855 lines
44 KiB
JavaScript
855 lines
44 KiB
JavaScript
/**
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* Absolute value. abs(a)==a if a>=0. abs(a)==-a if a<0
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*
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* @param a
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*
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* @returns The absolute value of a
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*/
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function abs(a) {
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return (a >= 0) ? a : -a;
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}
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/**
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* Returns the bitlength of a number
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*
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* @param a
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* @returns The bit length
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*/
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function bitLength(a) {
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if (typeof a === 'number')
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a = BigInt(a);
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if (a === 1n) {
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return 1;
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}
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let bits = 1;
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do {
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bits++;
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} while ((a >>= 1n) > 1n);
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return bits;
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}
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/**
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* An iterative implementation of the extended euclidean algorithm or extended greatest common divisor algorithm.
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* Take positive integers a, b as input, and return a triple (g, x, y), such that ax + by = g = gcd(a, b).
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*
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* @param a
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* @param b
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*
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* @throws {RangeError}
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* This excepction is thrown if a or b are less than 0
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*
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* @returns A triple (g, x, y), such that ax + by = g = gcd(a, b).
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*/
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function eGcd(a, b) {
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if (typeof a === 'number')
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a = BigInt(a);
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if (typeof b === 'number')
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b = BigInt(b);
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if (a <= 0n || b <= 0n)
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throw new RangeError('a and b MUST be > 0'); // a and b MUST be positive
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let x = 0n;
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let y = 1n;
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let u = 1n;
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let v = 0n;
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while (a !== 0n) {
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const q = b / a;
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const r = b % a;
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const m = x - (u * q);
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const n = y - (v * q);
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b = a;
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a = r;
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x = u;
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y = v;
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u = m;
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v = n;
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}
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return {
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g: b,
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x: x,
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y: y
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};
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}
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/**
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* Greatest-common divisor of two integers based on the iterative binary algorithm.
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*
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* @param a
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* @param b
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*
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* @returns The greatest common divisor of a and b
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*/
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function gcd(a, b) {
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let aAbs = (typeof a === 'number') ? BigInt(abs(a)) : abs(a);
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let bAbs = (typeof b === 'number') ? BigInt(abs(b)) : abs(b);
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if (aAbs === 0n) {
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return bAbs;
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}
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else if (bAbs === 0n) {
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return aAbs;
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}
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let shift = 0n;
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while (((aAbs | bAbs) & 1n) === 0n) {
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aAbs >>= 1n;
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bAbs >>= 1n;
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shift++;
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}
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while ((aAbs & 1n) === 0n)
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aAbs >>= 1n;
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do {
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while ((bAbs & 1n) === 0n)
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bAbs >>= 1n;
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if (aAbs > bAbs) {
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const x = aAbs;
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aAbs = bAbs;
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bAbs = x;
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}
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bAbs -= aAbs;
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} while (bAbs !== 0n);
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// rescale
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return aAbs << shift;
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}
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/**
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* The least common multiple computed as abs(a*b)/gcd(a,b)
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* @param a
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* @param b
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*
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* @returns The least common multiple of a and b
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*/
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function lcm(a, b) {
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if (typeof a === 'number')
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a = BigInt(a);
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if (typeof b === 'number')
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b = BigInt(b);
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if (a === 0n && b === 0n)
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return BigInt(0);
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// return abs(a * b) as bigint / gcd(a, b)
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return abs((a / gcd(a, b)) * b);
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}
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/**
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* Maximum. max(a,b)==a if a>=b. max(a,b)==b if a<=b
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*
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* @param a
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* @param b
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*
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* @returns Maximum of numbers a and b
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*/
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function max(a, b) {
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return (a >= b) ? a : b;
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}
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/**
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* Minimum. min(a,b)==b if a>=b. min(a,b)==a if a<=b
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*
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* @param a
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* @param b
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*
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* @returns Minimum of numbers a and b
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*/
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function min(a, b) {
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return (a >= b) ? b : a;
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}
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/**
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* Finds the smallest positive element that is congruent to a in modulo n
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*
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* @remarks
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* a and b must be the same type, either number or bigint
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*
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* @param a - An integer
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* @param n - The modulo
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*
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* @throws {RangeError}
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* Excpeption thrown when n is not > 0
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*
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* @returns A bigint with the smallest positive representation of a modulo n
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*/
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function toZn(a, n) {
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if (typeof a === 'number')
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a = BigInt(a);
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if (typeof n === 'number')
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n = BigInt(n);
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if (n <= 0n) {
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throw new RangeError('n must be > 0');
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}
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const aZn = a % n;
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return (aZn < 0n) ? aZn + n : aZn;
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}
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/**
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* Modular inverse.
