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weierstrass: remove affine Point

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Paul Miller 2023-01-24 05:42:44 +00:00
parent 17e5be5f1b
commit 2ed27da8eb
No known key found for this signature in database
GPG Key ID: 697079DA6878B89B
12 changed files with 253 additions and 314 deletions
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71
src/abstract/bls.ts
View File

@ -16,13 +16,18 @@ import * as ut from './utils.js';
// Types require separate import // Types require separate import
import { Hex, PrivKey } from './utils.js'; import { Hex, PrivKey } from './utils.js';
import * as htf from './hash-to-curve.js'; import * as htf from './hash-to-curve.js';
import { CurvePointsType, PointType, CurvePointsRes, weierstrassPoints } from './weierstrass.js'; import {
CurvePointsType,
ProjectivePointType as PPointType,
CurvePointsRes,
weierstrassPoints,
} from './weierstrass.js';
type Fp = bigint; // Can be different field? type Fp = bigint; // Can be different field?
export type SignatureCoder<Fp2> = { export type SignatureCoder<Fp2> = {
decode(hex: Hex): PointType<Fp2>; decode(hex: Hex): PPointType<Fp2>;
encode(point: PointType<Fp2>): Uint8Array; encode(point: PPointType<Fp2>): Uint8Array;
}; };
export type CurveType<Fp, Fp2, Fp6, Fp12> = { export type CurveType<Fp, Fp2, Fp6, Fp12> = {
@ -73,29 +78,29 @@ export type CurveFn<Fp, Fp2, Fp6, Fp12> = {
G1: ReturnType<(typeof htf.hashToCurve<Fp>)>, G1: ReturnType<(typeof htf.hashToCurve<Fp>)>,
G2: ReturnType<(typeof htf.hashToCurve<Fp2>)>, G2: ReturnType<(typeof htf.hashToCurve<Fp2>)>,
}, },
pairing: (P: PointType<Fp>, Q: PointType<Fp2>, withFinalExponent?: boolean) => Fp12; pairing: (P: PPointType<Fp>, Q: PPointType<Fp2>, withFinalExponent?: boolean) => Fp12;
getPublicKey: (privateKey: PrivKey) => Uint8Array; getPublicKey: (privateKey: PrivKey) => Uint8Array;
sign: { sign: {
(message: Hex, privateKey: PrivKey): Uint8Array; (message: Hex, privateKey: PrivKey): Uint8Array;
(message: PointType<Fp2>, privateKey: PrivKey): PointType<Fp2>; (message: PPointType<Fp2>, privateKey: PrivKey): PPointType<Fp2>;
}; };
verify: ( verify: (
signature: Hex | PointType<Fp2>, signature: Hex | PPointType<Fp2>,
message: Hex | PointType<Fp2>, message: Hex | PPointType<Fp2>,
publicKey: Hex | PointType<Fp> publicKey: Hex | PPointType<Fp>
) => boolean; ) => boolean;
aggregatePublicKeys: { aggregatePublicKeys: {
(publicKeys: Hex[]): Uint8Array; (publicKeys: Hex[]): Uint8Array;
(publicKeys: PointType<Fp>[]): PointType<Fp>; (publicKeys: PPointType<Fp>[]): PPointType<Fp>;
}; };
aggregateSignatures: { aggregateSignatures: {
(signatures: Hex[]): Uint8Array; (signatures: Hex[]): Uint8Array;
(signatures: PointType<Fp2>[]): PointType<Fp2>; (signatures: PPointType<Fp2>[]): PPointType<Fp2>;
}; };
verifyBatch: ( verifyBatch: (
signature: Hex | PointType<Fp2>, signature: Hex | PPointType<Fp2>,
messages: (Hex | PointType<Fp2>)[], messages: (Hex | PPointType<Fp2>)[],
publicKeys: (Hex | PointType<Fp>)[] publicKeys: (Hex | PPointType<Fp>)[]
) => boolean; ) => boolean;
utils: { utils: {
stringToBytes: typeof htf.stringToBytes; stringToBytes: typeof htf.stringToBytes;
@ -196,7 +201,7 @@ export function bls<Fp2, Fp6, Fp12>(
n: Fr.ORDER, n: Fr.ORDER,
...CURVE.G1, ...CURVE.G1,
}); });
const G1HashToCurve = htf.hashToCurve(G1.Point, CURVE.G1.mapToCurve, { const G1HashToCurve = htf.hashToCurve(G1.ProjectivePoint, CURVE.G1.mapToCurve, {
...CURVE.htfDefaults, ...CURVE.htfDefaults,
...CURVE.G1.htfDefaults, ...CURVE.G1.htfDefaults,
}); });
@ -226,7 +231,8 @@ export function bls<Fp2, Fp6, Fp12>(
n: Fr.ORDER, n: Fr.ORDER,
...CURVE.G2, ...CURVE.G2,
}); });
const G2HashToCurve = htf.hashToCurve(G2.Point, CURVE.G2.mapToCurve, { const C = G2.ProjectivePoint as htf.H2CPointConstructor<Fp2>; // TODO: fix
const G2HashToCurve = htf.hashToCurve(C, CURVE.G2.mapToCurve, {
...CURVE.htfDefaults, ...CURVE.htfDefaults,
...CURVE.G2.htfDefaults, ...CURVE.G2.htfDefaults,
}); });
@ -235,7 +241,7 @@ export function bls<Fp2, Fp6, Fp12>(
// Calculates bilinear pairing // Calculates bilinear pairing
function pairing(P: G1, Q: G2, withFinalExponent: boolean = true): Fp12 { function pairing(P: G1, Q: G2, withFinalExponent: boolean = true): Fp12 {
if (P.equals(G1.Point.ZERO) || Q.equals(G2.Point.ZERO)) if (P.equals(G1.ProjectivePoint.ZERO) || Q.equals(G2.ProjectivePoint.ZERO))
throw new Error('No pairings at point of Infinity'); throw new Error('No pairings at point of Infinity');
P.assertValidity(); P.assertValidity();
Q.assertValidity(); Q.assertValidity();
@ -243,25 +249,27 @@ export function bls<Fp2, Fp6, Fp12>(
const looped = millerLoopG1(P, Q); const looped = millerLoopG1(P, Q);
return withFinalExponent ? Fp12.finalExponentiate(looped) : looped; return withFinalExponent ? Fp12.finalExponentiate(looped) : looped;
} }
type G1 = typeof G1.Point.BASE; type G1 = typeof G1.ProjectivePoint.BASE;
type G2 = typeof G2.Point.BASE; type G2 = typeof G2.ProjectivePoint.BASE;
type G1Hex = Hex | G1; type G1Hex = Hex | G1;
type G2Hex = Hex | G2; type G2Hex = Hex | G2;
function normP1(point: G1Hex): G1 { function normP1(point: G1Hex): G1 {
return point instanceof G1.Point ? (point as G1) : G1.Point.fromHex(point); return point instanceof G1.ProjectivePoint ? (point as G1) : G1.ProjectivePoint.fromHex(point);
} }
function normP2(point: G2Hex): G2 { function normP2(point: G2Hex): G2 {
return point instanceof G2.Point ? point : Signature.decode(point); return point instanceof G2.ProjectivePoint ? point : Signature.decode(point);
} }
function normP2Hash(point: G2Hex, htfOpts?: htf.htfBasicOpts): G2 { function normP2Hash(point: G2Hex, htfOpts?: htf.htfBasicOpts): G2 {
return point instanceof G2.Point ? point : (G2HashToCurve.hashToCurve(point, htfOpts) as G2); return point instanceof G2.ProjectivePoint
? point
: (G2HashToCurve.hashToCurve(point, htfOpts) as G2);
} }
// Multiplies generator by private key. // Multiplies generator by private key.
// P = pk x G // P = pk x G
function getPublicKey(privateKey: PrivKey): Uint8Array { function getPublicKey(privateKey: PrivKey): Uint8Array {
return G1.Point.fromPrivateKey(privateKey).toRawBytes(true); return G1.ProjectivePoint.fromPrivateKey(privateKey).toRawBytes(true);
} }
// Executes `hashToCurve` on the message and then multiplies the result by private key. // Executes `hashToCurve` on the message and then multiplies the result by private key.
@ -272,7 +280,7 @@ export function bls<Fp2, Fp6, Fp12>(
const msgPoint = normP2Hash(message, htfOpts); const msgPoint = normP2Hash(message, htfOpts);
msgPoint.assertValidity(); msgPoint.assertValidity();
const sigPoint = msgPoint.multiply(G1.normalizePrivateKey(privateKey)); const sigPoint = msgPoint.multiply(G1.normalizePrivateKey(privateKey));
if (message instanceof G2.Point) return sigPoint; if (message instanceof G2.ProjectivePoint) return sigPoint;
return Signature.encode(sigPoint); return Signature.encode(sigPoint);
} }
@ -286,7 +294,7 @@ export function bls<Fp2, Fp6, Fp12>(
): boolean { ): boolean {
const P = normP1(publicKey); const P = normP1(publicKey);
const Hm = normP2Hash(message, htfOpts); const Hm = normP2Hash(message, htfOpts);
const G = G1.Point.BASE; const G = G1.ProjectivePoint.BASE;
const S = normP2(signature); const S = normP2(signature);
// Instead of doing 2 exponentiations, we use property of billinear maps // Instead of doing 2 exponentiations, we use property of billinear maps
// and do one exp after multiplying 2 points. // and do one exp after multiplying 2 points.
@ -305,8 +313,8 @@ export function bls<Fp2, Fp6, Fp12>(
const agg = publicKeys const agg = publicKeys
.map(normP1) .map(normP1)
.reduce((sum, p) => sum.add(G1.ProjectivePoint.fromAffine(p)), G1.ProjectivePoint.ZERO); .reduce((sum, p) => sum.add(G1.ProjectivePoint.fromAffine(p)), G1.ProjectivePoint.ZERO);
const aggAffine = agg.toAffine(); const aggAffine = agg; //.toAffine();
if (publicKeys[0] instanceof G1.Point) { if (publicKeys[0] instanceof G1.ProjectivePoint) {
aggAffine.assertValidity(); aggAffine.assertValidity();
return aggAffine; return aggAffine;
} }
@ -322,8 +330,8 @@ export function bls<Fp2, Fp6, Fp12>(
const agg = signatures const agg = signatures
.map(normP2) .map(normP2)
.reduce((sum, s) => sum.add(G2.ProjectivePoint.fromAffine(s)), G2.ProjectivePoint.ZERO); .reduce((sum, s) => sum.add(G2.ProjectivePoint.fromAffine(s)), G2.ProjectivePoint.ZERO);
const aggAffine = agg.toAffine(); const aggAffine = agg; //.toAffine();
if (signatures[0] instanceof G2.Point) { if (signatures[0] instanceof G2.ProjectivePoint) {
aggAffine.assertValidity(); aggAffine.assertValidity();
return aggAffine; return aggAffine;
} }
@ -350,13 +358,13 @@ export function bls<Fp2, Fp6, Fp12>(
const groupPublicKey = nMessages.reduce( const groupPublicKey = nMessages.reduce(
(groupPublicKey, subMessage, i) => (groupPublicKey, subMessage, i) =>
subMessage === message ? groupPublicKey.add(nPublicKeys[i]) : groupPublicKey, subMessage === message ? groupPublicKey.add(nPublicKeys[i]) : groupPublicKey,
G1.Point.ZERO G1.ProjectivePoint.ZERO
); );
// const msg = message instanceof PointG2 ? message : await PointG2.hashToCurve(message); // const msg = message instanceof PointG2 ? message : await PointG2.hashToCurve(message);
// Possible to batch pairing for same msg with different groupPublicKey here // Possible to batch pairing for same msg with different groupPublicKey here
paired.push(pairing(groupPublicKey, message, false)); paired.push(pairing(groupPublicKey, message, false));
} }
paired.push(pairing(G1.Point.BASE.negate(), sig, false)); paired.push(pairing(G1.ProjectivePoint.BASE.negate(), sig, false));
const product = paired.reduce((a, b) => Fp12.mul(a, b), Fp12.ONE); const product = paired.reduce((a, b) => Fp12.mul(a, b), Fp12.ONE);
const exp = Fp12.finalExponentiate(product); const exp = Fp12.finalExponentiate(product);
return Fp12.equals(exp, Fp12.ONE); return Fp12.equals(exp, Fp12.ONE);
@ -366,7 +374,8 @@ export function bls<Fp2, Fp6, Fp12>(
} }
// Pre-compute points. Refer to README. // Pre-compute points. Refer to README.
G1.Point.BASE._setWindowSize(4); // TODO
// G1.ProjectivePoint.BASE._setWindowSize(4);
return { return {
CURVE, CURVE,
Fr, Fr,

