104 lines
1.7 KiB
JavaScript
104 lines
1.7 KiB
JavaScript
function xgcd(a, b) {
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let [old_r, r] = [a, b];
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let [old_s, s] = [1n, 0n];
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let [old_t, t] = [0n, 1n];
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while (r !== 0n) {
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const quotient = old_r / r;
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[old_r, r] = [r, old_r - quotient * r];
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[old_s, s] = [s, old_s - quotient * s];
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[old_t, t] = [t, old_t - quotient * t];
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}
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return [old_r, old_s, old_t];
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}
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function modinv(x, modulus) {
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let [r, s, t] = xgcd(x, modulus);
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if (r !== 1n) {
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throw new Error(`no inverse exists - ${x} and ${modulus} are not coprime`);
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}
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if (s < 0n) {
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s += modulus;
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}
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return s;
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}
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function modpow(base, exponent, modulus) {
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if (exponent < 0n) {
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const p = modpow(base, -exponent, modulus);
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return modinv(p, modulus);
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}
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if (modulus === 1n) {
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return 0n;
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}
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let result = 1n;
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base %= modulus;
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while (exponent > 0n) {
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if (exponent % 2n === 1n) {
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result *= base;
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result %= modulus;
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}
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exponent >>= 1n;
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base *= base;
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base %= modulus;
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}
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return result;
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}
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function witness(a, n) {
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let d = n - 1n;
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let s = 0;
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while (d % 2n === 0n) {
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d /= 2n;
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s++;
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}
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let x = modpow(a, d, n);
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let y = null;
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for (let i = 0; i < s; i++) {
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y = modpow(x, 2n, n);
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if (y === 1n && x !== 1n && x !== n - 1n) {
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return true;
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}
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x = y
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}
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return y !== 1n
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}
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function randbigint() {
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return BigInt(Math.floor(Math.random() * Number.MAX_SAFE_INTEGER))
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}
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function isprime(n) {
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if (n === 2n) {
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return true;
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} else if (n % 2n === 0n) {
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return false;
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}
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const trials = 10;
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for (let i = 0; i < trials; i++) {
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const a = randbigint() % (n - 1n) + 1n;
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if (witness(a, n)) {
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return false;
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}
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}
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return true;
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}
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function tonelliShanks(n, p) {
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throw new Error("not implemented");
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}
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export { tonelliShanks, modinv, modpow, isprime };
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