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import { type CHash, type Hex, type PrivKey } from '../utils.ts';
import { type AffinePoint, type BasicCurve, type CurveLengths, type CurvePoint, type CurvePointCons } from './curve.ts';
import { type IField, type NLength } from './modular.ts';
export type { AffinePoint };
export type HmacFnSync = (key: Uint8Array, ...messages: Uint8Array[]) => Uint8Array;
type EndoBasis = [[bigint, bigint], [bigint, bigint]];
/**
* When Weierstrass curve has `a=0`, it becomes Koblitz curve.
* Koblitz curves allow using **efficiently-computable GLV endomorphism ψ**.
* Endomorphism uses 2x less RAM, speeds up precomputation by 2x and ECDH / key recovery by 20%.
* For precomputed wNAF it trades off 1/2 init time & 1/3 ram for 20% perf hit.
*
* Endomorphism consists of beta, lambda and splitScalar:
*
* 1. GLV endomorphism ψ transforms a point: `P = (x, y) ↦ ψ(P) = (β·x mod p, y)`
* 2. GLV scalar decomposition transforms a scalar: `k ≡ k₁ + k₂·λ (mod n)`
* 3. Then these are combined: `k·P = k₁·P + k₂·ψ(P)`
* 4. Two 128-bit point-by-scalar multiplications + one point addition is faster than
* one 256-bit multiplication.
*
* where
* * beta: β ∈ Fₚ with β³ = 1, β ≠ 1
* * lambda: λ ∈ Fₙ with λ³ = 1, λ ≠ 1
* * splitScalar decomposes k ↦ k₁, k₂, by using reduced basis vectors.
* Gauss lattice reduction calculates them from initial basis vectors `(n, 0), (-λ, 0)`
*
* Check out `test/misc/endomorphism.js` and
* [gist](https://gist.github.com/paulmillr/eb670806793e84df628a7c434a873066).
*/
export type EndomorphismOpts = {
beta: bigint;
basises?: EndoBasis;
splitScalar?: (k: bigint) => {
k1neg: boolean;
k1: bigint;
k2neg: boolean;
k2: bigint;
};
};
export type ScalarEndoParts = {
k1neg: boolean;
k1: bigint;
k2neg: boolean;
k2: bigint;
};
/**
* Splits scalar for GLV endomorphism.
*/
export declare function _splitEndoScalar(k: bigint, basis: EndoBasis, n: bigint): ScalarEndoParts;
export type ECDSASigFormat = 'compact' | 'recovered' | 'der';
export type ECDSARecoverOpts = {
prehash?: boolean;
};
export type ECDSAVerifyOpts = {
prehash?: boolean;
lowS?: boolean;
format?: ECDSASigFormat;
};
export type ECDSASignOpts = {
prehash?: boolean;
lowS?: boolean;
format?: ECDSASigFormat;
extraEntropy?: Uint8Array | boolean;
};
/** Instance methods for 3D XYZ projective points. */
export interface WeierstrassPoint<T> extends CurvePoint<T, WeierstrassPoint<T>> {
/** projective X coordinate. Different from affine x. */
readonly X: T;
/** projective Y coordinate. Different from affine y. */
readonly Y: T;
/** projective z coordinate */
readonly Z: T;
/** affine x coordinate. Different from projective X. */
get x(): T;
/** affine y coordinate. Different from projective Y. */
get y(): T;
/** Encodes point using IEEE P1363 (DER) encoding. First byte is 2/3/4. Default = isCompressed. */
toBytes(isCompressed?: boolean): Uint8Array;
toHex(isCompressed?: boolean): string;
/** @deprecated use `.X` */
readonly px: T;
/** @deprecated use `.Y` */
readonly py: T;
/** @deprecated use `.Z` */
readonly pz: T;
/** @deprecated use `toBytes` */
toRawBytes(isCompressed?: boolean): Uint8Array;
/** @deprecated use `multiplyUnsafe` */
multiplyAndAddUnsafe(Q: WeierstrassPoint<T>, a: bigint, b: bigint): WeierstrassPoint<T> | undefined;
/** @deprecated use `p.y % 2n === 0n` */
hasEvenY(): boolean;
/** @deprecated use `p.precompute(windowSize)` */
_setWindowSize(windowSize: number): void;
}
/** Static methods for 3D XYZ projective points. */
export interface WeierstrassPointCons<T> extends CurvePointCons<WeierstrassPoint<T>> {
/** Does NOT validate if the point is valid. Use `.assertValidity()`. */
new (X: T, Y: T, Z: T): WeierstrassPoint<T>;
CURVE(): WeierstrassOpts<T>;
/** @deprecated use `Point.BASE.multiply(Point.Fn.fromBytes(privateKey))` */
fromPrivateKey(privateKey: PrivKey): WeierstrassPoint<T>;
/** @deprecated use `import { normalizeZ } from '@noble/curves/abstract/curve.js';` */
normalizeZ(points: WeierstrassPoint<T>[]): WeierstrassPoint<T>[];
/** @deprecated use `import { pippenger } from '@noble/curves/abstract/curve.js';` */
msm(points: WeierstrassPoint<T>[], scalars: bigint[]): WeierstrassPoint<T>;
}
/**
* Weierstrass curve options.