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*
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* @param a The number to find an inverse for
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* @param n The modulo
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*
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* @throws {RangeError}
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* Excpeption thorwn when a does not have inverse modulo n
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*
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* @returns The inverse modulo n
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*/
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function modInv(a, n) {
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const egcd = eGcd(toZn(a, n), n);
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if (egcd.g !== 1n) {
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throw new RangeError(`${a.toString()} does not have inverse modulo ${n.toString()}`); // modular inverse does not exist
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}
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else {
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return toZn(egcd.x, n);
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}
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}
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/**
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* Modular exponentiation b**e mod n. Currently using the right-to-left binary method
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*
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* @param b base
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* @param e exponent
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* @param n modulo
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*
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* @throws {RangeError}
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* Excpeption thrown when n is not > 0
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*
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* @returns b**e mod n
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*/
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function modPow(b, e, n) {
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if (typeof b === 'number')
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b = BigInt(b);
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if (typeof e === 'number')
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e = BigInt(e);
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if (typeof n === 'number')
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n = BigInt(n);
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if (n <= 0n) {
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throw new RangeError('n must be > 0');
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}
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else if (n === 1n) {
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return 0n;
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}
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b = toZn(b, n);
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if (e < 0n) {
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return modInv(modPow(b, abs(e), n), n);
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}
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let r = 1n;
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while (e > 0) {
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if ((e % 2n) === 1n) {
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r = r * b % n;
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}
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e = e / 2n;
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b = b ** 2n % n;
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}
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return r;
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}
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function fromBuffer(buf) {
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let ret = 0n;
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for (const i of buf.values()) {
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const bi = BigInt(i);
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ret = (ret << 8n) + bi;
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}
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return ret;
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}
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/**
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* Secure random bytes for both node and browsers. Node version uses crypto.randomBytes() and browser one self.crypto.getRandomValues()
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*
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* @param byteLength - The desired number of random bytes
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* @param forceLength - If we want to force the output to have a bit length of 8*byteLength. It basically forces the msb to be 1
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*
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* @throws {RangeError}
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* byteLength MUST be > 0
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*
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* @returns A promise that resolves to a UInt8Array/Buffer (Browser/Node.js) filled with cryptographically secure random bytes
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*/
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function randBytes(byteLength, forceLength = false) {
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if (byteLength < 1)
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throw new RangeError('byteLength MUST be > 0');
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return new Promise(function (resolve, reject) {
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{ // browser
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const buf = new Uint8Array(byteLength);
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self.crypto.getRandomValues(buf);
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// If fixed length is required we put the first bit to 1 -> to get the necessary bitLength
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if (forceLength)
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buf[0] = buf[0] | 128;
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resolve(buf);
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}
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});
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}
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/**
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* Secure random bytes for both node and browsers. Node version uses crypto.randomFill() and browser one self.crypto.getRandomValues()
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*
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* @param byteLength - The desired number of random bytes
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* @param forceLength - If we want to force the output to have a bit length of 8*byteLength. It basically forces the msb to be 1
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*
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* @throws {RangeError}
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* byteLength MUST be > 0
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*
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* @returns A UInt8Array/Buffer (Browser/Node.js) filled with cryptographically secure random bytes
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*/
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function randBytesSync(byteLength, forceLength = false) {
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if (byteLength < 1)
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throw new RangeError('byteLength MUST be > 0');
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/* eslint-disable no-lone-blocks */
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{ // browser
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const buf = new Uint8Array(byteLength);
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self.crypto.getRandomValues(buf);
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// If fixed length is required we put the first bit to 1 -> to get the necessary bitLength
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if (forceLength)
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buf[0] = buf[0] | 128;
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return buf;
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}
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/* eslint-enable no-lone-blocks */
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}
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/**
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* Secure random bits for both node and browsers. Node version uses crypto.randomFill() and browser one self.crypto.getRandomValues()
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*
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* @param bitLength - The desired number of random bits
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* @param forceLength - If we want to force the output to have a specific bit length. It basically forces the msb to be 1
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*
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* @throws {RangeError}
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* bitLength MUST be > 0
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*
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* @returns A Promise that resolves to a UInt8Array/Buffer (Browser/Node.js) filled with cryptographically secure random bits