1
src/abstract/edwards.ts
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@ -93,7 +93,6 @@ export type CurveFn = {
getPublicKey: (privateKey: PrivKey, isCompressed?: boolean) => Uint8Array; getPublicKey: (privateKey: PrivKey, isCompressed?: boolean) => Uint8Array;
sign: (message: Hex, privateKey: Hex) => Uint8Array; sign: (message: Hex, privateKey: Hex) => Uint8Array;
verify: (sig: Hex, message: Hex, publicKey: Hex) => boolean; verify: (sig: Hex, message: Hex, publicKey: Hex) => boolean;
// Point: PointConstructor;
ExtendedPoint: ExtendedPointConstructor; ExtendedPoint: ExtendedPointConstructor;
utils: { utils: {
randomPrivateKey: () => Uint8Array; randomPrivateKey: () => Uint8Array;

21
src/abstract/hash-to-curve.ts
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@ -178,17 +178,16 @@ export function isogenyMap<T, F extends mod.Field<T>>(field: F, map: [T[], T[],
}; };
} }
export interface Point<T> extends Group<Point<T>> { export interface H2CPoint<T> extends Group<H2CPoint<T>> {
// readonly x: T; readonly x: T;
// readonly y: T; readonly y: T;
add(rhs: Point<T>): Point<T>; add(rhs: H2CPoint<T>): H2CPoint<T>;
toAffine(iz?: bigint): { x: T; y: T }; toAffine(iz?: bigint): { x: T; y: T };
clearCofactor(): Point<T>; clearCofactor(): H2CPoint<T>;
} }
export interface PointConstructor<T> extends GroupConstructor<Point<T>> { export interface H2CPointConstructor<T> extends GroupConstructor<H2CPoint<T>> {
// new (x: T, y: T): Point<T>; fromAffine(ap: { x: T; y: T }): H2CPoint<T>;
fromAffine(ap: { x: T; y: T }): Point<T>;
} }
export type MapToCurve<T> = (scalar: bigint[]) => { x: T; y: T }; export type MapToCurve<T> = (scalar: bigint[]) => { x: T; y: T };
@ -198,7 +197,11 @@ export type htfBasicOpts = {
DST: string; DST: string;
}; };
export function hashToCurve<T>(Point: PointConstructor<T>, mapToCurve: MapToCurve<T>, def: Opts) { export function hashToCurve<T>(
Point: H2CPointConstructor<T>,
mapToCurve: MapToCurve<T>,
def: Opts
) {
validateOpts(def); validateOpts(def);
if (typeof mapToCurve !== 'function') if (typeof mapToCurve !== 'function')
throw new Error('hashToCurve: mapToCurve() has not been defined'); throw new Error('hashToCurve: mapToCurve() has not been defined');

