Add eddsa prehashed mode, diffie-hellman

src/edwards.ts

@@ -11,7 +11,14 @@
 // 5. Domain function was no-op for ed25519, but adds some data even with empty context for ed448
 
 import * as mod from './modular.js';
-import { bytesToHex, concatBytes, ensureBytes, numberToBytesLE, nLength } from './utils.js';
+import {
+  bytesToHex,
+  concatBytes,
+  ensureBytes,
+  numberToBytesLE,
+  nLength,
+  hashToPrivateScalar,
+} from './utils.js';
 import { wNAF } from './group.js';
 
 // Be friendly to bad ECMAScript parsers by not using bigint literals like 123n
@@ -42,16 +49,21 @@ export type CurveType = {
   // Base point (x, y) aka generator point
   Gx: bigint;
   Gy: bigint;
-  // Other constants
-  a24: bigint;
-  // ECDH bits (can be different from N bits)
-  scalarBits: number;
   // Hashes
   hash: CHash; // Because we need outputLen for DRBG
   randomBytes: (bytesLength?: number) => Uint8Array;
-  adjustScalarBytes: (bytes: Uint8Array) => Uint8Array;
-  domain: (data: Uint8Array, ctx: Uint8Array, hflag: boolean) => Uint8Array;
-  uvRatio: (u: bigint, v: bigint) => { isValid: boolean; value: bigint };
+  adjustScalarBytes?: (bytes: Uint8Array) => Uint8Array;
+  domain?: (data: Uint8Array, ctx: Uint8Array, phflag: boolean) => Uint8Array;
+  uvRatio?: (u: bigint, v: bigint) => { isValid: boolean; value: bigint };
+  preHash?: CHash;
+  // ECDH related
+  // Other constants
+  a24: bigint; // Related to d, but cannot be derived from it
+  // ECDH bits (can be different from N bits)
+  montgomeryBits?: number;
+  basePointU?: string; // TODO: why not bigint?
+  powPminus2?: (x: bigint) => bigint;
+  UfromPoint?: (p: PointType) => Uint8Array;
 };
 
 // We accept hex strings besides Uint8Array for simplicity
@@ -67,18 +79,29 @@ function validateOpts(curve: CurveType) {
     if (typeof curve[i] !== 'bigint')
       throw new Error(`Invalid curve param ${i}=${curve[i]} (${typeof curve[i]})`);
   }
-  for (const i of ['scalarBits'] as const) {
-    if (typeof curve[i] !== 'number')
-      throw new Error(`Invalid curve param ${i}=${curve[i]} (${typeof curve[i]})`);
-  }
-  for (const i of ['nBitLength', 'nByteLength'] as const) {
+  for (const i of ['nBitLength', 'nByteLength', 'montgomeryBits'] as const) {
     if (curve[i] === undefined) continue; // Optional
     if (!Number.isSafeInteger(curve[i]))
       throw new Error(`Invalid curve param ${i}=${curve[i]} (${typeof curve[i]})`);
   }
-  for (const fn of ['randomBytes', 'adjustScalarBytes', 'domain', 'uvRatio'] as const) {
+  for (const fn of ['randomBytes'] as const) {
     if (typeof curve[fn] !== 'function') throw new Error(`Invalid ${fn} function`);
   }
+  for (const fn of [
+    'adjustScalarBytes',
+    'domain',
+    'uvRatio',
+    'powPminus2',
+    'UfromPoint',
+  ] as const) {
+    if (curve[fn] === undefined) continue; // Optional
+    if (typeof curve[fn] !== 'function') throw new Error(`Invalid ${fn} function`);
+  }
+  for (const i of ['basePointU'] as const) {
+    if (curve[i] === undefined) continue; // Optional
+    if (typeof curve[i] !== 'string')
+      throw new Error(`Invalid curve param ${i}=${curve[i]} (${typeof curve[i]})`);
+  }
   // Set defaults
   return Object.freeze({ ...nLength(curve.n, curve.nBitLength), ...curve } as const);
 }
@@ -131,7 +154,6 @@ export interface PointType {
   _setWindowSize(windowSize: number): void;
   toRawBytes(isCompressed?: boolean): Uint8Array;
   toHex(isCompressed?: boolean): string;
-  //  toX25519(): Uint8Array;
   isTorsionFree(): boolean;
   equals(other: PointType): boolean;
   negate(): PointType;
@@ -154,11 +176,20 @@ export type SigType = Hex | SignatureType;
 export type CurveFn = {
   CURVE: ReturnType<typeof validateOpts>;
   getPublicKey: (privateKey: PrivKey, isCompressed?: boolean) => Uint8Array;
+  getSharedSecret: (privateKey: PrivKey, publicKey: Hex) => Uint8Array;
   sign: (message: Hex, privateKey: Hex) => Uint8Array;
   verify: (sig: SigType, message: Hex, publicKey: PubKey) => boolean;
   Point: PointConstructor;
   ExtendedPoint: ExtendedPointConstructor;
   Signature: SignatureConstructor;
+  montgomeryCurve: {
+    BASE_POINT_U: string;
+    UfromPoint: (p: PointType) => Uint8Array;
+    scalarMult: (u: Hex, scalar: Hex) => Uint8Array;
+    scalarMultBase: (scalar: Hex) => Uint8Array;
+    getPublicKey: (privateKey: Hex) => Uint8Array;
+    getSharedSecret: (privateKey: Hex, publicKey: Hex) => Uint8Array;
+  };
   utils: {
     mod: (a: bigint, b?: bigint) => bigint;
     invert: (number: bigint, modulo?: bigint) => bigint;
@@ -184,11 +215,29 @@ export function twistedEdwards(curveDef: CurveType): CurveFn {
   const maxGroupElement = _2n ** BigInt(groupLen * 8); // previous POW_2_256
 
