newsroom/node_modules/@noble/curves/abstract/curve.js

"use strict";
Object.defineProperty(exports, "__esModule", { value: true });
exports.wNAF = void 0;
exports.negateCt = negateCt;
exports.normalizeZ = normalizeZ;
exports.mulEndoUnsafe = mulEndoUnsafe;
exports.pippenger = pippenger;
exports.precomputeMSMUnsafe = precomputeMSMUnsafe;
exports.validateBasic = validateBasic;
exports._createCurveFields = _createCurveFields;
/**
 * Methods for elliptic curve multiplication by scalars.
 * Contains wNAF, pippenger.
 * @module
 */
/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
const utils_ts_1 = require("../utils.js");
const modular_ts_1 = require("./modular.js");
const _0n = BigInt(0);
const _1n = BigInt(1);
function negateCt(condition, item) {
    const neg = item.negate();
    return condition ? neg : item;
}
/**
 * Takes a bunch of Projective Points but executes only one
 * inversion on all of them. Inversion is very slow operation,
 * so this improves performance massively.
 * Optimization: converts a list of projective points to a list of identical points with Z=1.
 */
function normalizeZ(c, points) {
    const invertedZs = (0, modular_ts_1.FpInvertBatch)(c.Fp, points.map((p) => p.Z));
    return points.map((p, i) => c.fromAffine(p.toAffine(invertedZs[i])));
}
function validateW(W, bits) {
    if (!Number.isSafeInteger(W) || W <= 0 || W > bits)
        throw new Error('invalid window size, expected [1..' + bits + '], got W=' + W);
}
function calcWOpts(W, scalarBits) {
    validateW(W, scalarBits);
    const windows = Math.ceil(scalarBits / W) + 1; // W=8 33. Not 32, because we skip zero
    const windowSize = 2 ** (W - 1); // W=8 128. Not 256, because we skip zero
    const maxNumber = 2 ** W; // W=8 256
    const mask = (0, utils_ts_1.bitMask)(W); // W=8 255 == mask 0b11111111
    const shiftBy = BigInt(W); // W=8 8
    return { windows, windowSize, mask, maxNumber, shiftBy };
}
function calcOffsets(n, window, wOpts) {
    const { windowSize, mask, maxNumber, shiftBy } = wOpts;
    let wbits = Number(n & mask); // extract W bits.
    let nextN = n >> shiftBy; // shift number by W bits.
    // What actually happens here:
    // const highestBit = Number(mask ^ (mask >> 1n));
    // let wbits2 = wbits - 1; // skip zero
    // if (wbits2 & highestBit) { wbits2 ^= Number(mask); // (~);
    // split if bits > max: +224 => 256-32
    if (wbits > windowSize) {
        // we skip zero, which means instead of `>= size-1`, we do `> size`
        wbits -= maxNumber; // -32, can be maxNumber - wbits, but then we need to set isNeg here.
        nextN += _1n; // +256 (carry)
    }
    const offsetStart = window * windowSize;
    const offset = offsetStart + Math.abs(wbits) - 1; // -1 because we skip zero
    const isZero = wbits === 0; // is current window slice a 0?
    const isNeg = wbits < 0; // is current window slice negative?
    const isNegF = window % 2 !== 0; // fake random statement for noise
    const offsetF = offsetStart; // fake offset for noise
    return { nextN, offset, isZero, isNeg, isNegF, offsetF };
}
function validateMSMPoints(points, c) {
    if (!Array.isArray(points))
        throw new Error('array expected');
    points.forEach((p, i) => {
        if (!(p instanceof c))
            throw new Error('invalid point at index ' + i);
    });
}
function validateMSMScalars(scalars, field) {
    if (!Array.isArray(scalars))
        throw new Error('array of scalars expected');
    scalars.forEach((s, i) => {
        if (!field.isValid(s))
            throw new Error('invalid scalar at index ' + i);
    });
}
// Since points in different groups cannot be equal (different object constructor),
// we can have single place to store precomputes.
// Allows to make points frozen / immutable.
const pointPrecomputes = new WeakMap();
const pointWindowSizes = new WeakMap();
function getW(P) {
    // To disable precomputes:
    // return 1;
    return pointWindowSizes.get(P) || 1;
}
function assert0(n) {
    if (n !== _0n)
        throw new Error('invalid wNAF');
}
/**
 * Elliptic curve multiplication of Point by scalar. Fragile.
 * Table generation takes **30MB of ram and 10ms on high-end CPU**,
 * but may take much longer on slow devices. Actual generation will happen on
 * first call of `multiply()`. By default, `BASE` point is precomputed.
 *
 * Scalars should always be less than curve order: this should be checked inside of a curve itself.