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*/
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function randBits(bitLength, forceLength = false) {
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if (bitLength < 1)
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throw new RangeError('bitLength MUST be > 0');
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const byteLength = Math.ceil(bitLength / 8);
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const bitLengthMod8 = bitLength % 8;
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return new Promise((resolve, reject) => {
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randBytes(byteLength, false).then(function (rndBytes) {
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if (bitLengthMod8 !== 0) {
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// Fill with 0's the extra bits
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rndBytes[0] = rndBytes[0] & (2 ** bitLengthMod8 - 1);
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}
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if (forceLength) {
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const mask = (bitLengthMod8 !== 0) ? 2 ** (bitLengthMod8 - 1) : 128;
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rndBytes[0] = rndBytes[0] | mask;
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}
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resolve(rndBytes);
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});
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});
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}
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/**
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* Secure random bits for both node and browsers. Node version uses crypto.randomFill() and browser one self.crypto.getRandomValues()
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* @param bitLength - The desired number of random bits
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* @param forceLength - If we want to force the output to have a specific bit length. It basically forces the msb to be 1
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*
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* @throws {RangeError}
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* bitLength MUST be > 0
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*
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* @returns A Uint8Array/Buffer (Browser/Node.js) filled with cryptographically secure random bits
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*/
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function randBitsSync(bitLength, forceLength = false) {
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if (bitLength < 1)
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throw new RangeError('bitLength MUST be > 0');
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const byteLength = Math.ceil(bitLength / 8);
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const rndBytes = randBytesSync(byteLength, false);
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const bitLengthMod8 = bitLength % 8;
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if (bitLengthMod8 !== 0) {
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// Fill with 0's the extra bits
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rndBytes[0] = rndBytes[0] & (2 ** bitLengthMod8 - 1);
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}
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if (forceLength) {
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const mask = (bitLengthMod8 !== 0) ? 2 ** (bitLengthMod8 - 1) : 128;
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rndBytes[0] = rndBytes[0] | mask;
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}
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return rndBytes;
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}
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/**
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* Returns a cryptographically secure random integer between [min,max].
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* @param max Returned value will be <= max
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* @param min Returned value will be >= min
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*
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* @throws {RangeError}
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* Arguments MUST be: max > min
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*
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* @returns A cryptographically secure random bigint between [min,max]
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*/
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function randBetween(max, min = 1n) {
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if (max <= min)
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throw new RangeError('Arguments MUST be: max > min');
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const interval = max - min;
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const bitLen = bitLength(interval);
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let rnd;
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do {
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const buf = randBitsSync(bitLen);
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rnd = fromBuffer(buf);
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} while (rnd > interval);
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return rnd + min;
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}
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function _workerUrl(workerCode) {
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workerCode = `(() => {${workerCode}})()`; // encapsulate IIFE
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const _blob = new Blob([workerCode], { type: 'text/javascript' });
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return window.URL.createObjectURL(_blob);
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}
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let _useWorkers = false; // The following is just to check whether we can use workers
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/* eslint-disable no-lone-blocks */
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{ // Native JS
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if (self.Worker !== undefined)
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_useWorkers = true;
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}
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/**
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* The test first tries if any of the first 250 small primes are a factor of the input number and then passes several
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* iterations of Miller-Rabin Probabilistic Primality Test (FIPS 186-4 C.3.1)
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*
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* @param w - A positive integer to be tested for primality
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* @param iterations - The number of iterations for the primality test. The value shall be consistent with Table C.1, C.2 or C.3
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* @param disableWorkers - Disable the use of workers for the primality test
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*
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* @throws {RangeError}
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* w MUST be >= 0
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*
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* @returns A promise that resolves to a boolean that is either true (a probably prime number) or false (definitely composite)
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*/
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function isProbablyPrime(w, iterations = 16, disableWorkers = false) {
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if (typeof w === 'number') {
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w = BigInt(w);
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}
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if (w < 0n)
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throw RangeError('w MUST be >= 0');
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{ // browser
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return new Promise((resolve, reject) => {
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const worker = new Worker(_isProbablyPrimeWorkerUrl());
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worker.onmessage = (event) => {
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worker.terminate();
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resolve(event.data.isPrime);
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};
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worker.onmessageerror = (event) => {
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reject(event);
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};
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const msg = {
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rnd: w,
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iterations: iterations,
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id: 0
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};
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worker.postMessage(msg);
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});
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}
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}
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function _isProbablyPrime(w, iterations) {
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/*
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PREFILTERING. Even values but 2 are not primes, so don't test.