   // Function overrides
-  const { adjustScalarBytes, randomBytes, uvRatio } = CURVE;
+  const { P, randomBytes } = CURVE;
+  const modP = (a: bigint) => mod.mod(a, P);
 
-  function modP(a: bigint) {
-    return mod.mod(a, CURVE.P);
+  // sqrt(u/v)
+  function _uvRatio(u: bigint, v: bigint) {
+    try {
+      const value = mod.sqrt(u * mod.invert(v, P), P);
+      return { isValid: true, value };
+    } catch (e) {
+      return { isValid: false, value: _0n };
+    }
   }
+  const uvRatio = CURVE.uvRatio || _uvRatio;
+
+  const _powPminus2 = (x: bigint) => mod.pow(x, P - _2n, P);
+  const powPminus2 = CURVE.powPminus2 || _powPminus2;
+  const _adjustScalarBytes = (bytes: Uint8Array) => bytes; // NOOP
+  const adjustScalarBytes = CURVE.adjustScalarBytes || _adjustScalarBytes;
+  function _domain(data: Uint8Array, ctx: Uint8Array, phflag: boolean) {
+    if (ctx.length || phflag) throw new Error('Contexts/pre-hash are not supported');
+    return data;
+  }
+  const domain = CURVE.domain || _domain; // NOOP
 
   /**
    * Extended Point works in extended coordinates: (x, y, z, t) ∋ (x=x/z, y=y/z, t=xy).
@@ -213,7 +262,7 @@ export function twistedEdwards(curveDef: CurveType): CurveFn {
     static toAffineBatch(points: ExtendedPoint[]): Point[] {
       const toInv = mod.invertBatch(
         points.map((p) => p.z),
-        CURVE.P
+        P
       );
       return points.map((p, i) => p.toAffine(toInv[i]));
     }
@@ -341,7 +390,7 @@ export function twistedEdwards(curveDef: CurveType): CurveFn {
     toAffine(invZ?: bigint): Point {
       const { x, y, z } = this;
       const is0 = this.equals(ExtendedPoint.ZERO);
-      if (invZ == null) invZ = is0 ? _8n : mod.invert(z, CURVE.P); // 8 was chosen arbitrarily
+      if (invZ == null) invZ = is0 ? _8n : mod.invert(z, P); // 8 was chosen arbitrarily
       const ax = modP(x * invZ);
       const ay = modP(y * invZ);
       const zz = modP(z * invZ);
@@ -419,9 +468,7 @@ export function twistedEdwards(curveDef: CurveType): CurveFn {
       // 2, set x <-- p - x.  Return the decoded point (x,y).
       const isXOdd = (x & _1n) === _1n;
       const isLastByteOdd = (lastByte & 0x80) !== 0;
-      if (isLastByteOdd !== isXOdd) {
-        x = modP(-x);
-      }
+      if (isLastByteOdd !== isXOdd) x = modP(-x);
       return new Point(x, y);
     }
 
@@ -575,26 +622,36 @@ export function twistedEdwards(curveDef: CurveType): CurveFn {
     return getExtendedPublicKey(privateKey).pointBytes;
   }
 
