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Add modular division

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Paul Miller 2022-12-15 22:11:40 +00:00
parent 989af14b10
commit 7d746a7408
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2 changed files with 14 additions and 3 deletions
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7
README.md
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@ -69,12 +69,13 @@ secp256k1.sign(randomBytes(32), secp256k1.utils.randomPrivateKey());
import { twistedEdwards } from '@noble/curves/edwards'; // Twisted Edwards curve
import { sha512 } from '@noble/hashes/sha512';
import { div } from '@noble/curves/modular';
const ed25519 = twistedEdwards({
a: -1n,
d: 37095705934669439343138083508754565189542113879843219016388785533085940283555n,
P: 57896044618658097711785492504343953926634992332820282019728792003956564819949n,
n: 7237005577332262213973186563042994240857116359379907606001950938285454250989n,
d: div(-121665n, 121666n, 2n ** 255n - 19n), // -121665n/121666n
P: 2n ** 255n - 19n,
n: 2n ** 252n + 27742317777372353535851937790883648493n,
h: 8n,
Gx: 15112221349535400772501151409588531511454012693041857206046113283949847762202n,
Gy: 46316835694926478169428394003475163141307993866256225615783033603165251855960n,

10
src/modular.ts
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@ -64,6 +64,16 @@ export function invert(number: bigint, modulo: bigint): bigint {
return mod(x, modulo);
}
/**
* Division over finite field.
* `a/b mod p == a * invert(b) mod p`
*/
export function div(numerator: bigint, denominator: bigint, modulo: bigint): bigint {
const num = mod(numerator, modulo);
const iden = invert(denominator, modulo);
return mod(num * iden, modulo);
}
/**
* Takes a list of numbers, efficiently inverts all of them.
* @param nums list of bigints