@noble/curves
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Audited & minimal JS implementation of elliptic curve cryptography
195 lines • 8.36 kB
TypeScript
/**
* Methods for elliptic curve multiplication by scalars.
* Contains wNAF, pippenger.
* @module
*/
/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
import { type Signer } from '../utils.ts';
import { type IField } from './modular.ts';
export type AffinePoint<T> = {
x: T;
y: T;
} & {
Z?: never;
};
/** Base interface for all elliptic curve Points. */
export interface CurvePoint<F, P extends CurvePoint<F, P>> {
/** Affine x coordinate. Different from projective / extended X coordinate. */
x: F;
/** Affine y coordinate. Different from projective / extended Y coordinate. */
y: F;
Z?: F;
double(): P;
negate(): P;
add(other: P): P;
subtract(other: P): P;
equals(other: P): boolean;
multiply(scalar: bigint): P;
assertValidity(): void;
clearCofactor(): P;
is0(): boolean;
isTorsionFree(): boolean;
isSmallOrder(): boolean;
multiplyUnsafe(scalar: bigint): P;
/**
* Massively speeds up `p.multiply(n)` by using precompute tables (caching). See {@link wNAF}.
* @param isLazy calculate cache now. Default (true) ensures it's deferred to first `multiply()`
*/
precompute(windowSize?: number, isLazy?: boolean): P;
/** Converts point to 2D xy affine coordinates */
toAffine(invertedZ?: F): AffinePoint<F>;
toBytes(): Uint8Array;
toHex(): string;
}
/** Base interface for all elliptic curve Point constructors. */
export interface CurvePointCons<P extends CurvePoint<any, P>> {
[Symbol.hasInstance]: (item: unknown) => boolean;
BASE: P;
ZERO: P;
/** Field for basic curve math */
Fp: IField<P_F<P>>;
/** Scalar field, for scalars in multiply and others */
Fn: IField<bigint>;
/** Creates point from x, y. Does NOT validate if the point is valid. Use `.assertValidity()`. */
fromAffine(p: AffinePoint<P_F<P>>): P;
fromBytes(bytes: Uint8Array): P;
fromHex(hex: string): P;
}
/** Returns Fp type from Point (P_F<P> == P.F) */
export type P_F<P extends CurvePoint<any, P>> = P extends CurvePoint<infer F, P> ? F : never;
/** Returns Fp type from PointCons (PC_F<PC> == PC.P.F) */
export type PC_F<PC extends CurvePointCons<CurvePoint<any, any>>> = PC['Fp']['ZERO'];
/** Returns Point type from PointCons (PC_P<PC> == PC.P) */
export type PC_P<PC extends CurvePointCons<CurvePoint<any, any>>> = PC['ZERO'];
export type PC_ANY = CurvePointCons<CurvePoint<any, CurvePoint<any, CurvePoint<any, CurvePoint<any, CurvePoint<any, CurvePoint<any, CurvePoint<any, CurvePoint<any, CurvePoint<any, CurvePoint<any, any>>>>>>>>>>>;
export interface CurveLengths {
secretKey?: number;
publicKey?: number;
publicKeyUncompressed?: number;
publicKeyHasPrefix?: boolean;
signature?: number;
seed?: number;
}
export type Mapper<T> = (i: T[]) => T[];
export declare function negateCt<T extends {
negate: () => T;
}>(condition: boolean, item: T): T;
/**
* 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.
*/
export declare function normalizeZ<P extends CurvePoint<any, P>, PC extends CurvePointCons<P>>(c: PC, points: P[]): P[];
/**
* 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
*/
export declare class wNAF<PC extends PC_ANY> {
private readonly BASE;
private readonly ZERO;
private readonly Fn;
readonly bits: number;
constructor(Point: PC, bits: number);
_unsafeLadder(elm: PC_P<PC>, n: bigint, p?: PC_P<PC>): PC_P<PC>;
/**
* 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
*/
private precomputeWindow;
/**
* 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
*/
private wNAF;
/**
* 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
*/
private wNAFUnsafe;
private getPrecomputes;
cached(point: PC_P<PC>, scalar: bigint, transform?: Mapper<PC_P<PC>>): {
p: PC_P<PC>;
f: PC_P<PC>;
};
unsafe(point: PC_P<PC>, scalar: bigint, transform?: Mapper<PC_P<PC>>, prev?: PC_P<PC>): PC_P<PC>;
createCache(P: PC_P<PC>, W: number): void;
hasCache(elm: PC_P<PC>): boolean;
}
/**
* Endomorphism-specific multiplication for Koblitz curves.
* Cost: 128 dbl, 0-256 adds.
*/
export declare function mulEndoUnsafe<P extends CurvePoint<any, P>, PC extends CurvePointCons<P>>(Point: PC, point: P, k1: bigint, k2: bigint): {
p1: P;
p2: P;
};
/**
* 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)
*/
export declare function pippenger<P extends CurvePoint<any, P>, PC extends CurvePointCons<P>>(c: PC, points: P[], scalars: bigint[]): P;
/**
* 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
*/
export declare function precomputeMSMUnsafe<P extends CurvePoint<any, P>, PC extends CurvePointCons<P>>(c: PC, points: P[], windowSize: number): (scalars: bigint[]) => P;
export type ValidCurveParams<T> = {
p: bigint;
n: bigint;
h: bigint;
a: T;
b?: T;
d?: T;
Gx: T;
Gy: T;
};
export type FpFn<T> = {
Fp: IField<T>;
Fn: IField<bigint>;
};
/** Validates CURVE opts and creates fields */
export declare function createCurveFields<T>(type: 'weierstrass' | 'edwards', CURVE: ValidCurveParams<T>, curveOpts?: Partial<FpFn<T>>, FpFnLE?: boolean): FpFn<T> & {
CURVE: ValidCurveParams<T>;
};
type KeygenFn = (seed?: Uint8Array, isCompressed?: boolean) => {
secretKey: Uint8Array;
publicKey: Uint8Array;
};
export declare function createKeygen(randomSecretKey: Function, getPublicKey: Signer['getPublicKey']): KeygenFn;
export {};
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