+  const EMPTY = new Uint8Array();
+  function hashDomainToScalar(message: Uint8Array, context: Hex = EMPTY) {
+    context = ensureBytes(context);
+    return modlLE(CURVE.hash(domain(message, context, !!CURVE.preHash)));
+  }
+
   /** Signs message with privateKey. RFC8032 5.1.6 */
-  function sign(message: Hex, privateKey: Hex): Uint8Array {
+  function sign(message: Hex, privateKey: Hex, context?: Hex): Uint8Array {
     message = ensureBytes(message);
+    if (CURVE.preHash) message = CURVE.preHash(message);
     const { prefix, scalar, pointBytes } = getExtendedPublicKey(privateKey);
-    const rDomain = CURVE.domain(concatBytes(prefix, message), new Uint8Array(), false);
-    const r = modlLE(CURVE.hash(rDomain)); // r = hash(prefix + msg)
+    const r = hashDomainToScalar(concatBytes(prefix, message), context);
     const R = Point.BASE.multiply(r); // R = rG
-    const kDomain = CURVE.domain(
-      concatBytes(R.toRawBytes(), pointBytes, message),
-      new Uint8Array(),
-      false
-    );
-    const k = modlLE(CURVE.hash(kDomain)); // k = hash(R+P+msg)
+    const k = hashDomainToScalar(concatBytes(R.toRawBytes(), pointBytes, message), context); // k = hash(R+P+msg)
     const s = mod.mod(r + k * scalar, CURVE_ORDER); // s = r + kp
     return new Signature(R, s).toRawBytes();
   }
 
-  // Helper functions because we have async and sync methods.
-  function prepareVerification(sig: SigType, message: Hex, publicKey: PubKey) {
+  /**
+   * Verifies EdDSA signature against message and public key.
+   * An extended group equation is checked.
+   * RFC8032 5.1.7
+   * Compliant with ZIP215:
+   * 0 <= sig.R/publicKey < 2**256 (can be >= curve.P)
+   * 0 <= sig.s < l
+   * Not compliant with RFC8032: it's not possible to comply to both ZIP & RFC at the same time.
+   */
+  function verify(sig: SigType, message: Hex, publicKey: PubKey, context?: Hex): boolean {
     message = ensureBytes(message);
+    if (CURVE.preHash) message = CURVE.preHash(message);
     // When hex is passed, we check public key fully.
     // When Point instance is passed, we assume it has already been checked, for performance.
     // If user passes Point/Sig instance, we assume it has been already verified.
@@ -614,40 +671,189 @@ export function twistedEdwards(curveDef: CurveType): CurveFn {
 
     const { r, s } = sig;
     const SB = ExtendedPoint.BASE.multiplyUnsafe(s);
-    return { r, s, SB, pub: publicKey, msg: message };
-  }
-
-  function finishVerification(publicKey: Point, r: Point, SB: ExtendedPoint, hashed: Uint8Array) {
-    const k = modlLE(hashed);
+    const k = hashDomainToScalar(
+      concatBytes(r.toRawBytes(), publicKey.toRawBytes(), message),
+      context
+    );
     const kA = ExtendedPoint.fromAffine(publicKey).multiplyUnsafe(k);
     const RkA = ExtendedPoint.fromAffine(r).add(kA);
     // [8][S]B = [8]R + [8][k]A'
     return RkA.subtract(SB).multiplyUnsafe(CURVE.h).equals(ExtendedPoint.ZERO);
   }
 
-  /**
-   * Verifies EdDSA signature against message and public key.
-   * An extended group equation is checked.
-   * RFC8032 5.1.7
-   * Compliant with ZIP215:
-   * 0 <= sig.R/publicKey < 2**256 (can be >= curve.P)
-   * 0 <= sig.s < l
-   * Not compliant with RFC8032: it's not possible to comply to both ZIP & RFC at the same time.
-   */
-  function verify(sig: SigType, message: Hex, publicKey: PubKey): boolean {
-    const { r, SB, msg, pub } = prepareVerification(sig, message, publicKey);
-    const domain = CURVE.domain(
-      concatBytes(r.toRawBytes(), pub.toRawBytes(), msg),
-      new Uint8Array([]),
-      false
-    );
-    const hashed = CURVE.hash(domain);
-    return finishVerification(pub, r, SB, hashed);
-  }
-
   // Enable precomputes. Slows down first publicKey computation by 20ms.
   Point.BASE._setWindowSize(8);
 