*
* * p: prime characteristic (order) of finite field, in which arithmetics is done
* * n: order of prime subgroup a.k.a total amount of valid curve points
* * h: cofactor, usually 1. h*n is group order; n is subgroup order
* * a: formula param, must be in field of p
* * b: formula param, must be in field of p
* * Gx: x coordinate of generator point a.k.a. base point
* * Gy: y coordinate of generator point
*/
export type WeierstrassOpts<T> = Readonly<{
p: bigint;
n: bigint;
h: bigint;
a: T;
b: T;
Gx: T;
Gy: T;
}>;
export type WeierstrassExtraOpts<T> = Partial<{
Fp: IField<T>;
Fn: IField<bigint>;
allowInfinityPoint: boolean;
endo: EndomorphismOpts;
isTorsionFree: (c: WeierstrassPointCons<T>, point: WeierstrassPoint<T>) => boolean;
clearCofactor: (c: WeierstrassPointCons<T>, point: WeierstrassPoint<T>) => WeierstrassPoint<T>;
fromBytes: (bytes: Uint8Array) => AffinePoint<T>;
toBytes: (c: WeierstrassPointCons<T>, point: WeierstrassPoint<T>, isCompressed: boolean) => Uint8Array;
}>;
/**
* Options for ECDSA signatures over a Weierstrass curve.
*
* * lowS: (default: true) whether produced / verified signatures occupy low half of ecdsaOpts.p. Prevents malleability.
* * hmac: (default: noble-hashes hmac) function, would be used to init hmac-drbg for k generation.
* * randomBytes: (default: webcrypto os-level CSPRNG) custom method for fetching secure randomness.
* * bits2int, bits2int_modN: used in sigs, sometimes overridden by curves
*/
export type ECDSAOpts = Partial<{
lowS: boolean;
hmac: HmacFnSync;
randomBytes: (bytesLength?: number) => Uint8Array;
bits2int: (bytes: Uint8Array) => bigint;
bits2int_modN: (bytes: Uint8Array) => bigint;
}>;
/**
* Elliptic Curve Diffie-Hellman interface.
* Provides keygen, secret-to-public conversion, calculating shared secrets.
*/
export interface ECDH {
keygen: (seed?: Uint8Array) => {
secretKey: Uint8Array;
publicKey: Uint8Array;
};
getPublicKey: (secretKey: PrivKey, isCompressed?: boolean) => Uint8Array;
getSharedSecret: (secretKeyA: PrivKey, publicKeyB: Hex, isCompressed?: boolean) => Uint8Array;
Point: WeierstrassPointCons<bigint>;
utils: {
isValidSecretKey: (secretKey: PrivKey) => boolean;
isValidPublicKey: (publicKey: Uint8Array, isCompressed?: boolean) => boolean;
randomSecretKey: (seed?: Uint8Array) => Uint8Array;
/** @deprecated use `randomSecretKey` */
randomPrivateKey: (seed?: Uint8Array) => Uint8Array;
/** @deprecated use `isValidSecretKey` */
isValidPrivateKey: (secretKey: PrivKey) => boolean;
/** @deprecated use `Point.Fn.fromBytes()` */
normPrivateKeyToScalar: (key: PrivKey) => bigint;
/** @deprecated use `point.precompute()` */
precompute: (windowSize?: number, point?: WeierstrassPoint<bigint>) => WeierstrassPoint<bigint>;
};
lengths: CurveLengths;
}
/**
* ECDSA interface.
* Only supported for prime fields, not Fp2 (extension fields).
