CrandallField(10760600708254618966),
CrandallField(16769767337539665921),
CrandallField(5534023221388089754),
CrandallField(2049638230143736946),
CrandallField(16140901062381928449),
CrandallField(2635249153041947502),
],
[
CrandallField(15987178195121148178),
CrandallField(1317624576520973751),
CrandallField(5675921252705733081),
CrandallField(10760600708254618966),
CrandallField(16769767337539665921),
CrandallField(5534023221388089754),
CrandallField(2049638230143736946),
CrandallField(16140901062381928449),
],
];
/// A field designed for use with the Crandall reduction algorithm.
///
/// Its order is
@ -224,6 +308,17 @@ impl Field for CrandallField {
let x74 = x73 * x39;
x74
}
fn mds_8(vec: [Self; 8]) -> [Self; 8] {
let mut result = [Self::ZERO; 8];
for r in 0..8 {
for c in 0..8 {
let entry = CAUCHY_MDS_8[r][c];
result[r] += entry * vec[c];
}
}
result
}
}
impl Neg for CrandallField {

2
src/field/field.rs
View File

@ -5,8 +5,8 @@ use std::iter::{Product, Sum};
use std::ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, Sub, SubAssign};
use num::Integer;
use rand::Rng;
use rand::rngs::OsRng;
use rand::Rng;
use crate::util::bits_u64;