355
src/abstract/weierstrass.ts
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@ -109,48 +109,50 @@ export type SignOpts = { lowS?: boolean; extraEntropy?: Entropy };
* TODO: https://www.typescriptlang.org/docs/handbook/release-notes/typescript-2-7.html#unique-symbol * TODO: https://www.typescriptlang.org/docs/handbook/release-notes/typescript-2-7.html#unique-symbol
*/ */
export interface AffinePoint<T> {
x: T;
y: T;
}
// Instance for 3d XYZ points // Instance for 3d XYZ points
export interface ProjectivePointType<T> extends Group<ProjectivePointType<T>> { export interface ProjectivePointType<T> extends Group<ProjectivePointType<T>> {
readonly x: T; readonly x: T;
readonly y: T; readonly y: T;
readonly z: T; readonly z: T;
multiply(scalar: bigint, affinePoint?: PointType<T>): ProjectivePointType<T>; multiply(scalar: bigint): ProjectivePointType<T>;
multiplyUnsafe(scalar: bigint): ProjectivePointType<T>; multiplyUnsafe(scalar: bigint): ProjectivePointType<T>;
toAffine(invZ?: T): PointType<T>; multiplyAndAddUnsafe(
Q: ProjectivePointType<T>,
a: bigint,
b: bigint
): ProjectivePointType<T> | undefined;
toAffine(invZ?: T): AffinePoint<T>;
isTorsionFree(): boolean;
clearCofactor(): ProjectivePointType<T>; clearCofactor(): ProjectivePointType<T>;
} assertValidity(): void;
// Static methods for 3d XYZ points
export interface ProjectiveConstructor<T> extends GroupConstructor<ProjectivePointType<T>> {
new (x: T, y: T, z: T): ProjectivePointType<T>;
fromAffine(p: PointType<T>): ProjectivePointType<T>;
toAffineBatch(points: ProjectivePointType<T>[]): PointType<T>[];
normalizeZ(points: ProjectivePointType<T>[]): ProjectivePointType<T>[];
}
// Instance for 2d XY points
export interface PointType<T> extends Group<PointType<T>> {
readonly x: T;
readonly y: T;
_setWindowSize(windowSize: number): void;
hasEvenY(): boolean; hasEvenY(): boolean;
toRawBytes(isCompressed?: boolean): Uint8Array; toRawBytes(isCompressed?: boolean): Uint8Array;
toHex(isCompressed?: boolean): string; toHex(isCompressed?: boolean): string;
assertValidity(): void;
multiplyAndAddUnsafe(Q: PointType<T>, a: bigint, b: bigint): PointType<T> | undefined;
clearCofactor(): PointType<T>;
toAffine(iz?: bigint): { x: T; y: T };
} }
// Static methods for 2d XY points // Static methods for 3d XYZ points
export interface PointConstructor<T> extends GroupConstructor<PointType<T>> { export interface ProjectiveConstructor<T> extends GroupConstructor<ProjectivePointType<T>> {
new (x: T, y: T): PointType<T>; new (x: T, y: T, z?: T): ProjectivePointType<T>;
fromAffine(ap: { x: T; y: T }): PointType<T>; fromAffine(p: AffinePoint<T>): ProjectivePointType<T>;
fromHex(hex: Hex): PointType<T>; toAffineBatch(points: ProjectivePointType<T>[]): AffinePoint<T>[];
fromPrivateKey(privateKey: PrivKey): PointType<T>; normalizeZ(points: ProjectivePointType<T>[]): ProjectivePointType<T>[];
fromAffine(ap: { x: T; y: T }): ProjectivePointType<T>;
fromHex(hex: Hex): ProjectivePointType<T>;
fromPrivateKey(privateKey: PrivKey): ProjectivePointType<T>;
} }
export type CurvePointsType<T> = BasicCurve<T> & { export type CurvePointsType<T> = BasicCurve<T> & {
// Bytes // Bytes
fromBytes: (bytes: Uint8Array) => { x: T; y: T }; fromBytes: (bytes: Uint8Array) => { x: T; y: T };
toBytes: (c: PointConstructor<T>, point: PointType<T>, compressed: boolean) => Uint8Array; toBytes: (
c: ProjectiveConstructor<T>,
point: ProjectivePointType<T>,
compressed: boolean
) => Uint8Array;
}; };
function validatePointOpts<T>(curve: CurvePointsType<T>) { function validatePointOpts<T>(curve: CurvePointsType<T>) {
@ -184,7 +186,7 @@ function validatePointOpts<T>(curve: CurvePointsType<T>) {
} }
export type CurvePointsRes<T> = { export type CurvePointsRes<T> = {
Point: PointConstructor<T>; // Point: PointConstructor<T>;
ProjectivePoint: ProjectiveConstructor<T>; ProjectivePoint: ProjectiveConstructor<T>;
normalizePrivateKey: (key: PrivKey) => bigint; normalizePrivateKey: (key: PrivKey) => bigint;
weierstrassEquation: (x: T) => T; weierstrassEquation: (x: T) => T;
@ -194,7 +196,6 @@ export type CurvePointsRes<T> = {
// Be friendly to bad ECMAScript parsers by not using bigint literals like 123n // Be friendly to bad ECMAScript parsers by not using bigint literals like 123n
const _0n = BigInt(0); const _0n = BigInt(0);
const _1n = BigInt(1); const _1n = BigInt(1);
const _3n = BigInt(3);
export function weierstrassPoints<T>(opts: CurvePointsType<T>) { export function weierstrassPoints<T>(opts: CurvePointsType<T>) {
const CURVE = validatePointOpts(opts); const CURVE = validatePointOpts(opts);
@ -263,17 +264,19 @@ export function weierstrassPoints<T>(opts: CurvePointsType<T>) {
* We're doing calculations in projective, because its operations don't require costly inversion. * We're doing calculations in projective, because its operations don't require costly inversion.
*/ */
class ProjectivePoint implements ProjectivePointType<T> { class ProjectivePoint implements ProjectivePointType<T> {
constructor(readonly x: T, readonly y: T, readonly z: T) {} constructor(readonly x: T, readonly y: T, readonly z: T = Fp.ONE) {}
static readonly BASE = new ProjectivePoint(CURVE.Gx, CURVE.Gy, Fp.ONE); static readonly BASE = new ProjectivePoint(CURVE.Gx, CURVE.Gy, Fp.ONE);
static readonly ZERO = new ProjectivePoint(Fp.ZERO, Fp.ONE, Fp.ZERO); static readonly ZERO = new ProjectivePoint(Fp.ZERO, Fp.ONE, Fp.ZERO);
static fromAffine(p: Point): ProjectivePoint { static fromAffine(p: AffinePoint<T>): ProjectivePoint {
if (!(p instanceof Point)) { // TODO: validate
throw new TypeError('ProjectivePoint#fromAffine: expected Point'); // if (!(p instanceof Point)) {
} // throw new TypeError('ProjectivePoint#fromAffine: expected Point');
// }
// fromAffine(x:0, y:0) would produce (x:0, y:0, z:1), but we need (x:0, y:1, z:0) // fromAffine(x:0, y:0) would produce (x:0, y:0, z:1), but we need (x:0, y:1, z:0)
if (p.equals(Point.ZERO)) return ProjectivePoint.ZERO; // if (p.equals(Point.ZERO)) return ProjectivePoint.ZERO;
if (Fp.equals(p.x, Fp.ZERO) && Fp.equals(p.y, Fp.ZERO)) return ProjectivePoint.ZERO;
return new ProjectivePoint(p.x, p.y, Fp.ONE); return new ProjectivePoint(p.x, p.y, Fp.ONE);
} }
@ -282,7 +285,7 @@ export function weierstrassPoints<T>(opts: CurvePointsType<T>) {
* inversion on all of them. Inversion is very slow operation, * inversion on all of them. Inversion is very slow operation,
* so this improves performance massively. * so this improves performance massively.
*/ */
static toAffineBatch(points: ProjectivePoint[]): Point[] { static toAffineBatch(points: ProjectivePoint[]): AffinePoint<T>[] {
const toInv = Fp.invertBatch(points.map((p) => p.z)); const toInv = Fp.invertBatch(points.map((p) => p.z));
return points.map((p, i) => p.toAffine(toInv[i])); return points.map((p, i) => p.toAffine(toInv[i]));
} }
@ -445,25 +448,6 @@ export function weierstrassPoints<T>(opts: CurvePointsType<T>) {
k2p = new ProjectivePoint(Fp.mul(k2p.x, CURVE.endo.beta), k2p.y, k2p.z); k2p = new ProjectivePoint(Fp.mul(k2p.x, CURVE.endo.beta), k2p.y, k2p.z);
return k1p.add(k2p); return k1p.add(k2p);
} }
/**
* Implements w-ary non-adjacent form for calculating ec multiplication.
*/
private wNAF(n: bigint, affinePoint?: Point): { p: ProjectivePoint; f: ProjectivePoint } {
if (!affinePoint && this.equals(ProjectivePoint.BASE)) affinePoint = Point.BASE;
const W = (affinePoint && affinePoint._WINDOW_SIZE) || 1;
// Calculate precomputes on a first run, reuse them after
let precomputes = affinePoint && pointPrecomputes.get(affinePoint);
if (!precomputes) {
precomputes = wnaf.precomputeWindow(this, W) as ProjectivePoint[];
if (affinePoint && W !== 1) {
precomputes = ProjectivePoint.normalizeZ(precomputes);
pointPrecomputes.set(affinePoint, precomputes);
}
}
return wnaf.wNAF(W, precomputes, n);
}
/** /**
* Constant time multiplication. * Constant time multiplication.
* Uses wNAF method. Windowed method may be 10% faster, * Uses wNAF method. Windowed method may be 10% faster,
@ -472,7 +456,7 @@ export function weierstrassPoints<T>(opts: CurvePointsType<T>) {
* @param affinePoint optional point ot save cached precompute windows on it * @param affinePoint optional point ot save cached precompute windows on it
* @returns New point * @returns New point
*/ */
multiply(scalar: bigint, affinePoint?: Point): ProjectivePoint { multiply(scalar: bigint): ProjectivePoint {
let n = normalizeScalar(scalar); let n = normalizeScalar(scalar);
// Real point. // Real point.
@ -481,15 +465,15 @@ export function weierstrassPoints<T>(opts: CurvePointsType<T>) {
let fake: ProjectivePoint; let fake: ProjectivePoint;
if (CURVE.endo) { if (CURVE.endo) {
const { k1neg, k1, k2neg, k2 } = CURVE.endo.splitScalar(n); const { k1neg, k1, k2neg, k2 } = CURVE.endo.splitScalar(n);
let { p: k1p, f: f1p } = this.wNAF(k1, affinePoint); let { p: k1p, f: f1p } = wNAF_TMP_FN(this, k1);
let { p: k2p, f: f2p } = this.wNAF(k2, affinePoint); let { p: k2p, f: f2p } = wNAF_TMP_FN(this, k2);
k1p = wnaf.constTimeNegate(k1neg, k1p); k1p = wnaf.constTimeNegate(k1neg, k1p);
k2p = wnaf.constTimeNegate(k2neg, k2p); k2p = wnaf.constTimeNegate(k2neg, k2p);
k2p = new ProjectivePoint(Fp.mul(k2p.x, CURVE.endo.beta), k2p.y, k2p.z); k2p = new ProjectivePoint(Fp.mul(k2p.x, CURVE.endo.beta), k2p.y, k2p.z);
point = k1p.add(k2p); point = k1p.add(k2p);
fake = f1p.add(f2p); fake = f1p.add(f2p);
} else { } else {
const { p, f } = this.wNAF(n, affinePoint); const { p, f } = wNAF_TMP_FN(this, n);
point = p; point = p;
fake = f; fake = f;
} }
@ -500,7 +484,7 @@ export function weierstrassPoints<T>(opts: CurvePointsType<T>) {
// Converts Projective point to affine (x, y) coordinates. // Converts Projective point to affine (x, y) coordinates.
// Can accept precomputed Z^-1 - for example, from invertBatch. // Can accept precomputed Z^-1 - for example, from invertBatch.
// (x, y, z) ∋ (x=x/z, y=y/z) // (x, y, z) ∋ (x=x/z, y=y/z)
toAffine(invZ?: T): Point { toAffine(invZ?: T): AffinePoint<T> {
const { x, y, z } = this; const { x, y, z } = this;