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1 is not a prime and the M-R algorithm needs w>1.
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*/
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if (w === 2n)
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return true;
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else if ((w & 1n) === 0n || w === 1n)
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return false;
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/*
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Test if any of the first 250 small primes are a factor of w. 2 is not tested because it was already tested above.
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*/
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const firstPrimes = [
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3n,
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5n,
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7n,
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11n,
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13n,
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17n,
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19n,
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23n,
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29n,
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31n,
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37n,
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41n,
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43n,
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47n,
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53n,
|
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59n,
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61n,
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67n,
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71n,
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73n,
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||
79n,
|
||
83n,
|
||
89n,
|
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97n,
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||
101n,
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||
103n,
|
||
107n,
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||
109n,
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||
113n,
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||
127n,
|
||
131n,
|
||
137n,
|
||
139n,
|
||
149n,
|
||
151n,
|
||
157n,
|
||
163n,
|
||
167n,
|
||
173n,
|
||
179n,
|
||
181n,
|
||
191n,
|
||
193n,
|
||
197n,
|
||
199n,
|
||
211n,
|
||
223n,
|
||
227n,
|
||
229n,
|
||
233n,
|
||
239n,
|
||
241n,
|
||
251n,
|
||
257n,
|
||
263n,
|
||
269n,
|
||
271n,
|
||
277n,
|
||
281n,
|
||
283n,
|
||
293n,
|
||
307n,
|
||
311n,
|
||
313n,
|
||
317n,
|
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331n,
|
||
337n,
|
||
347n,
|
||
349n,
|
||
353n,
|
||
359n,
|
||
367n,
|
||
373n,
|
||
379n,
|
||
383n,
|
||
389n,
|
||
397n,
|
||
401n,
|
||
409n,
|
||
419n,
|
||
421n,
|
||
431n,
|
||
433n,
|
||
439n,
|
||
443n,
|
||
449n,
|
||
457n,
|
||
461n,
|
||
463n,
|
||
467n,
|
||
479n,
|
||
487n,
|
||
491n,
|
||
499n,
|
||
503n,
|
||
509n,
|
||
521n,
|
||
523n,
|
||
541n,
|
||
547n,
|
||
557n,
|
||
563n,
|
||
569n,
|
||
571n,
|
||
577n,
|
||
587n,
|
||
593n,
|
||
599n,
|
||
601n,
|
||
607n,
|
||
613n,
|
||
617n,
|
||
619n,
|
||
631n,
|
||
641n,
|
||
643n,
|
||
647n,
|
||
653n,
|
||
659n,
|
||
661n,
|
||
673n,
|
||
677n,
|
||
683n,
|
||
691n,
|
||
701n,
|
||
709n,
|
||
719n,
|
||
727n,
|
||
733n,
|
||
739n,
|
||
743n,
|
||
751n,
|
||
757n,
|
||
761n,
|
||
769n,
|
||
773n,