*/
export interface ECDSA extends ECDH {
sign: (message: Hex, secretKey: PrivKey, opts?: ECDSASignOpts) => ECDSASigRecovered;
verify: (signature: Uint8Array, message: Uint8Array, publicKey: Uint8Array, opts?: ECDSAVerifyOpts) => boolean;
recoverPublicKey(signature: Uint8Array, message: Uint8Array, opts?: ECDSARecoverOpts): Uint8Array;
Signature: ECDSASignatureCons;
}
export declare class DERErr extends Error {
constructor(m?: string);
}
export type IDER = {
Err: typeof DERErr;
_tlv: {
encode: (tag: number, data: string) => string;
decode(tag: number, data: Uint8Array): {
v: Uint8Array;
l: Uint8Array;
};
};
_int: {
encode(num: bigint): string;
decode(data: Uint8Array): bigint;
};
toSig(hex: string | Uint8Array): {
r: bigint;
s: bigint;
};
hexFromSig(sig: {
r: bigint;
s: bigint;
}): string;
};
/**
* ASN.1 DER encoding utilities. ASN is very complex & fragile. Format:
*
* [0x30 (SEQUENCE), bytelength, 0x02 (INTEGER), intLength, R, 0x02 (INTEGER), intLength, S]
*
* Docs: https://letsencrypt.org/docs/a-warm-welcome-to-asn1-and-der/, https://luca.ntop.org/Teaching/Appunti/asn1.html
*/
export declare const DER: IDER;
export declare function _normFnElement(Fn: IField<bigint>, key: PrivKey): bigint;
/**
* Creates weierstrass Point constructor, based on specified curve options.
*
* @example
```js
const opts = {
p: BigInt('0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff'),
n: BigInt('0xffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551'),
h: BigInt(1),
a: BigInt('0xffffffff00000001000000000000000000000000fffffffffffffffffffffffc'),
b: BigInt('0x5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b'),
Gx: BigInt('0x6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296'),
Gy: BigInt('0x4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5'),
};
const p256_Point = weierstrass(opts);
```
*/
export declare function weierstrassN<T>(params: WeierstrassOpts<T>, extraOpts?: WeierstrassExtraOpts<T>): WeierstrassPointCons<T>;
/** Methods of ECDSA signature instance. */
export interface ECDSASignature {
readonly r: bigint;
readonly s: bigint;
readonly recovery?: number;
addRecoveryBit(recovery: number): ECDSASigRecovered;
hasHighS(): boolean;
toBytes(format?: string): Uint8Array;
toHex(format?: string): string;
/** @deprecated */
assertValidity(): void;
/** @deprecated */
normalizeS(): ECDSASignature;
/** @deprecated use standalone method `curve.recoverPublicKey(sig.toBytes('recovered'), msg)` */
recoverPublicKey(msgHash: Hex): WeierstrassPoint<bigint>;
/** @deprecated use `.toBytes('compact')` */
toCompactRawBytes(): Uint8Array;
/** @deprecated use `.toBytes('compact')` */
toCompactHex(): string;
/** @deprecated use `.toBytes('der')` */
toDERRawBytes(): Uint8Array;
/** @deprecated use `.toBytes('der')` */
toDERHex(): string;
}
export type ECDSASigRecovered = ECDSASignature & {
readonly recovery: number;
};
/** Methods of ECDSA signature constructor. */
export type ECDSASignatureCons = {
new (r: bigint, s: bigint, recovery?: number): ECDSASignature;
fromBytes(bytes: Uint8Array, format?: ECDSASigFormat): ECDSASignature;
fromHex(hex: string, format?: ECDSASigFormat): ECDSASignature;
/** @deprecated use `.fromBytes(bytes, 'compact')` */
fromCompact(hex: Hex): ECDSASignature;
/** @deprecated use `.fromBytes(bytes, 'der')` */
fromDER(hex: Hex): ECDSASignature;
};
/**
* Implementation of the Shallue and van de Woestijne method for any weierstrass curve.
* TODO: check if there is a way to merge this with uvRatio in Edwards; move to modular.
* b = True and y = sqrt(u / v) if (u / v) is square in F, and
* b = False and y = sqrt(Z * (u / v)) otherwise.
* @param Fp
* @param Z
* @returns
*/
export declare function SWUFpSqrtRatio<T>(Fp: IField<T>, Z: T): (u: T, v: T) => {
isValid: boolean;
value: T;
};
/**
* Simplified Shallue-van de Woestijne-Ulas Method
* https://www.rfc-editor.org/rfc/rfc9380#section-6.6.2
*/
export declare function mapToCurveSimpleSWU<T>(Fp: IField<T>, opts: {
A: T;
B: T;
Z: T;
}): (u: T) => {
x: T;
y: T;
};
/**
* Sometimes users only need getPublicKey, getSharedSecret, and secret key handling.
* This helper ensures no signature functionality is present. Less code, smaller bundle size.
*/
export declare function ecdh(Point: WeierstrassPointCons<bigint>, ecdhOpts?: {
randomBytes?: (bytesLength?: number) => Uint8Array;
}): ECDH;
/**
* Creates ECDSA signing interface for given elliptic curve `Point` and `hash` function.
* We need `hash` for 2 features:
* 1. Message prehash-ing. NOT used if `sign` / `verify` are called with `prehash: false`
* 2. k generation in `sign`, using HMAC-drbg(hash)
*
* ECDSAOpts are only rarely needed.