const is0 = this.equals(ProjectivePoint.ZERO); const is0 = this.equals(ProjectivePoint.ZERO);
// If invZ was 0, we return zero point. However we still want to execute // If invZ was 0, we return zero point. However we still want to execute
@ -509,9 +493,9 @@ export function weierstrassPoints<T>(opts: CurvePointsType<T>) {
const ax = Fp.mul(x, invZ); const ax = Fp.mul(x, invZ);
const ay = Fp.mul(y, invZ); const ay = Fp.mul(y, invZ);
const zz = Fp.mul(z, invZ); const zz = Fp.mul(z, invZ);
if (is0) return Point.ZERO; if (is0) return { x: Fp.ZERO, y: Fp.ZERO };
if (!Fp.equals(zz, Fp.ONE)) throw new Error('invZ was invalid'); if (!Fp.equals(zz, Fp.ONE)) throw new Error('invZ was invalid');
return new Point(ax, ay); return { x: ax, y: ay };
} }
isTorsionFree(): boolean { isTorsionFree(): boolean {
const { h: cofactor, isTorsionFree } = CURVE; const { h: cofactor, isTorsionFree } = CURVE;
@ -525,89 +509,33 @@ export function weierstrassPoints<T>(opts: CurvePointsType<T>) {
if (clearCofactor) return clearCofactor(ProjectivePoint, this) as ProjectivePoint; if (clearCofactor) return clearCofactor(ProjectivePoint, this) as ProjectivePoint;
return this.multiplyUnsafe(CURVE.h); return this.multiplyUnsafe(CURVE.h);
} }
}
const _bits = CURVE.nBitLength;
const wnaf = wNAF(ProjectivePoint, CURVE.endo ? Math.ceil(_bits / 2) : _bits);
function assertPrjPoint(other: unknown) {
if (!(other instanceof ProjectivePoint)) throw new TypeError('ProjectivePoint expected');
}
// Stores precomputed values for points.
const pointPrecomputes = new WeakMap<Point, ProjectivePoint[]>();
/**
* Default Point works in default aka affine coordinates: (x, y)
*/
class Point implements PointType<T> {
/** /**
* Base point aka generator. Any public_key = Point.BASE * private_key * Efficiently calculate `aP + bQ`.
* Unsafe, can expose private key, if used incorrectly.
* TODO: Utilize Shamir's trick
* @returns non-zero affine point
*/ */
static BASE: Point = new Point(CURVE.Gx, CURVE.Gy); multiplyAndAddUnsafe(Q: ProjectivePoint, a: bigint, b: bigint): ProjectivePoint | undefined {
/** const P = this;
* Identity point aka point at infinity. p - p = zero_p; p + zero_p = p const aP =
*/ a === _0n || a === _1n || !P.equals(ProjectivePoint.BASE)
static ZERO: Point = new Point(Fp.ZERO, Fp.ZERO); ? P.multiplyUnsafe(a)
static fromAffine(ap: { x: T; y: T }) { : P.multiply(a);
return new Point(ap.x, ap.y); const bQ = ProjectivePoint.fromAffine(Q).multiplyUnsafe(b);
} const sum = aP.add(bQ);
toAffine(iz?: bigint) { return sum.equals(ProjectivePoint.ZERO) ? undefined : sum;
return { x: this.x, y: this.y };
} }
// 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.
_WINDOW_SIZE?: number;
constructor(readonly x: T, readonly y: T) {}
// "Private method", don't use it directly
_setWindowSize(windowSize: number) {
this._WINDOW_SIZE = windowSize;
pointPrecomputes.delete(this);
}
// Checks for y % 2 == 0
hasEvenY(): boolean {
if (Fp.isOdd) return !Fp.isOdd(this.y);
throw new Error("Field doesn't support isOdd");
}
/**
* Converts hash string or Uint8Array to Point.
* @param hex short/long ECDSA hex
*/
static fromHex(hex: Hex): Point {
const { x, y } = CURVE.fromBytes(ut.ensureBytes(hex));
const point = new Point(x, y);
point.assertValidity();
return point;
}
// Multiplies generator point by privateKey.
static fromPrivateKey(privateKey: PrivKey) {
return Point.BASE.multiply(normalizePrivateKey(privateKey));
}
toRawBytes(isCompressed = true): Uint8Array {
this.assertValidity();
return CURVE.toBytes(Point, this, isCompressed);
}
toHex(isCompressed = true): string {
return bytesToHex(this.toRawBytes(isCompressed));
}
// A point on curve is valid if it conforms to equation. // A point on curve is valid if it conforms to equation.
assertValidity(): void { assertValidity(): void {
// Zero is valid point too! // Zero is valid point too!
if (this.equals(Point.ZERO)) { if (this.equals(ProjectivePoint.ZERO)) {
if (CURVE.allowInfinityPoint) return; if (CURVE.allowInfinityPoint) return;
throw new Error('Point at infinity'); throw new Error('Point at infinity');
} }
// Some 3rd-party test vectors require different wording between here & `fromCompressedHex` // Some 3rd-party test vectors require different wording between here & `fromCompressedHex`
const msg = 'Point is not on elliptic curve'; const msg = 'Point is not on elliptic curve';
const { x, y } = this; const { x, y } = this.toAffine();
// Check if x, y are valid field elements // Check if x, y are valid field elements
if (!Fp.isValid(x) || !Fp.isValid(y)) throw new Error(msg); if (!Fp.isValid(x) || !Fp.isValid(y)) throw new Error(msg);
const left = Fp.square(y); // y² const left = Fp.square(y); // y²
@ -615,68 +543,64 @@ export function weierstrassPoints<T>(opts: CurvePointsType<T>) {
if (!Fp.equals(left, right)) throw new Error(msg); if (!Fp.equals(left, right)) throw new Error(msg);
if (!this.isTorsionFree()) throw new Error('Point must be of prime-order subgroup'); if (!this.isTorsionFree()) throw new Error('Point must be of prime-order subgroup');
} }
hasEvenY(): boolean {
equals(other: Point): boolean { const { y } = this.toAffine();
if (!(other instanceof Point)) throw new TypeError('Point#equals: expected Point'); if (Fp.isOdd) return !Fp.isOdd(y);
return Fp.equals(this.x, other.x) && Fp.equals(this.y, other.y); throw new Error("Field doesn't support isOdd");
}
toRawBytes(isCompressed = true): Uint8Array {
this.assertValidity();
return CURVE.toBytes(ProjectivePoint, this, isCompressed);
} }
// Returns the same point with inverted `y` toHex(isCompressed = true): string {
negate() { return bytesToHex(this.toRawBytes(isCompressed));
return new Point(this.x, Fp.negate(this.y));
}
protected toProj() {
return ProjectivePoint.fromAffine(this);
}
// Adds point to itself
double() {
return this.toProj().double().toAffine();
}
add(other: Point) {
return this.toProj().add(ProjectivePoint.fromAffine(other)).toAffine();
}
subtract(other: Point) {
return this.add(other.negate());
}
multiply(scalar: bigint) {
return this.toProj().multiply(scalar, this).toAffine();
}
multiplyUnsafe(scalar: bigint) {
return this.toProj().multiplyUnsafe(scalar).toAffine();
}
clearCofactor() {
return this.toProj().clearCofactor().toAffine();
}
isTorsionFree(): boolean {
return this.toProj().isTorsionFree();
} }
/** /**
* Efficiently calculate `aP + bQ`. * Converts hash string or Uint8Array to Point.
* Unsafe, can expose private key, if used incorrectly. * @param hex short/long ECDSA hex
* TODO: Utilize Shamir's trick
* @returns non-zero affine point
*/ */
multiplyAndAddUnsafe(Q: Point, a: bigint, b: bigint): Point | undefined { static fromHex(hex: Hex): ProjectivePoint {
const P = this.toProj(); const { x, y } = CURVE.fromBytes(ut.ensureBytes(hex));
const aP = const point = new ProjectivePoint(x, y);
a === _0n || a === _1n || this !== Point.BASE ? P.multiplyUnsafe(a) : P.multiply(a); point.assertValidity();
const bQ = ProjectivePoint.fromAffine(Q).multiplyUnsafe(b); return point;
const sum = aP.add(bQ); }
return sum.equals(ProjectivePoint.ZERO) ? undefined : sum.toAffine();
// Multiplies generator point by privateKey.
static fromPrivateKey(privateKey: PrivKey) {
return ProjectivePoint.BASE.multiply(normalizePrivateKey(privateKey));
} }
} }
const _bits = CURVE.nBitLength;
const wnaf = wNAF(ProjectivePoint, CURVE.endo ? Math.ceil(_bits / 2) : _bits);
const { BASE: G } = ProjectivePoint;
let Gpows: ProjectivePoint[] | undefined = undefined; // precomputes for base point G
function wNAF_TMP_FN(P: ProjectivePoint, n: bigint): { p: ProjectivePoint; f: ProjectivePoint } {
const C = ProjectivePoint;
if (P.equals(G)) {
const W = 8;
if (!Gpows) {
const denorm = wnaf.precomputeWindow(P, W) as ProjectivePoint[];
const norm = C.toAffineBatch(denorm).map(C.fromAffine);
Gpows = norm;
}
const comp = Gpows;
return wnaf.wNAF(W, comp, n);
}
const W = 1;
const denorm = wnaf.precomputeWindow(P, W) as ProjectivePoint[];
// const norm = C.toAffineBatch(denorm).map(C.fromAffine);
const norm = denorm;
return wnaf.wNAF(W, norm, n);
}
function assertPrjPoint(other: unknown) {
if (!(other instanceof ProjectivePoint)) throw new TypeError('ProjectivePoint expected');
}
return { return {
Point: Point as PointConstructor<T>,
ProjectivePoint: ProjectivePoint as ProjectiveConstructor<T>, ProjectivePoint: ProjectivePoint as ProjectiveConstructor<T>,
normalizePrivateKey, normalizePrivateKey,
weierstrassEquation, weierstrassEquation,
@ -693,7 +617,7 @@ export interface SignatureType {
copyWithRecoveryBit(recovery: number): SignatureType; copyWithRecoveryBit(recovery: number): SignatureType;
hasHighS(): boolean; hasHighS(): boolean;
normalizeS(): SignatureType; normalizeS(): SignatureType;
recoverPublicKey(msgHash: Hex): PointType<bigint>; recoverPublicKey(msgHash: Hex): ProjectivePointType<bigint>;
// DER-encoded // DER-encoded
toDERRawBytes(isCompressed?: boolean): Uint8Array; toDERRawBytes(isCompressed?: boolean): Uint8Array;
toDERHex(isCompressed?: boolean): string; toDERHex(isCompressed?: boolean): string;
@ -707,7 +631,7 @@ export type SignatureConstructor = {
fromDER(hex: Hex): SignatureType; fromDER(hex: Hex): SignatureType;
}; };
export type PubKey = Hex | PointType<bigint>; export type PubKey = Hex | ProjectivePointType<bigint>;
export type CurveType = BasicCurve<bigint> & { export type CurveType = BasicCurve<bigint> & {
// Default options // Default options
@ -745,14 +669,13 @@ export type CurveFn = {
lowS?: boolean; lowS?: boolean;
} }
) => boolean; ) => boolean;
Point: PointConstructor<bigint>;
ProjectivePoint: ProjectiveConstructor<bigint>; ProjectivePoint: ProjectiveConstructor<bigint>;
Signature: SignatureConstructor; Signature: SignatureConstructor;
utils: { utils: {
_bigintToBytes: (num: bigint) => Uint8Array; _bigintToBytes: (num: bigint) => Uint8Array;
_bigintToString: (num: bigint) => string; _bigintToString: (num: bigint) => string;
_normalizePrivateKey: (key: PrivKey) => bigint; _normalizePrivateKey: (key: PrivKey) => bigint;