 * Creates precomputation tables for fast multiplication:
 * - private scalar is split by fixed size windows of W bits
 * - every window point is collected from window's table & added to accumulator
 * - since windows are different, same point inside tables won't be accessed more than once per calc
 * - each multiplication is 'Math.ceil(CURVE_ORDER / 𝑊) + 1' point additions (fixed for any scalar)
 * - +1 window is neccessary for wNAF
 * - wNAF reduces table size: 2x less memory + 2x faster generation, but 10% slower multiplication
 *
 * @todo Research returning 2d JS array of windows, instead of a single window.
 * This would allow windows to be in different memory locations
 */
class wNAF {
    // Parametrized with a given Point class (not individual point)
    constructor(Point, bits) {
        this.BASE = Point.BASE;
        this.ZERO = Point.ZERO;
        this.Fn = Point.Fn;
        this.bits = bits;
    }
    // non-const time multiplication ladder
    _unsafeLadder(elm, n, p = this.ZERO) {
        let d = elm;
        while (n > _0n) {
            if (n & _1n)
                p = p.add(d);
            d = d.double();
            n >>= _1n;
        }
        return p;
    }
    /**
     * Creates a wNAF precomputation window. Used for caching.
     * Default window size is set by `utils.precompute()` and is equal to 8.
     * Number of precomputed points depends on the curve size:
     * 2^(𝑊−1) * (Math.ceil(𝑛 / 𝑊) + 1), where:
     * - 𝑊 is the window size
     * - 𝑛 is the bitlength of the curve order.
     * For a 256-bit curve and window size 8, the number of precomputed points is 128 * 33 = 4224.
     * @param point Point instance
     * @param W window size
     * @returns precomputed point tables flattened to a single array
     */
    precomputeWindow(point, W) {
        const { windows, windowSize } = calcWOpts(W, this.bits);
        const points = [];
        let p = point;
        let base = p;
        for (let window = 0; window < windows; window++) {
            base = p;
            points.push(base);
            // i=1, bc we skip 0
            for (let i = 1; i < windowSize; i++) {
                base = base.add(p);
                points.push(base);
            }
            p = base.double();
        }
        return points;
    }
    /**
     * Implements ec multiplication using precomputed tables and w-ary non-adjacent form.
     * More compact implementation:
     * https://github.com/paulmillr/noble-secp256k1/blob/47cb1669b6e506ad66b35fe7d76132ae97465da2/index.ts#L502-L541
     * @returns real and fake (for const-time) points
     */
    wNAF(W, precomputes, n) {
        // Scalar should be smaller than field order
        if (!this.Fn.isValid(n))
            throw new Error('invalid scalar');
        // Accumulators
        let p = this.ZERO;
        let f = this.BASE;
        // This code was first written with assumption that 'f' and 'p' will never be infinity point:
        // since each addition is multiplied by 2 ** W, it cannot cancel each other. However,
        // there is negate now: it is possible that negated element from low value
        // would be the same as high element, which will create carry into next window.
        // It's not obvious how this can fail, but still worth investigating later.
        const wo = calcWOpts(W, this.bits);
        for (let window = 0; window < wo.windows; window++) {
            // (n === _0n) is handled and not early-exited. isEven and offsetF are used for noise
            const { nextN, offset, isZero, isNeg, isNegF, offsetF } = calcOffsets(n, window, wo);
            n = nextN;
            if (isZero) {
                // bits are 0: add garbage to fake point
                // Important part for const-time getPublicKey: add random "noise" point to f.
                f = f.add(negateCt(isNegF, precomputes[offsetF]));
            }
            else {
                // bits are 1: add to result point
                p = p.add(negateCt(isNeg, precomputes[offset]));
            }
        }
        assert0(n);
        // Return both real and fake points: JIT won't eliminate f.
        // At this point there is a way to F be infinity-point even if p is not,
        // which makes it less const-time: around 1 bigint multiply.
        return { p, f };
    }
    /**
     * Implements ec unsafe (non const-time) multiplication using precomputed tables and w-ary non-adjacent form.
     * @param acc accumulator point to add result of multiplication
     * @returns point
     */
    wNAFUnsafe(W, precomputes, n, acc = this.ZERO) {
        const wo = calcWOpts(W, this.bits);
        for (let window = 0; window < wo.windows; window++) {
            if (n === _0n)
                break; // Early-exit, skip 0 value
            const { nextN, offset, isZero, isNeg } = calcOffsets(n, window, wo);
            n = nextN;
            if (isZero) {
                // Window bits are 0: skip processing.