*
* @example
* ```js
* const p256_Point = weierstrass(...);
* const p256_sha256 = ecdsa(p256_Point, sha256);
* const p256_sha224 = ecdsa(p256_Point, sha224);
* const p256_sha224_r = ecdsa(p256_Point, sha224, { randomBytes: (length) => { ... } });
* ```
*/
export declare function ecdsa(Point: WeierstrassPointCons<bigint>, hash: CHash, ecdsaOpts?: ECDSAOpts): ECDSA;
/** @deprecated use ECDSASignature */
export type SignatureType = ECDSASignature;
/** @deprecated use ECDSASigRecovered */
export type RecoveredSignatureType = ECDSASigRecovered;
/** @deprecated switch to Uint8Array signatures in format 'compact' */
export type SignatureLike = {
r: bigint;
s: bigint;
};
export type ECDSAExtraEntropy = Hex | boolean;
/** @deprecated use `ECDSAExtraEntropy` */
export type Entropy = Hex | boolean;
export type BasicWCurve<T> = BasicCurve<T> & {
a: T;
b: T;
allowedPrivateKeyLengths?: readonly number[];
wrapPrivateKey?: boolean;
endo?: EndomorphismOpts;
isTorsionFree?: (c: WeierstrassPointCons<T>, point: WeierstrassPoint<T>) => boolean;
clearCofactor?: (c: WeierstrassPointCons<T>, point: WeierstrassPoint<T>) => WeierstrassPoint<T>;
};
/** @deprecated use ECDSASignOpts */
export type SignOpts = ECDSASignOpts;
/** @deprecated use ECDSASignOpts */
export type VerOpts = ECDSAVerifyOpts;
/** @deprecated use WeierstrassPoint */
export type ProjPointType<T> = WeierstrassPoint<T>;
/** @deprecated use WeierstrassPointCons */
export type ProjConstructor<T> = WeierstrassPointCons<T>;
/** @deprecated use ECDSASignatureCons */
export type SignatureConstructor = ECDSASignatureCons;
export type CurvePointsType<T> = BasicWCurve<T> & {
fromBytes?: (bytes: Uint8Array) => AffinePoint<T>;
toBytes?: (c: WeierstrassPointCons<T>, point: WeierstrassPoint<T>, isCompressed: boolean) => Uint8Array;
};
export type CurvePointsTypeWithLength<T> = Readonly<CurvePointsType<T> & Partial<NLength>>;
export type CurvePointsRes<T> = {
Point: WeierstrassPointCons<T>;
/** @deprecated use `Point.CURVE()` */
CURVE: CurvePointsType<T>;
/** @deprecated use `Point` */
ProjectivePoint: WeierstrassPointCons<T>;
/** @deprecated use `Point.Fn.fromBytes(privateKey)` */
normPrivateKeyToScalar: (key: PrivKey) => bigint;
/** @deprecated */
weierstrassEquation: (x: T) => T;
/** @deprecated use `Point.Fn.isValidNot0(num)` */
isWithinCurveOrder: (num: bigint) => boolean;
};
/** @deprecated use `Uint8Array` */
export type PubKey = Hex | WeierstrassPoint<bigint>;
export type CurveType = BasicWCurve<bigint> & {
hash: CHash;
hmac?: HmacFnSync;
randomBytes?: (bytesLength?: number) => Uint8Array;
lowS?: boolean;
bits2int?: (bytes: Uint8Array) => bigint;
bits2int_modN?: (bytes: Uint8Array) => bigint;
};
export type CurveFn = {
/** @deprecated use `Point.CURVE()` */
CURVE: CurvePointsType<bigint>;
keygen: ECDSA['keygen'];
getPublicKey: ECDSA['getPublicKey'];
getSharedSecret: ECDSA['getSharedSecret'];
sign: ECDSA['sign'];
verify: ECDSA['verify'];
Point: WeierstrassPointCons<bigint>;
/** @deprecated use `Point` */
ProjectivePoint: WeierstrassPointCons<bigint>;
Signature: ECDSASignatureCons;
utils: ECDSA['utils'];
lengths: ECDSA['lengths'];
};
/** @deprecated use `weierstrass` in newer releases */
export declare function weierstrassPoints<T>(c: CurvePointsTypeWithLength<T>): CurvePointsRes<T>;
export type WsPointComposed<T> = {
CURVE: WeierstrassOpts<T>;
curveOpts: WeierstrassExtraOpts<T>;
};
export type WsComposed = {
/** @deprecated use `Point.CURVE()` */
CURVE: WeierstrassOpts<bigint>;
hash: CHash;
curveOpts: WeierstrassExtraOpts<bigint>;
ecdsaOpts: ECDSAOpts;
};
export declare function _legacyHelperEquat<T>(Fp: IField<T>, a: T, b: T): (x: T) => T;
export declare function weierstrass(c: CurveType): CurveFn;
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