_normalizePublicKey: (publicKey: PubKey) => PointType<bigint>; _normalizePublicKey: (publicKey: PubKey) => ProjectivePointType<bigint>;
_isWithinCurveOrder: (num: bigint) => boolean; _isWithinCurveOrder: (num: bigint) => boolean;
_isValidFieldElement: (num: bigint) => boolean; _isValidFieldElement: (num: bigint) => boolean;
_weierstrassEquation: (x: bigint) => bigint; _weierstrassEquation: (x: bigint) => bigint;
@ -827,16 +750,18 @@ export function weierstrass(curveDef: CurveType): CurveFn {
return _0n < num && num < Fp.ORDER; return _0n < num && num < Fp.ORDER;
} }
const { Point, ProjectivePoint, normalizePrivateKey, weierstrassEquation, isWithinCurveOrder } = const { ProjectivePoint, normalizePrivateKey, weierstrassEquation, isWithinCurveOrder } =
weierstrassPoints({ weierstrassPoints({
...CURVE, ...CURVE,
toBytes(c, point, isCompressed: boolean): Uint8Array { toBytes(c, point, isCompressed: boolean): Uint8Array {
const x = Fp.toBytes(point.x); const a = point.toAffine();
const x = Fp.toBytes(a.x);
const cat = ut.concatBytes; const cat = ut.concatBytes;
if (isCompressed) { if (isCompressed) {
// TODO: hasEvenY
return cat(Uint8Array.from([point.hasEvenY() ? 0x02 : 0x03]), x); return cat(Uint8Array.from([point.hasEvenY() ? 0x02 : 0x03]), x);
} else { } else {
return cat(Uint8Array.from([0x04]), x, Fp.toBytes(point.y)); return cat(Uint8Array.from([0x04]), x, Fp.toBytes(a.y));
} }
}, },
fromBytes(bytes: Uint8Array) { fromBytes(bytes: Uint8Array) {
@ -864,7 +789,7 @@ export function weierstrass(curveDef: CurveType): CurveFn {
} }
}, },
}); });
type Point = typeof Point.BASE; // type Point = typeof ProjectivePoint.BASE;
// Do we need these functions at all? // Do we need these functions at all?
function numToField(num: bigint): Uint8Array { function numToField(num: bigint): Uint8Array {
@ -877,12 +802,12 @@ export function weierstrass(curveDef: CurveType): CurveFn {
/** /**
* Normalizes hex, bytes, Point to Point. Checks for curve equation. * Normalizes hex, bytes, Point to Point. Checks for curve equation.
*/ */
function normalizePublicKey(publicKey: PubKey): PointType<bigint> { function normalizePublicKey(publicKey: PubKey): ProjectivePointType<bigint> {
if (publicKey instanceof Point) { if (publicKey instanceof ProjectivePoint) {
publicKey.assertValidity(); publicKey.assertValidity();
return publicKey; return publicKey;
} else if (publicKey instanceof Uint8Array || typeof publicKey === 'string') { } else if (publicKey instanceof Uint8Array || typeof publicKey === 'string') {
return Point.fromHex(publicKey); return ProjectivePoint.fromHex(publicKey);
// This can happen because PointType can be instance of different class // This can happen because PointType can be instance of different class
} else throw new Error(`Unknown type of public key: ${publicKey}`); } else throw new Error(`Unknown type of public key: ${publicKey}`);
} }
@ -952,7 +877,7 @@ export function weierstrass(curveDef: CurveType): CurveFn {
* @param msgHash message hash * @param msgHash message hash
* @returns Point corresponding to public key * @returns Point corresponding to public key
*/ */
recoverPublicKey(msgHash: Hex): Point { recoverPublicKey(msgHash: Hex): typeof ProjectivePoint.BASE {
const { r, s, recovery } = this; const { r, s, recovery } = this;
if (recovery == null) throw new Error('Cannot recover: recovery bit is not present'); if (recovery == null) throw new Error('Cannot recover: recovery bit is not present');
if (![0, 1, 2, 3].includes(recovery)) throw new Error('Cannot recover: invalid recovery bit'); if (![0, 1, 2, 3].includes(recovery)) throw new Error('Cannot recover: invalid recovery bit');
@ -966,8 +891,8 @@ export function weierstrass(curveDef: CurveType): CurveFn {
const u1 = mod.mod(-h * rinv, n); const u1 = mod.mod(-h * rinv, n);
const u2 = mod.mod(s * rinv, n); const u2 = mod.mod(s * rinv, n);
const prefix = recovery & 1 ? '03' : '02'; const prefix = recovery & 1 ? '03' : '02';
const R = Point.fromHex(prefix + numToFieldStr(radj)); const R = ProjectivePoint.fromHex(prefix + numToFieldStr(radj));
const Q = Point.BASE.multiplyAndAddUnsafe(R, u1, u2); // unsafe is fine: no priv data leaked const Q = ProjectivePoint.BASE.multiplyAndAddUnsafe(R, u1, u2); // unsafe is fine: no priv data leaked
if (!Q) throw new Error('Cannot recover: point at infinify'); if (!Q) throw new Error('Cannot recover: point at infinify');
Q.assertValidity(); Q.assertValidity();
return Q; return Q;
@ -1050,11 +975,13 @@ export function weierstrass(curveDef: CurveType): CurveFn {
* @param windowSize 2, 4, 8, 16 * @param windowSize 2, 4, 8, 16
* @returns cached point * @returns cached point
*/ */
precompute(windowSize = 8, point = Point.BASE): Point { precompute(windowSize = 8, point = ProjectivePoint.BASE): typeof ProjectivePoint.BASE {
const cached = point === Point.BASE ? point : new Point(point.x, point.y); return ProjectivePoint.BASE;
cached._setWindowSize(windowSize); // return cache
cached.multiply(_3n); // const cached = point === Point.BASE ? point : new Point(point.x, point.y);
return cached; // cached._setWindowSize(windowSize);
// cached.multiply(_3n);
// return cached;
}, },
}; };
@ -1065,7 +992,7 @@ export function weierstrass(curveDef: CurveType): CurveFn {
* @returns Public key, full when isCompressed=false; short when isCompressed=true * @returns Public key, full when isCompressed=false; short when isCompressed=true
*/ */
function getPublicKey(privateKey: PrivKey, isCompressed = true): Uint8Array { function getPublicKey(privateKey: PrivKey, isCompressed = true): Uint8Array {
return Point.fromPrivateKey(privateKey).toRawBytes(isCompressed); return ProjectivePoint.fromPrivateKey(privateKey).toRawBytes(isCompressed);
} }
/** /**
@ -1077,7 +1004,7 @@ export function weierstrass(curveDef: CurveType): CurveFn {
const len = (arr || str) && (item as Hex).length; const len = (arr || str) && (item as Hex).length;
if (arr) return len === compressedLen || len === uncompressedLen; if (arr) return len === compressedLen || len === uncompressedLen;
if (str) return len === 2 * compressedLen || len === 2 * uncompressedLen; if (str) return len === 2 * compressedLen || len === 2 * uncompressedLen;
if (item instanceof Point) return true; if (item instanceof ProjectivePoint) return true;
return false; return false;
} }
@ -1170,7 +1097,7 @@ export function weierstrass(curveDef: CurveType): CurveFn {
if (!isWithinCurveOrder(k)) return; if (!isWithinCurveOrder(k)) return;
// Important: all mod() calls in the function must be done over `n` // Important: all mod() calls in the function must be done over `n`
const ik = mod.invert(k, n); const ik = mod.invert(k, n);
const q = Point.BASE.multiply(k); const q = ProjectivePoint.BASE.multiply(k).toAffine();
// r = x mod n // r = x mod n
const r = mod.mod(q.x, n); const r = mod.mod(q.x, n);
if (r === _0n) return; if (r === _0n) return;
@ -1215,7 +1142,7 @@ export function weierstrass(curveDef: CurveType): CurveFn {
} }
// Enable precomputes. Slows down first publicKey computation by 20ms. // Enable precomputes. Slows down first publicKey computation by 20ms.
Point.BASE._setWindowSize(8); // Point.BASE._setWindowSize(8);
/** /**
* Verifies a signature against message hash and public key. * Verifies a signature against message hash and public key.
@ -1236,24 +1163,26 @@ export function weierstrass(curveDef: CurveType): CurveFn {
publicKey: PubKey, publicKey: PubKey,
opts: { lowS?: boolean } = { lowS: CURVE.lowS } opts: { lowS?: boolean } = { lowS: CURVE.lowS }
): boolean { ): boolean {
let _sig: Signature | undefined = undefined;
try { try {
if (signature instanceof Signature) { if (signature instanceof Signature) {
signature.assertValidity(); signature.assertValidity();
_sig = signature;
} else { } else {
// Signature can be represented in 2 ways: compact (64-byte) & DER (variable-length). // Signature can be represented in 2 ways: compact (64-byte) & DER (variable-length).
// Since DER can also be 64 bytes, we check for it first. // Since DER can also be 64 bytes, we check for it first.
try { try {
signature = Signature.fromDER(signature as Hex); _sig = Signature.fromDER(signature as Hex);
} catch (derError) { } catch (derError) {
if (!(derError instanceof DERError)) throw derError; if (!(derError instanceof DERError)) throw derError;
signature = Signature.fromCompact(signature as Hex); _sig = Signature.fromCompact(signature as Hex);
} }
} }
msgHash = ut.ensureBytes(msgHash); msgHash = ut.ensureBytes(msgHash);
} catch (error) { } catch (error) {
return false; return false;
} }
if (opts.lowS && signature.hasHighS()) return false; if (opts.lowS && _sig.hasHighS()) return false;
let P; let P;
try { try {
P = normalizePublicKey(publicKey); P = normalizePublicKey(publicKey);
@ -1261,7 +1190,7 @@ export function weierstrass(curveDef: CurveType): CurveFn {
return false; return false;
} }
const { n } = CURVE; const { n } = CURVE;
const { r, s } = signature; const { r, s } = _sig;
const h = bits2int_modN(msgHash); // Cannot use fields methods, since it is group element const h = bits2int_modN(msgHash); // Cannot use fields methods, since it is group element
const sinv = mod.invert(s, n); // s^-1 const sinv = mod.invert(s, n); // s^-1
@ -1271,7 +1200,7 @@ export function weierstrass(curveDef: CurveType): CurveFn {
// Some implementations compare R.x in projective, without inversion. // Some implementations compare R.x in projective, without inversion.
// The speed-up is <5%, so we don't complicate the code. // The speed-up is <5%, so we don't complicate the code.
const R = Point.BASE.multiplyAndAddUnsafe(P, u1, u2); const R = ProjectivePoint.BASE.multiplyAndAddUnsafe(P, u1, u2)?.toAffine();
if (!R) return false; if (!R) return false;
const v = mod.mod(R.x, n); const v = mod.mod(R.x, n);
return v === r; return v === r;
@ -1283,7 +1212,7 @@ export function weierstrass(curveDef: CurveType): CurveFn {
sign, sign,
signUnhashed, signUnhashed,
verify, verify,
Point, // Point,
ProjectivePoint, ProjectivePoint,
Signature, Signature,
utils, utils,

