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weierstrass: adjust SWUFpSqrtRatio to not use exp operator

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Paul Miller 2023-05-06 12:38:53 +00:00
parent 5edafbac97
commit 90e87f7ab1
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1 changed files with 9 additions and 4 deletions
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13
src/abstract/weierstrass.ts
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@ -1107,10 +1107,14 @@ export function SWUFpSqrtRatio<T>(Fp: mod.IField<T>, Z: T) {
let l = _0n; let l = _0n;
for (let o = q - _1n; o % _2n === _0n; o /= _2n) l += _1n; for (let o = q - _1n; o % _2n === _0n; o /= _2n) l += _1n;
const c1 = l; // 1. c1, the largest integer such that 2^c1 divides q - 1. const c1 = l; // 1. c1, the largest integer such that 2^c1 divides q - 1.
const c2 = (q - _1n) / _2n ** c1; // 2. c2 = (q - 1) / (2^c1) # Integer arithmetic // We need 2n ** c1 and 2n ** (c1-1). We can't use **; but we can use <<.
// 2n ** c1 == 2n << (c1-1)
const _2n_pow_c1_1 = _2n << (c1 - _1n - _1n);
const _2n_pow_c1 = _2n_pow_c1_1 * _2n;
const c2 = (q - _1n) / _2n_pow_c1; // 2. c2 = (q - 1) / (2^c1) # Integer arithmetic
const c3 = (c2 - _1n) / _2n; // 3. c3 = (c2 - 1) / 2 # Integer arithmetic const c3 = (c2 - _1n) / _2n; // 3. c3 = (c2 - 1) / 2 # Integer arithmetic
const c4 = _2n ** c1 - _1n; // 4. c4 = 2^c1 - 1 # Integer arithmetic const c4 = _2n_pow_c1 - _1n; // 4. c4 = 2^c1 - 1 # Integer arithmetic
const c5 = _2n ** (c1 - _1n); // 5. c5 = 2^(c1 - 1) # Integer arithmetic const c5 = _2n_pow_c1_1; // 5. c5 = 2^(c1 - 1) # Integer arithmetic
const c6 = Fp.pow(Z, c2); // 6. c6 = Z^c2 const c6 = Fp.pow(Z, c2); // 6. c6 = Z^c2
const c7 = Fp.pow(Z, (c2 + _1n) / _2n); // 7. c7 = Z^((c2 + 1) / 2) const c7 = Fp.pow(Z, (c2 + _1n) / _2n); // 7. c7 = Z^((c2 + 1) / 2)
let sqrtRatio = (u: T, v: T): { isValid: boolean; value: T } => { let sqrtRatio = (u: T, v: T): { isValid: boolean; value: T } => {
@ -1132,7 +1136,8 @@ export function SWUFpSqrtRatio<T>(Fp: mod.IField<T>, Z: T) {
tv4 = Fp.cmov(tv5, tv4, isQR); // 16. tv4 = CMOV(tv5, tv4, isQR) tv4 = Fp.cmov(tv5, tv4, isQR); // 16. tv4 = CMOV(tv5, tv4, isQR)
// 17. for i in (c1, c1 - 1, ..., 2): // 17. for i in (c1, c1 - 1, ..., 2):
for (let i = c1; i > _1n; i--) { for (let i = c1; i > _1n; i--) {
let tv5 = _2n ** (i - _2n); // 18. tv5 = i - 2; 19. tv5 = 2^tv5 let tv5 = i - _2n; // 18. tv5 = i - 2
tv5 = _2n << (tv5 - _1n); // 19. tv5 = 2^tv5
let tvv5 = Fp.pow(tv4, tv5); // 20. tv5 = tv4^tv5 let tvv5 = Fp.pow(tv4, tv5); // 20. tv5 = tv4^tv5
const e1 = Fp.eql(tvv5, Fp.ONE); // 21. e1 = tv5 == 1 const e1 = Fp.eql(tvv5, Fp.ONE); // 21. e1 = tv5 == 1
tv2 = Fp.mul(tv3, tv1); // 22. tv2 = tv3 * tv1 tv2 = Fp.mul(tv3, tv1); // 22. tv2 = tv3 * tv1