|
||
787n,
|
||
797n,
|
||
809n,
|
||
811n,
|
||
821n,
|
||
823n,
|
||
827n,
|
||
829n,
|
||
839n,
|
||
853n,
|
||
857n,
|
||
859n,
|
||
863n,
|
||
877n,
|
||
881n,
|
||
883n,
|
||
887n,
|
||
907n,
|
||
911n,
|
||
919n,
|
||
929n,
|
||
937n,
|
||
941n,
|
||
947n,
|
||
953n,
|
||
967n,
|
||
971n,
|
||
977n,
|
||
983n,
|
||
991n,
|
||
997n,
|
||
1009n,
|
||
1013n,
|
||
1019n,
|
||
1021n,
|
||
1031n,
|
||
1033n,
|
||
1039n,
|
||
1049n,
|
||
1051n,
|
||
1061n,
|
||
1063n,
|
||
1069n,
|
||
1087n,
|
||
1091n,
|
||
1093n,
|
||
1097n,
|
||
1103n,
|
||
1109n,
|
||
1117n,
|
||
1123n,
|
||
1129n,
|
||
1151n,
|
||
1153n,
|
||
1163n,
|
||
1171n,
|
||
1181n,
|
||
1187n,
|
||
1193n,
|
||
1201n,
|
||
1213n,
|
||
1217n,
|
||
1223n,
|
||
1229n,
|
||
1231n,
|
||
1237n,
|
||
1249n,
|
||
1259n,
|
||
1277n,
|
||
1279n,
|
||
1283n,
|
||
1289n,
|
||
1291n,
|
||
1297n,
|
||
1301n,
|
||
1303n,
|
||
1307n,
|
||
1319n,
|
||
1321n,
|
||
1327n,
|
||
1361n,
|
||
1367n,
|
||
1373n,
|
||
1381n,
|
||
1399n,
|
||
1409n,
|
||
1423n,
|
||
1427n,
|
||
1429n,
|
||
1433n,
|
||
1439n,
|
||
1447n,
|
||
1451n,
|
||
1453n,
|
||
1459n,
|
||
1471n,
|
||
1481n,
|
||
1483n,
|
||
1487n,
|
||
1489n,
|
||
1493n,
|
||
1499n,
|
||
1511n,
|
||
1523n,
|
||
1531n,
|
||
1543n,
|
||
1549n,
|
||
1553n,
|
||
1559n,
|
||
1567n,
|
||
1571n,
|
||
1579n,
|
||
1583n,
|
||
1597n
|
||
];
|
||
for (let i = 0; i < firstPrimes.length && (firstPrimes[i] <= w); i++) {
|
||
const p = firstPrimes[i];
|
||
if (w === p)
|
||
return true;
|
||
else if (w % p === 0n)
|
||
return false;
|
||
}
|
||
/*
|
||
1. Let a be the largest integer such that 2**a divides w−1.
|
||
2. m = (w−1) / 2**a.
|
||
3. wlen = len (w).
|
||
4. For i = 1 to iterations do
|
||
4.1 Obtain a string b of wlen bits from an RBG.
|
||
Comment: Ensure that 1 < b < w−1.
|
||
4.2 If ((b ≤ 1) or (b ≥ w−1)), then go to step 4.1.
|
||
4.3 z = b**m mod w.
|
||
4.4 If ((z = 1) or (z = w − 1)), then go to step 4.7.
|
||
4.5 For j = 1 to a − 1 do.
|
||
4.5.1 z = z**2 mod w.
|
||
4.5.2 If (z = w−1), then go to step 4.7.
|
||
4.5.3 If (z = 1), then go to step 4.6.
|
||
4.6 Return COMPOSITE.
|
||
4.7 Continue.
|
||
Comment: Increment i for the do-loop in step 4.
|
||
5. Return PROBABLY PRIME.
|
||
*/
|
||
let a = 0n;
|
||
const d = w - 1n;
|
||
let aux = d;
|
||
while (aux % 2n === 0n) {
|
||
aux /= 2n;
|
||
++a;
|
||
}
|
||
const m = d / (2n ** a);
|
||
do {
|
||
const b = randBetween(d, 2n);
|
||
let z = modPow(b, m, w);
|
||
if (z === 1n || z === d)
|
||
continue;
|
||
let j = 1;
|
||
while (j < a) {
|
||
z = modPow(z, 2n, w);
|
||
if (z === d)
|
||
break;
|
||
if (z === 1n)
|
||
return false;
|
||
j++;
|
||
}
|
||
if (z !== d)
|
||
return false;
|
||
} while (--iterations !== 0);
|
||
return true;
|
||
}
|
||
function _isProbablyPrimeWorkerUrl() {
|
||
// Let's us first add all the required functions
|
||
let workerCode = `'use strict';const ${eGcd.name}=${eGcd.toString()};const ${modInv.name}=${modInv.toString()};const ${modPow.name}=${modPow.toString()};const ${toZn.name}=${toZn.toString()};const ${randBitsSync.name}=${randBitsSync.toString()};const ${randBytesSync.name}=${randBytesSync.toString()};const ${randBetween.name}=${randBetween.toString()};const ${isProbablyPrime.name}=${_isProbablyPrime.toString()};${bitLength.toString()};${fromBuffer.toString()};`;
|
||
workerCode += `onmessage=async function(_e){const _m={isPrime:await ${isProbablyPrime.name}(_e.data.rnd,_e.data.iterations),value:_e.data.rnd,id:_e.data.id};postMessage(_m);}`;
|
||
return _workerUrl(workerCode);
|
||
}
|
||
|
||
/**
|
||
* A probably-prime (Miller-Rabin), cryptographically-secure, random-number generator.
