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