13
src/bls12-381.ts
View File

@ -28,7 +28,6 @@ import {
} from './abstract/utils.js'; } from './abstract/utils.js';
// Types // Types
import { import {
PointType,
ProjectivePointType, ProjectivePointType,
ProjectiveConstructor, ProjectiveConstructor,
mapToCurveSimpleSWU, mapToCurveSimpleSWU,
@ -1035,7 +1034,7 @@ export const bls12_381: CurveFn<Fp, Fp2, Fp6, Fp12> = bls({
return { x: Fp.create(x), y: Fp.create(y) }; return { x: Fp.create(x), y: Fp.create(y) };
} else if (bytes.length === 96) { } else if (bytes.length === 96) {
// Check if the infinity flag is set // Check if the infinity flag is set
if ((bytes[0] & (1 << 6)) !== 0) return bls12_381.G1.Point.ZERO; if ((bytes[0] & (1 << 6)) !== 0) return bls12_381.G1.ProjectivePoint.ZERO;
const x = bytesToNumberBE(bytes.slice(0, Fp.BYTES)); const x = bytesToNumberBE(bytes.slice(0, Fp.BYTES));
const y = bytesToNumberBE(bytes.slice(Fp.BYTES)); const y = bytesToNumberBE(bytes.slice(Fp.BYTES));
return { x: Fp.create(x), y: Fp.create(y) }; return { x: Fp.create(x), y: Fp.create(y) };
@ -1188,7 +1187,7 @@ export const bls12_381: CurveFn<Fp, Fp2, Fp6, Fp12> = bls({
}, },
Signature: { Signature: {
// TODO: Optimize, it's very slow because of sqrt. // TODO: Optimize, it's very slow because of sqrt.
decode(hex: Hex): PointType<Fp2> { decode(hex: Hex): ProjectivePointType<Fp2> {
hex = ensureBytes(hex); hex = ensureBytes(hex);
const P = Fp.ORDER; const P = Fp.ORDER;
const half = hex.length / 2; const half = hex.length / 2;
@ -1198,7 +1197,7 @@ export const bls12_381: CurveFn<Fp, Fp2, Fp6, Fp12> = bls({
const z2 = bytesToNumberBE(hex.slice(half)); const z2 = bytesToNumberBE(hex.slice(half));
// Indicates the infinity point // Indicates the infinity point
const bflag1 = bitGet(z1, I_BIT_POS); const bflag1 = bitGet(z1, I_BIT_POS);
if (bflag1 === 1n) return bls12_381.G2.Point.ZERO; if (bflag1 === 1n) return bls12_381.G2.ProjectivePoint.ZERO;
const x1 = Fp.create(z1 & Fp.MASK); const x1 = Fp.create(z1 & Fp.MASK);
const x2 = Fp.create(z2); const x2 = Fp.create(z2);
@ -1215,14 +1214,14 @@ export const bls12_381: CurveFn<Fp, Fp2, Fp6, Fp12> = bls({
const isGreater = y1 > 0n && (y1 * 2n) / P !== aflag1; const isGreater = y1 > 0n && (y1 * 2n) / P !== aflag1;
const isZero = y1 === 0n && (y0 * 2n) / P !== aflag1; const isZero = y1 === 0n && (y0 * 2n) / P !== aflag1;
if (isGreater || isZero) y = Fp2.negate(y); if (isGreater || isZero) y = Fp2.negate(y);
const point = new bls12_381.G2.Point(x, y); const point = bls12_381.G2.ProjectivePoint.fromAffine({ x, y });
point.assertValidity(); point.assertValidity();
return point; return point;
}, },
encode(point: PointType<Fp2>) { encode(point: ProjectivePointType<Fp2>) {
// NOTE: by some reasons it was missed in bls12-381, looks like bug // NOTE: by some reasons it was missed in bls12-381, looks like bug
point.assertValidity(); point.assertValidity();
if (point.equals(bls12_381.G2.Point.ZERO)) if (point.equals(bls12_381.G2.ProjectivePoint.ZERO))
return concatBytes(COMPRESSED_ZERO, numberToBytesBE(0n, Fp.BYTES)); return concatBytes(COMPRESSED_ZERO, numberToBytesBE(0n, Fp.BYTES));
const { re: x0, im: x1 } = Fp2.reim(point.x); const { re: x0, im: x1 } = Fp2.reim(point.x);
const { re: y0, im: y1 } = Fp2.reim(point.y); const { re: y0, im: y1 } = Fp2.reim(point.y);

2
src/p256.ts
View File

@ -38,7 +38,7 @@ export const P256 = createCurve(
export const secp256r1 = P256; export const secp256r1 = P256;
const { hashToCurve, encodeToCurve } = htf.hashToCurve( const { hashToCurve, encodeToCurve } = htf.hashToCurve(
secp256r1.Point, secp256r1.ProjectivePoint,
(scalars: bigint[]) => mapSWU(scalars[0]), (scalars: bigint[]) => mapSWU(scalars[0]),
{ {
DST: 'P256_XMD:SHA-256_SSWU_RO_', DST: 'P256_XMD:SHA-256_SSWU_RO_',

2
src/p384.ts
View File

@ -42,7 +42,7 @@ export const P384 = createCurve({
export const secp384r1 = P384; export const secp384r1 = P384;
const { hashToCurve, encodeToCurve } = htf.hashToCurve( const { hashToCurve, encodeToCurve } = htf.hashToCurve(
secp384r1.Point, secp384r1.ProjectivePoint,
(scalars: bigint[]) => mapSWU(scalars[0]), (scalars: bigint[]) => mapSWU(scalars[0]),
{ {
DST: 'P384_XMD:SHA-384_SSWU_RO_', DST: 'P384_XMD:SHA-384_SSWU_RO_',

2
src/p521.ts
View File

@ -53,7 +53,7 @@ export const P521 = createCurve({
export const secp521r1 = P521; export const secp521r1 = P521;
const { hashToCurve, encodeToCurve } = htf.hashToCurve( const { hashToCurve, encodeToCurve } = htf.hashToCurve(
secp521r1.Point, secp521r1.ProjectivePoint,
(scalars: bigint[]) => mapSWU(scalars[0]), (scalars: bigint[]) => mapSWU(scalars[0]),
{ {
DST: 'P521_XMD:SHA-512_SSWU_RO_', DST: 'P521_XMD:SHA-512_SSWU_RO_',

16
src/secp256k1.ts
View File

@ -2,7 +2,7 @@
import { sha256 } from '@noble/hashes/sha256'; import { sha256 } from '@noble/hashes/sha256';
import { Fp as Field, mod, pow2 } from './abstract/modular.js'; import { Fp as Field, mod, pow2 } from './abstract/modular.js';
import { createCurve } from './_shortw_utils.js'; import { createCurve } from './_shortw_utils.js';
import { PointType, mapToCurveSimpleSWU } from './abstract/weierstrass.js'; import { ProjectivePointType as PointType, mapToCurveSimpleSWU } from './abstract/weierstrass.js';
import { import {
ensureBytes, ensureBytes,
concatBytes, concatBytes,
@ -148,7 +148,7 @@ export const secp256k1 = createCurve(
); );
const { hashToCurve, encodeToCurve } = htf.hashToCurve( const { hashToCurve, encodeToCurve } = htf.hashToCurve(
secp256k1.Point, secp256k1.ProjectivePoint,
(scalars: bigint[]) => { (scalars: bigint[]) => {
const { x, y } = mapSWU(Fp.create(scalars[0])); const { x, y } = mapSWU(Fp.create(scalars[0]));
return isoMap(x, y); return isoMap(x, y);
@ -173,7 +173,7 @@ const normalizePrivateKey = secp256k1.utils._normalizePrivateKey;
// TODO: export? // TODO: export?
function normalizePublicKey(publicKey: Hex | PointType<bigint>): PointType<bigint> { function normalizePublicKey(publicKey: Hex | PointType<bigint>): PointType<bigint> {
if (publicKey instanceof secp256k1.Point) { if (publicKey instanceof secp256k1.ProjectivePoint) {
publicKey.assertValidity(); publicKey.assertValidity();
return publicKey; return publicKey;
} else { } else {
@ -187,7 +187,7 @@ function normalizePublicKey(publicKey: Hex | PointType<bigint>): PointType<bigin
const isYOdd = (y & _1n) === _1n; const isYOdd = (y & _1n) === _1n;
// Schnorr // Schnorr
if (isYOdd) y = secp256k1.CURVE.Fp.negate(y); if (isYOdd) y = secp256k1.CURVE.Fp.negate(y);
const point = new secp256k1.Point(x, y); const point = secp256k1.ProjectivePoint.fromAffine({ x, y });
point.assertValidity(); point.assertValidity();
return point; return point;
} }
@ -250,7 +250,7 @@ class SchnorrSignature {
} }
function schnorrGetScalar(priv: bigint) { function schnorrGetScalar(priv: bigint) {
const point = secp256k1.Point.fromPrivateKey(priv); const point = secp256k1.ProjectivePoint.fromPrivateKey(priv);
const scalar = point.hasEvenY() ? priv : secp256k1.CURVE.n - priv; const scalar = point.hasEvenY() ? priv : secp256k1.CURVE.n - priv;
return { point, scalar, x: toRawX(point) }; return { point, scalar, x: toRawX(point) };
} }
@ -301,12 +301,12 @@ function schnorrVerify(signature: Hex, message: Hex, publicKey: Hex): boolean {
// Finalize // Finalize
// R = s⋅G - e⋅P // R = s⋅G - e⋅P
// -eP == (n-e)P // -eP == (n-e)P
const R = secp256k1.Point.BASE.multiplyAndAddUnsafe( const R = secp256k1.ProjectivePoint.BASE.multiplyAndAddUnsafe(
P, P,
normalizePrivateKey(s), normalizePrivateKey(s),
mod(-e, secp256k1.CURVE.n) mod(-e, secp256k1.CURVE.n)
); );
if (!R || !R.hasEvenY() || R.x !== r) return false; if (!R || !R.hasEvenY() || R.toAffine().x !== r) return false;
return true; return true;
} catch (error) { } catch (error) {
return false; return false;
@ -317,7 +317,7 @@ export const schnorr = {
Signature: SchnorrSignature, Signature: SchnorrSignature,
// Schnorr's pubkey is just `x` of Point (BIP340) // Schnorr's pubkey is just `x` of Point (BIP340)
getPublicKey: (privateKey: PrivKey): Uint8Array => getPublicKey: (privateKey: PrivKey): Uint8Array =>
toRawX(secp256k1.Point.fromPrivateKey(privateKey)), toRawX(secp256k1.ProjectivePoint.fromPrivateKey(privateKey)),
sign: schnorrSign, sign: schnorrSign,
verify: schnorrVerify, verify: schnorrVerify,
}; };