|
||
* The browser version uses web workers to parallelise prime look up. Therefore, it does not lock the UI
|
||
* main process, and it can be much faster (if several cores or cpu are available).
|
||
* The node version can also use worker_threads if they are available (enabled by default with Node 11 and
|
||
* and can be enabled at runtime executing node --experimental-worker with node >=10.5.0).
|
||
*
|
||
* @param bitLength - The required bit length for the generated prime
|
||
* @param iterations - The number of iterations for the Miller-Rabin Probabilistic Primality Test
|
||
*
|
||
* @throws {RangeError}
|
||
* bitLength MUST be > 0
|
||
*
|
||
* @returns A promise that resolves to a bigint probable prime of bitLength bits.
|
||
*/
|
||
function prime(bitLength, iterations = 16) {
|
||
if (bitLength < 1)
|
||
throw new RangeError('bitLength MUST be > 0');
|
||
/* c8 ignore start */
|
||
if (!_useWorkers) { // If there is no support for workers
|
||
let rnd = 0n;
|
||
do {
|
||
rnd = fromBuffer(randBitsSync(bitLength, true));
|
||
} while (!_isProbablyPrime(rnd, iterations));
|
||
return new Promise((resolve) => { resolve(rnd); });
|
||
}
|
||
/* c8 ignore stop */
|
||
return new Promise((resolve, reject) => {
|
||
const workerList = [];
|
||
const _onmessage = (msg, newWorker) => {
|
||
if (msg.isPrime) {
|
||
// if a prime number has been found, stop all the workers, and return it
|
||
for (let j = 0; j < workerList.length; j++) {
|
||
workerList[j].terminate(); // eslint-disable-line @typescript-eslint/no-floating-promises
|
||
}
|
||
while (workerList.length > 0) {
|
||
workerList.pop();
|
||
}
|
||
resolve(msg.value);
|
||
}
|
||
else { // if a composite is found, make the worker test another random number
|
||
const buf = randBitsSync(bitLength, true);
|
||
const rnd = fromBuffer(buf);
|
||
try {
|
||
const msgToWorker = {
|
||
rnd: rnd,
|
||
iterations: iterations,
|
||
id: msg.id
|
||
};
|
||
newWorker.postMessage(msgToWorker);
|
||
}
|
||
catch (error) {
|
||
// The worker has already terminated. There is nothing to handle here
|
||
}
|
||
}
|
||
};
|
||
{ // browser
|
||
const workerURL = _isProbablyPrimeWorkerUrl();
|
||
for (let i = 0; i < self.navigator.hardwareConcurrency - 1; i++) {
|
||
const newWorker = new Worker(workerURL);
|
||
newWorker.onmessage = (event) => _onmessage(event.data, newWorker);
|
||
workerList.push(newWorker);
|
||
}
|
||
}
|
||
for (let i = 0; i < workerList.length; i++) {
|
||
randBits(bitLength, true).then(function (buf) {
|
||
const rnd = fromBuffer(buf);
|
||
workerList[i].postMessage({
|
||
rnd: rnd,
|
||
iterations: iterations,
|
||
id: i
|
||
});
|
||
}).catch(reject);
|
||
}
|
||
});
|
||
}
|
||
/**
|
||
* A probably-prime (Miller-Rabin), cryptographically-secure, random-number generator.
|
||
* The sync version is NOT RECOMMENDED since it won't use workers and thus it'll be slower and may freeze thw window in browser's javascript. Please consider using prime() instead.
|
||
*
|
||
* @param bitLength - The required bit length for the generated prime
|
||
* @param iterations - The number of iterations for the Miller-Rabin Probabilistic Primality Test
|
||
*
|
||
* @throws {RangeError}
|
||
* bitLength MUST be > 0
|
||
*
|
||
* @returns A bigint probable prime of bitLength bits.
|
||
*/
|
||
function primeSync(bitLength, iterations = 16) {
|
||
if (bitLength < 1)
|
||
throw new RangeError('bitLength MUST be > 0');
|
||
let rnd = 0n;
|
||
do {
|
||
rnd = fromBuffer(randBitsSync(bitLength, true));
|
||
} while (!_isProbablyPrime(rnd, iterations));
|
||
return rnd;
|
||
}
|
||
|
||
export { abs, bitLength, eGcd, gcd, isProbablyPrime, lcm, max, min, modInv, modPow, prime, primeSync, randBetween, randBits, randBitsSync, randBytes, randBytesSync, toZn };
|
||
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