                // Move to next window.
                continue;
            }
            else {
                const item = precomputes[offset];
                acc = acc.add(isNeg ? item.negate() : item); // Re-using acc allows to save adds in MSM
            }
        }
        assert0(n);
        return acc;
    }
    getPrecomputes(W, point, transform) {
        // Calculate precomputes on a first run, reuse them after
        let comp = pointPrecomputes.get(point);
        if (!comp) {
            comp = this.precomputeWindow(point, W);
            if (W !== 1) {
                // Doing transform outside of if brings 15% perf hit
                if (typeof transform === 'function')
                    comp = transform(comp);
                pointPrecomputes.set(point, comp);
            }
        }
        return comp;
    }
    cached(point, scalar, transform) {
        const W = getW(point);
        return this.wNAF(W, this.getPrecomputes(W, point, transform), scalar);
    }
    unsafe(point, scalar, transform, prev) {
        const W = getW(point);
        if (W === 1)
            return this._unsafeLadder(point, scalar, prev); // For W=1 ladder is ~x2 faster
        return this.wNAFUnsafe(W, this.getPrecomputes(W, point, transform), scalar, prev);
    }
    // We calculate precomputes for elliptic curve point multiplication
    // using windowed method. This specifies window size and
    // stores precomputed values. Usually only base point would be precomputed.
    createCache(P, W) {
        validateW(W, this.bits);
        pointWindowSizes.set(P, W);
        pointPrecomputes.delete(P);
    }
    hasCache(elm) {
        return getW(elm) !== 1;
    }
}
exports.wNAF = wNAF;
/**
 * Endomorphism-specific multiplication for Koblitz curves.
 * Cost: 128 dbl, 0-256 adds.
 */
function mulEndoUnsafe(Point, point, k1, k2) {
    let acc = point;
    let p1 = Point.ZERO;
    let p2 = Point.ZERO;
    while (k1 > _0n || k2 > _0n) {
        if (k1 & _1n)
            p1 = p1.add(acc);
        if (k2 & _1n)
            p2 = p2.add(acc);
        acc = acc.double();
        k1 >>= _1n;
        k2 >>= _1n;
    }
    return { p1, p2 };
}
/**
 * Pippenger algorithm for multi-scalar multiplication (MSM, Pa + Qb + Rc + ...).
 * 30x faster vs naive addition on L=4096, 10x faster than precomputes.
 * For N=254bit, L=1, it does: 1024 ADD + 254 DBL. For L=5: 1536 ADD + 254 DBL.
 * Algorithmically constant-time (for same L), even when 1 point + scalar, or when scalar = 0.
 * @param c Curve Point constructor
 * @param fieldN field over CURVE.N - important that it's not over CURVE.P
 * @param points array of L curve points
 * @param scalars array of L scalars (aka secret keys / bigints)
 */
function pippenger(c, fieldN, points, scalars) {
    // If we split scalars by some window (let's say 8 bits), every chunk will only
    // take 256 buckets even if there are 4096 scalars, also re-uses double.
    // TODO:
    // - https://eprint.iacr.org/2024/750.pdf
    // - https://tches.iacr.org/index.php/TCHES/article/view/10287
    // 0 is accepted in scalars
    validateMSMPoints(points, c);
    validateMSMScalars(scalars, fieldN);
    const plength = points.length;
    const slength = scalars.length;
    if (plength !== slength)
        throw new Error('arrays of points and scalars must have equal length');
    // if (plength === 0) throw new Error('array must be of length >= 2');
    const zero = c.ZERO;
    const wbits = (0, utils_ts_1.bitLen)(BigInt(plength));
    let windowSize = 1; // bits
    if (wbits > 12)
        windowSize = wbits - 3;
    else if (wbits > 4)
        windowSize = wbits - 2;
    else if (wbits > 0)
        windowSize = 2;
    const MASK = (0, utils_ts_1.bitMask)(windowSize);
    const buckets = new Array(Number(MASK) + 1).fill(zero); // +1 for zero array
    const lastBits = Math.floor((fieldN.BITS - 1) / windowSize) * windowSize;
    let sum = zero;
    for (let i = lastBits; i >= 0; i -= windowSize) {
        buckets.fill(zero);
        for (let j = 0; j < slength; j++) {
            const scalar = scalars[j];
            const wbits = Number((scalar >> BigInt(i)) & MASK);
            buckets[wbits] = buckets[wbits].add(points[j]);
        }
        let resI = zero; // not using this will do small speed-up, but will lose ct
        // Skip first bucket, because it is zero
        for (let j = buckets.length - 1, sumI = zero; j > 0; j--) {
            sumI = sumI.add(buckets[j]);
            resI = resI.add(sumI);
        }
        sum = sum.add(resI);
        if (i !== 0)
            for (let j = 0; j < windowSize; j++)
                sum = sum.double();
    }
    return sum;
}
/**
 * Precomputed multi-scalar multiplication (MSM, Pa + Qb + Rc + ...).