15
src/stark.ts
View File

@ -113,11 +113,10 @@ function verify0x(signature: Hex, msgHash: Hex, pubKey: Hex) {
return starkCurve.verify(sig, ensureBytes0x(msgHash), ensureBytes0x(pubKey)); return starkCurve.verify(sig, ensureBytes0x(msgHash), ensureBytes0x(pubKey));
} }
const { CURVE, Point, ProjectivePoint, Signature } = starkCurve; const { CURVE, ProjectivePoint, Signature } = starkCurve;
export const utils = starkCurve.utils; export const utils = starkCurve.utils;
export { export {
CURVE, CURVE,
Point,
Signature, Signature,
ProjectivePoint, ProjectivePoint,
getPublicKey0x as getPublicKey, getPublicKey0x as getPublicKey,
@ -180,23 +179,23 @@ export function getAccountPath(
// https://docs.starkware.co/starkex/pedersen-hash-function.html // https://docs.starkware.co/starkex/pedersen-hash-function.html
const PEDERSEN_POINTS_AFFINE = [ const PEDERSEN_POINTS_AFFINE = [
new Point( new ProjectivePoint(
2089986280348253421170679821480865132823066470938446095505822317253594081284n, 2089986280348253421170679821480865132823066470938446095505822317253594081284n,
1713931329540660377023406109199410414810705867260802078187082345529207694986n 1713931329540660377023406109199410414810705867260802078187082345529207694986n
), ),
new Point( new ProjectivePoint(
996781205833008774514500082376783249102396023663454813447423147977397232763n, 996781205833008774514500082376783249102396023663454813447423147977397232763n,
1668503676786377725805489344771023921079126552019160156920634619255970485781n 1668503676786377725805489344771023921079126552019160156920634619255970485781n
), ),
new Point( new ProjectivePoint(
2251563274489750535117886426533222435294046428347329203627021249169616184184n, 2251563274489750535117886426533222435294046428347329203627021249169616184184n,
1798716007562728905295480679789526322175868328062420237419143593021674992973n 1798716007562728905295480679789526322175868328062420237419143593021674992973n
), ),
new Point( new ProjectivePoint(
2138414695194151160943305727036575959195309218611738193261179310511854807447n, 2138414695194151160943305727036575959195309218611738193261179310511854807447n,
113410276730064486255102093846540133784865286929052426931474106396135072156n 113410276730064486255102093846540133784865286929052426931474106396135072156n
), ),
new Point( new ProjectivePoint(
2379962749567351885752724891227938183011949129833673362440656643086021394946n, 2379962749567351885752724891227938183011949129833673362440656643086021394946n,
776496453633298175483985398648758586525933812536653089401905292063708816422n 776496453633298175483985398648758586525933812536653089401905292063708816422n
), ),
@ -253,7 +252,7 @@ export function pedersen(x: PedersenArg, y: PedersenArg) {
let point: ProjectivePoint = PEDERSEN_POINTS[0]; let point: ProjectivePoint = PEDERSEN_POINTS[0];
point = pedersenSingle(point, x, PEDERSEN_POINTS1); point = pedersenSingle(point, x, PEDERSEN_POINTS1);
point = pedersenSingle(point, y, PEDERSEN_POINTS2); point = pedersenSingle(point, y, PEDERSEN_POINTS2);
return bytesToHexEth(point.toAffine().toRawBytes(true).slice(1)); return bytesToHexEth(point.toRawBytes(true).slice(1));
} }
export function hashChain(data: PedersenArg[], fn = pedersen) { export function hashChain(data: PedersenArg[], fn = pedersen) {

10
test/nist.test.js
View File

@ -46,7 +46,7 @@ should('wychenproof ECDSA vectors', () => {
if (group.key.curve === 'secp224r1' && group.sha !== 'SHA-224') { if (group.key.curve === 'secp224r1' && group.sha !== 'SHA-224') {
if (group.sha === 'SHA-256') CURVE = CURVE.create(sha256); if (group.sha === 'SHA-256') CURVE = CURVE.create(sha256);
} }
const pubKey = CURVE.Point.fromHex(group.key.uncompressed); const pubKey = CURVE.ProjectivePoint.fromHex(group.key.uncompressed);
deepStrictEqual(pubKey.x, BigInt(`0x${group.key.wx}`)); deepStrictEqual(pubKey.x, BigInt(`0x${group.key.wx}`));
deepStrictEqual(pubKey.y, BigInt(`0x${group.key.wy}`)); deepStrictEqual(pubKey.y, BigInt(`0x${group.key.wy}`));
for (const test of group.tests) { for (const test of group.tests) {
@ -87,7 +87,7 @@ should('wychenproof ECDH vectors', () => {
for (const test of group.tests) { for (const test of group.tests) {
if (test.result === 'valid' || test.result === 'acceptable') { if (test.result === 'valid' || test.result === 'acceptable') {
try { try {
const pub = CURVE.Point.fromHex(test.public); const pub = CURVE.ProjectivePoint.fromHex(test.public);
} catch (e) { } catch (e) {
if (e.message.includes('Point.fromHex: received invalid point.')) continue; if (e.message.includes('Point.fromHex: received invalid point.')) continue;
throw e; throw e;
@ -147,7 +147,7 @@ for (const name in WYCHEPROOF_ECDH) {
for (const test of group.tests) { for (const test of group.tests) {
if (test.result === 'valid' || test.result === 'acceptable') { if (test.result === 'valid' || test.result === 'acceptable') {
try { try {
const pub = curve.Point.fromHex(test.public); const pub = curve.ProjectivePoint.fromHex(test.public);
} catch (e) { } catch (e) {
if (e.message.includes('Point.fromHex: received invalid point.')) continue; if (e.message.includes('Point.fromHex: received invalid point.')) continue;
throw e; throw e;
@ -309,7 +309,7 @@ const WYCHEPROOF_ECDSA = {
}; };
function runWycheproof(name, CURVE, group, index) { function runWycheproof(name, CURVE, group, index) {
const pubKey = CURVE.Point.fromHex(group.key.uncompressed); const pubKey = CURVE.ProjectivePoint.fromHex(group.key.uncompressed);
deepStrictEqual(pubKey.x, BigInt(`0x${group.key.wx}`)); deepStrictEqual(pubKey.x, BigInt(`0x${group.key.wx}`));
deepStrictEqual(pubKey.y, BigInt(`0x${group.key.wy}`)); deepStrictEqual(pubKey.y, BigInt(`0x${group.key.wy}`));
for (const test of group.tests) { for (const test of group.tests) {
@ -367,7 +367,7 @@ should('RFC6979', () => {
const curve = NIST[v.curve]; const curve = NIST[v.curve];
deepStrictEqual(curve.CURVE.n, hexToBigint(v.q)); deepStrictEqual(curve.CURVE.n, hexToBigint(v.q));
const pubKey = curve.getPublicKey(v.private); const pubKey = curve.getPublicKey(v.private);
const pubPoint = curve.Point.fromHex(pubKey); const pubPoint = curve.ProjectivePoint.fromHex(pubKey);
deepStrictEqual(pubPoint.x, hexToBigint(v.Ux)); deepStrictEqual(pubPoint.x, hexToBigint(v.Ux));
deepStrictEqual(pubPoint.y, hexToBigint(v.Uy)); deepStrictEqual(pubPoint.y, hexToBigint(v.Uy));
for (const c of v.cases) { for (const c of v.cases) {

