@turnkey/crypto/dist/math.js

Encryption, decryption, and key related utility functions

'use strict';

/**
 * Compute the modular square root using the Tonelli-Shanks algorithm.
 */
const modSqrt = (x, p) => {
    if (p <= BigInt(0)) {
        throw new Error("p must be positive");
    }
    const base = x % p;
    // Check if p % 4 == 3 (applies to NIST curves P-256, P-384, and P-521)
    if (testBit(p, 0) && testBit(p, 1)) {
        const q = (p + BigInt(1)) >> BigInt(2);
        const squareRoot = modPow(base, q, p);
        if ((squareRoot * squareRoot) % p !== base) {
            throw new Error("could not find a modular square root");
        }
        return squareRoot;
    }
    // Other elliptic curve types not supported
    throw new Error("unsupported modulus value");
};
/**
 * Test if a specific bit is set.
 */
const testBit = (n, i) => {
    const m = BigInt(1) << BigInt(i);
    return (n & m) !== BigInt(0);
};
/**
 * Compute the modular exponentiation.
 */
const modPow = (b, exp, p) => {
    if (exp === BigInt(0)) {
        return BigInt(1);
    }
    let result = b % p;
    const exponentBitString = exp.toString(2);
    for (let i = 1; i < exponentBitString.length; ++i) {
        result = (result * result) % p;
        if (exponentBitString[i] === "1") {
            result = (result * b) % p;
        }
    }
    return result;
};

exports.modSqrt = modSqrt;
exports.testBit = testBit;
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