 * @param c Curve Point constructor
 * @param fieldN field over CURVE.N - important that it's not over CURVE.P
 * @param points array of L curve points
 * @returns function which multiplies points with scaars
 */
function precomputeMSMUnsafe(c, fieldN, points, windowSize) {
    /**
     * Performance Analysis of Window-based Precomputation
     *
     * Base Case (256-bit scalar, 8-bit window):
     * - Standard precomputation requires:
     *   - 31 additions per scalar × 256 scalars = 7,936 ops
     *   - Plus 255 summary additions = 8,191 total ops
     *   Note: Summary additions can be optimized via accumulator
     *
     * Chunked Precomputation Analysis:
     * - Using 32 chunks requires:
     *   - 255 additions per chunk
     *   - 256 doublings
     *   - Total: (255 × 32) + 256 = 8,416 ops
     *
     * Memory Usage Comparison:
     * Window Size | Standard Points | Chunked Points
     * ------------|-----------------|---------------
     *     4-bit   |     520         |      15
     *     8-bit   |    4,224        |     255
     *    10-bit   |   13,824        |   1,023
     *    16-bit   |  557,056        |  65,535
     *
     * Key Advantages:
     * 1. Enables larger window sizes due to reduced memory overhead
     * 2. More efficient for smaller scalar counts:
     *    - 16 chunks: (16 × 255) + 256 = 4,336 ops
     *    - ~2x faster than standard 8,191 ops
     *
     * Limitations:
     * - Not suitable for plain precomputes (requires 256 constant doublings)
     * - Performance degrades with larger scalar counts:
     *   - Optimal for ~256 scalars
     *   - Less efficient for 4096+ scalars (Pippenger preferred)
     */
    validateW(windowSize, fieldN.BITS);
    validateMSMPoints(points, c);
    const zero = c.ZERO;
    const tableSize = 2 ** windowSize - 1; // table size (without zero)
    const chunks = Math.ceil(fieldN.BITS / windowSize); // chunks of item
    const MASK = (0, utils_ts_1.bitMask)(windowSize);
    const tables = points.map((p) => {
        const res = [];
        for (let i = 0, acc = p; i < tableSize; i++) {
            res.push(acc);
            acc = acc.add(p);
        }
        return res;
    });
    return (scalars) => {
        validateMSMScalars(scalars, fieldN);
        if (scalars.length > points.length)
            throw new Error('array of scalars must be smaller than array of points');
        let res = zero;
        for (let i = 0; i < chunks; i++) {
            // No need to double if accumulator is still zero.
            if (res !== zero)
                for (let j = 0; j < windowSize; j++)
                    res = res.double();
            const shiftBy = BigInt(chunks * windowSize - (i + 1) * windowSize);
            for (let j = 0; j < scalars.length; j++) {
                const n = scalars[j];
                const curr = Number((n >> shiftBy) & MASK);
                if (!curr)
                    continue; // skip zero scalars chunks
                res = res.add(tables[j][curr - 1]);
            }
        }
        return res;
    };
}
// TODO: remove
/** @deprecated */
function validateBasic(curve) {
    (0, modular_ts_1.validateField)(curve.Fp);
    (0, utils_ts_1.validateObject)(curve, {
        n: 'bigint',
        h: 'bigint',
        Gx: 'field',
        Gy: 'field',
    }, {
        nBitLength: 'isSafeInteger',
        nByteLength: 'isSafeInteger',
    });
    // Set defaults
    return Object.freeze({
        ...(0, modular_ts_1.nLength)(curve.n, curve.nBitLength),
        ...curve,
        ...{ p: curve.Fp.ORDER },
    });
}
function createField(order, field, isLE) {
    if (field) {
        if (field.ORDER !== order)
            throw new Error('Field.ORDER must match order: Fp == p, Fn == n');
        (0, modular_ts_1.validateField)(field);
        return field;
    }
    else {
        return (0, modular_ts_1.Field)(order, { isLE });
    }
}
/** Validates CURVE opts and creates fields */
function _createCurveFields(type, CURVE, curveOpts = {}, FpFnLE) {
    if (FpFnLE === undefined)
        FpFnLE = type === 'edwards';
    if (!CURVE || typeof CURVE !== 'object')
        throw new Error(`expected valid ${type} CURVE object`);
    for (const p of ['p', 'n', 'h']) {
        const val = CURVE[p];
        if (!(typeof val === 'bigint' && val > _0n))
            throw new Error(`CURVE.${p} must be positive bigint`);
    }
    const Fp = createField(CURVE.p, curveOpts.Fp, FpFnLE);
    const Fn = createField(CURVE.n, curveOpts.Fn, FpFnLE);
    const _b = type === 'weierstrass' ? 'b' : 'd';
    const params = ['Gx', 'Gy', 'a', _b];
    for (const p of params) {
        // @ts-ignore
        if (!Fp.isValid(CURVE[p]))
            throw new Error(`CURVE.${p} must be valid field element of CURVE.Fp`);
    }
    CURVE = Object.freeze(Object.assign({}, CURVE));
    return { CURVE, Fp, Fn };
}
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