59
test/secp256k1.test.js
View File

@ -13,6 +13,7 @@ import { hexToBytes, bytesToHex } from '@noble/hashes/utils';
const hex = bytesToHex; const hex = bytesToHex;
const secp = secp256k1; const secp = secp256k1;
const Point = secp.ProjectivePoint;
const privatesTxt = readFileSync('./test/vectors/privates-2.txt', 'utf-8'); const privatesTxt = readFileSync('./test/vectors/privates-2.txt', 'utf-8');
const schCsv = readFileSync('./test/vectors/schnorr.csv', 'utf-8'); const schCsv = readFileSync('./test/vectors/schnorr.csv', 'utf-8');
@ -37,15 +38,15 @@ describe('secp256k1', () => {
.filter((line) => line) .filter((line) => line)
.map((line) => line.split(':')); .map((line) => line.split(':'));
for (let [priv, x, y] of data) { for (let [priv, x, y] of data) {
const point = secp.Point.fromPrivateKey(BigInt(priv)); const point = Point.fromPrivateKey(BigInt(priv));
deepStrictEqual(toBEHex(point.x), x); deepStrictEqual(toBEHex(point.x), x);
deepStrictEqual(toBEHex(point.y), y); deepStrictEqual(toBEHex(point.y), y);
const point2 = secp.Point.fromHex(secp.getPublicKey(toBEHex(BigInt(priv)))); const point2 = Point.fromHex(secp.getPublicKey(toBEHex(BigInt(priv))));
deepStrictEqual(toBEHex(point2.x), x); deepStrictEqual(toBEHex(point2.x), x);
deepStrictEqual(toBEHex(point2.y), y); deepStrictEqual(toBEHex(point2.y), y);
const point3 = secp.Point.fromHex(secp.getPublicKey(hexToBytes(toBEHex(BigInt(priv))))); const point3 = Point.fromHex(secp.getPublicKey(hexToBytes(toBEHex(BigInt(priv)))));
deepStrictEqual(toBEHex(point3.x), x); deepStrictEqual(toBEHex(point3.x), x);
deepStrictEqual(toBEHex(point3.y), y); deepStrictEqual(toBEHex(point3.y), y);
} }
@ -62,15 +63,15 @@ describe('secp256k1', () => {
.filter((line) => line) .filter((line) => line)
.map((line) => line.split(':')); .map((line) => line.split(':'));
for (let [priv, x, y] of data) { for (let [priv, x, y] of data) {
const point = secp.Point.fromPrivateKey(BigInt(priv)); const point = Point.fromPrivateKey(BigInt(priv));
deepStrictEqual(toBEHex(point.x), x); deepStrictEqual(toBEHex(point.x), x);
deepStrictEqual(toBEHex(point.y), y); deepStrictEqual(toBEHex(point.y), y);
const point2 = secp.Point.fromHex(secp.getPublicKey(toBEHex(BigInt(priv)))); const point2 = Point.fromHex(secp.getPublicKey(toBEHex(BigInt(priv))));
deepStrictEqual(toBEHex(point2.x), x); deepStrictEqual(toBEHex(point2.x), x);
deepStrictEqual(toBEHex(point2.y), y); deepStrictEqual(toBEHex(point2.y), y);
const point3 = secp.Point.fromHex(secp.getPublicKey(hexToBytes(toBEHex(BigInt(priv))))); const point3 = Point.fromHex(secp.getPublicKey(hexToBytes(toBEHex(BigInt(priv)))));
deepStrictEqual(toBEHex(point3.x), x); deepStrictEqual(toBEHex(point3.x), x);
deepStrictEqual(toBEHex(point3.y), y); deepStrictEqual(toBEHex(point3.y), y);
} }
@ -81,9 +82,9 @@ describe('secp256k1', () => {
for (const vector of points.valid.isPoint) { for (const vector of points.valid.isPoint) {
const { P, expected } = vector; const { P, expected } = vector;
if (expected) { if (expected) {
secp.Point.fromHex(P); Point.fromHex(P);
} else { } else {
throws(() => secp.Point.fromHex(P)); throws(() => Point.fromHex(P));
} }
} }
}); });
@ -91,7 +92,7 @@ describe('secp256k1', () => {
should('.fromPrivateKey()', () => { should('.fromPrivateKey()', () => {
for (const vector of points.valid.pointFromScalar) { for (const vector of points.valid.pointFromScalar) {
const { d, expected } = vector; const { d, expected } = vector;
let p = secp.Point.fromPrivateKey(d); let p = Point.fromPrivateKey(d);
deepStrictEqual(p.toHex(true), expected); deepStrictEqual(p.toHex(true), expected);
} }
}); });
@ -99,26 +100,26 @@ describe('secp256k1', () => {
should('#toHex(compressed)', () => { should('#toHex(compressed)', () => {
for (const vector of points.valid.pointCompress) { for (const vector of points.valid.pointCompress) {
const { P, compress, expected } = vector; const { P, compress, expected } = vector;
let p = secp.Point.fromHex(P); let p = Point.fromHex(P);
deepStrictEqual(p.toHex(compress), expected); deepStrictEqual(p.toHex(compress), expected);
} }
}); });
should('#toHex() roundtrip (failed case)', () => { should('#toHex() roundtrip (failed case)', () => {
const point1 = const point1 =
secp.Point.fromPrivateKey( Point.fromPrivateKey(
88572218780422190464634044548753414301110513745532121983949500266768436236425n 88572218780422190464634044548753414301110513745532121983949500266768436236425n
); );
// const hex = point1.toHex(true); // const hex = point1.toHex(true);
// deepStrictEqual(secp.Point.fromHex(hex).toHex(true), hex); // deepStrictEqual(Point.fromHex(hex).toHex(true), hex);
}); });
should('#toHex() roundtrip', () => { should('#toHex() roundtrip', () => {
fc.assert( fc.assert(
fc.property(FC_BIGINT, (x) => { fc.property(FC_BIGINT, (x) => {
const point1 = secp.Point.fromPrivateKey(x); const point1 = Point.fromPrivateKey(x);
const hex = point1.toHex(true); const hex = point1.toHex(true);
deepStrictEqual(secp.Point.fromHex(hex).toHex(true), hex); deepStrictEqual(Point.fromHex(hex).toHex(true), hex);
}) })
); );
}); });
@ -126,8 +127,8 @@ describe('secp256k1', () => {
should('#add(other)', () => { should('#add(other)', () => {
for (const vector of points.valid.pointAdd) { for (const vector of points.valid.pointAdd) {
const { P, Q, expected } = vector; const { P, Q, expected } = vector;
let p = secp.Point.fromHex(P); let p = Point.fromHex(P);
let q = secp.Point.fromHex(Q); let q = Point.fromHex(Q);
if (expected) { if (expected) {
deepStrictEqual(p.add(q).toHex(true), expected); deepStrictEqual(p.add(q).toHex(true), expected);
} else { } else {
@ -141,7 +142,7 @@ describe('secp256k1', () => {
should('#multiply(privateKey)', () => { should('#multiply(privateKey)', () => {
for (const vector of points.valid.pointMultiply) { for (const vector of points.valid.pointMultiply) {
const { P, d, expected } = vector; const { P, d, expected } = vector;
const p = secp.Point.fromHex(P); const p = Point.fromHex(P);
if (expected) { if (expected) {
deepStrictEqual(p.multiply(hexToNumber(d)).toHex(true), expected); deepStrictEqual(p.multiply(hexToNumber(d)).toHex(true), expected);
} else { } else {
@ -155,13 +156,13 @@ describe('secp256k1', () => {
const { P, d } = vector; const { P, d } = vector;
if (hexToNumber(d) < secp.CURVE.n) { if (hexToNumber(d) < secp.CURVE.n) {
throws(() => { throws(() => {
const p = secp.Point.fromHex(P); const p = Point.fromHex(P);
p.multiply(hexToNumber(d)).toHex(true); p.multiply(hexToNumber(d)).toHex(true);
}); });
} }
} }
for (const num of [0n, 0, -1n, -1, 1.1]) { for (const num of [0n, 0, -1n, -1, 1.1]) {
throws(() => secp.Point.BASE.multiply(num)); throws(() => Point.BASE.multiply(num));
} }
}); });
}); });
@ -280,7 +281,7 @@ describe('secp256k1', () => {
const PRIV_KEY = 0x2n; const PRIV_KEY = 0x2n;
const WRONG_PRIV_KEY = 0x22n; const WRONG_PRIV_KEY = 0x22n;
const signature = secp.sign(MSG, PRIV_KEY); const signature = secp.sign(MSG, PRIV_KEY);
const publicKey = secp.Point.fromPrivateKey(WRONG_PRIV_KEY).toHex(); const publicKey = Point.fromPrivateKey(WRONG_PRIV_KEY).toHex();
deepStrictEqual(publicKey.length, 66); deepStrictEqual(publicKey.length, 66);
deepStrictEqual(secp.verify(signature, MSG, publicKey), false); deepStrictEqual(secp.verify(signature, MSG, publicKey), false);
}); });
@ -313,7 +314,7 @@ describe('secp256k1', () => {
const r = 1n; const r = 1n;
const s = 115792089237316195423570985008687907852837564279074904382605163141518162728904n; const s = 115792089237316195423570985008687907852837564279074904382605163141518162728904n;
const pub = new secp.Point(x, y); const pub = new Point(x, y);
const signature = new secp.Signature(2n, 2n); const signature = new secp.Signature(2n, 2n);
signature.r = r; signature.r = r;
signature.s = s; signature.s = s;
@ -328,7 +329,7 @@ describe('secp256k1', () => {
const y = 32670510020758816978083085130507043184471273380659243275938904335757337482424n; const y = 32670510020758816978083085130507043184471273380659243275938904335757337482424n;
const r = 104546003225722045112039007203142344920046999340768276760147352389092131869133n; const r = 104546003225722045112039007203142344920046999340768276760147352389092131869133n;
const s = 96900796730960181123786672629079577025401317267213807243199432755332205217369n; const s = 96900796730960181123786672629079577025401317267213807243199432755332205217369n;
const pub = new secp.Point(x, y); const pub = new Point(x, y);
const sig = new secp.Signature(r, s); const sig = new secp.Signature(r, s);
deepStrictEqual(secp.verify(sig, msg, pub), false); deepStrictEqual(secp.verify(sig, msg, pub), false);
}); });
@ -338,7 +339,7 @@ describe('secp256k1', () => {
const y = 17482644437196207387910659778872952193236850502325156318830589868678978890912n; const y = 17482644437196207387910659778872952193236850502325156318830589868678978890912n;
const r = 432420386565659656852420866390673177323n; const r = 432420386565659656852420866390673177323n;
const s = 115792089237316195423570985008687907852837564279074904382605163141518161494334n; const s = 115792089237316195423570985008687907852837564279074904382605163141518161494334n;
const pub = new secp.Point(x, y); const pub = new Point(x, y);
const sig = new secp.Signature(r, s); const sig = new secp.Signature(r, s);
deepStrictEqual(secp.verify(sig, msg, pub, { strict: false }), true); deepStrictEqual(secp.verify(sig, msg, pub, { strict: false }), true);
}); });
@ -376,7 +377,7 @@ describe('secp256k1', () => {
should('recover public key from recovery bit', () => { should('recover public key from recovery bit', () => {
const message = '00000000000000000000000000000000000000000000000000000000deadbeef'; const message = '00000000000000000000000000000000000000000000000000000000deadbeef';
const privateKey = 123456789n; const privateKey = 123456789n;
const publicKey = secp.Point.fromHex(secp.getPublicKey(privateKey)).toHex(false); const publicKey = Point.fromHex(secp.getPublicKey(privateKey)).toHex(false);
const sig = secp.sign(message, privateKey); const sig = secp.sign(message, privateKey);
const recoveredPubkey = sig.recoverPublicKey(message); const recoveredPubkey = sig.recoverPublicKey(message);
// const recoveredPubkey = secp.recoverPublicKey(message, signature, recovery); // const recoveredPubkey = secp.recoverPublicKey(message, signature, recovery);
@ -451,7 +452,7 @@ describe('secp256k1', () => {
should('have proper curve equation in assertValidity()', () => { should('have proper curve equation in assertValidity()', () => {
throws(() => { throws(() => {
const { Fp } = secp.CURVE; const { Fp } = secp.CURVE;
let point = new secp.Point(Fp.create(-2n), Fp.create(-1n)); let point = new Point(Fp.create(-2n), Fp.create(-1n));
point.assertValidity(); point.assertValidity();
}); });
}); });
@ -472,15 +473,15 @@ describe('secp256k1', () => {
}, },
pointAddScalar: (p, tweak, isCompressed) => { pointAddScalar: (p, tweak, isCompressed) => {
const P = secp.Point.fromHex(p); const P = Point.fromHex(p);
const t = normal(tweak); const t = normal(tweak);
const Q = secp.Point.BASE.multiplyAndAddUnsafe(P, t, 1n); const Q = Point.BASE.multiplyAndAddUnsafe(P, t, 1n);
if (!Q) throw new Error('Tweaked point at infinity'); if (!Q) throw new Error('Tweaked point at infinity');
return Q.toRawBytes(isCompressed); return Q.toRawBytes(isCompressed);
}, },
pointMultiply: (p, tweak, isCompressed) => { pointMultiply: (p, tweak, isCompressed) => {
const P = secp.Point.fromHex(p); const P = Point.fromHex(p);
const h = typeof tweak === 'string' ? tweak : bytesToHex(tweak); const h = typeof tweak === 'string' ? tweak : bytesToHex(tweak);
const t = BigInt(`0x${h}`); const t = BigInt(`0x${h}`);
return P.multiply(t).toRawBytes(isCompressed); return P.multiply(t).toRawBytes(isCompressed);
@ -528,7 +529,7 @@ describe('secp256k1', () => {
should('wychenproof vectors', () => { should('wychenproof vectors', () => {
for (let group of wp.testGroups) { for (let group of wp.testGroups) {
const pubKey = secp.Point.fromHex(group.key.uncompressed); const pubKey = Point.fromHex(group.key.uncompressed);
for (let test of group.tests) { for (let test of group.tests) {
const m = secp.CURVE.hash(hexToBytes(test.msg)); const m = secp.CURVE.hash(hexToBytes(test.msg));
if (test.result === 'valid' || test.result === 'acceptable') { if (test.result === 'valid' || test.result === 'acceptable') {