+  // ECDH (X22519/X448)
+  // https://datatracker.ietf.org/doc/html/rfc7748
+  // Every twisted Edwards curve is birationally equivalent to an elliptic curve in Montgomery form and vice versa.
+  const montgomeryBits = CURVE.montgomeryBits || CURVE.nBitLength;
+  const montgomeryBytes = Math.ceil(montgomeryBits / 8);
+
+  // cswap from RFC7748
+  function cswap(swap: bigint, x_2: bigint, x_3: bigint): [bigint, bigint] {
+    const dummy = modP(swap * (x_2 - x_3));
+    x_2 = modP(x_2 - dummy);
+    x_3 = modP(x_3 + dummy);
+    return [x_2, x_3];
+  }
+
+  // x25519 from 4
+  /**
+   *
+   * @param pointU u coordinate (x) on Montgomery Curve 25519
+   * @param scalar by which the point would be multiplied
+   * @returns new Point on Montgomery curve
+   */
+  function montgomeryLadder(pointU: bigint, scalar: bigint): bigint {
+    const { P } = CURVE;
+    const u = normalizeScalar(pointU, P);
+    // Section 5: Implementations MUST accept non-canonical values and process them as
+    // if they had been reduced modulo the field prime.
+    const k = normalizeScalar(scalar, P);
+    // The constant a24 is (486662 - 2) / 4 = 121665 for curve25519/X25519
+    const a24 = CURVE.a24;
+    const x_1 = u;
+    let x_2 = _1n;
+    let z_2 = _0n;
+    let x_3 = u;
+    let z_3 = _1n;
+    let swap = _0n;
+    let sw: [bigint, bigint];
+    for (let t = BigInt(montgomeryBits - 1); t >= _0n; t--) {
+      const k_t = (k >> t) & _1n;
+      swap ^= k_t;
+      sw = cswap(swap, x_2, x_3);
+      x_2 = sw[0];
+      x_3 = sw[1];
+      sw = cswap(swap, z_2, z_3);
+      z_2 = sw[0];
+      z_3 = sw[1];
+      swap = k_t;
+
+      const A = x_2 + z_2;
+      const AA = modP(A * A);
+      const B = x_2 - z_2;
+      const BB = modP(B * B);
+      const E = AA - BB;
+      const C = x_3 + z_3;
+      const D = x_3 - z_3;
+      const DA = modP(D * A);
+      const CB = modP(C * B);
+      const dacb = DA + CB;
+      const da_cb = DA - CB;
+      x_3 = modP(dacb * dacb);
+      z_3 = modP(x_1 * modP(da_cb * da_cb));
+      x_2 = modP(AA * BB);
+      z_2 = modP(E * (AA + modP(a24 * E)));
+    }
+    // (x_2, x_3) = cswap(swap, x_2, x_3)
+    sw = cswap(swap, x_2, x_3);
+    x_2 = sw[0];
+    x_3 = sw[1];
+    // (z_2, z_3) = cswap(swap, z_2, z_3)
+    sw = cswap(swap, z_2, z_3);
+    z_2 = sw[0];
+    z_3 = sw[1];
+    // z_2^(p - 2)
+    const z2 = powPminus2(z_2);
+    // Return x_2 * (z_2^(p - 2))
+    return modP(x_2 * z2);
+  }
+
+  function encodeUCoordinate(u: bigint): Uint8Array {
+    return numberToBytesLE(modP(u), montgomeryBytes);
+  }
+
+  function decodeUCoordinate(uEnc: Hex): bigint {
+    const u = ensureBytes(uEnc, montgomeryBytes);
+    // Section 5: When receiving such an array, implementations of X25519
+    // MUST mask the most significant bit in the final byte.
+    // This is very ugly way, but it works because fieldLen-1 is outside of bounds for X448, so this becomes NOOP
+    // fieldLen - scalaryBytes = 1 for X448 and = 0 for X25519
+    u[fieldLen - 1] &= 127; // 0b0111_1111
+    return bytesToNumberLE(u);
+  }
+
+  function decodeScalar(n: Hex): bigint {
+    const bytes = ensureBytes(n);
+    if (bytes.length !== montgomeryBytes && bytes.length !== fieldLen)
+      throw new Error(`Expected ${montgomeryBytes} or ${fieldLen} bytes, got ${bytes.length}`);
+    return bytesToNumberLE(adjustScalarBytes(bytes));
+  }
+  /*
+    Converts Point to Montgomery Curve
+    - u, v: curve25519 coordinates
+    - x, y: ed25519 coordinates
+    RFC 7748 (https://www.rfc-editor.org/rfc/rfc7748) says
+    - The birational maps are (25519):
+     (u, v) = ((1+y)/(1-y), sqrt(-486664)*u/x)
+     (x, y) = (sqrt(-486664)*u/v, (u-1)/(u+1))
+    - The birational maps are (448):
+     (u, v) = ((y-1)/(y+1), sqrt(156324)*u/x)
+     (x, y) = (sqrt(156324)*u/v, (1+u)/(1-u))
+
+    But original Twisted Edwards paper (https://eprint.iacr.org/2008/013.pdf) and hyperelliptics (http://hyperelliptic.org/EFD/g1p/data/twisted/coordinates)
+    says that mapping is always:
+    - u = (1+y)/(1-y)
+    - v = 2 (1+y)/(x(1-y))
+    - x = 2 u/v
+    - y = (u-1)/(u+1)
+
+    Which maps correctly, but to completely different curve. There is different mapping for ed448 (which done with replaceble function).
+    Returns 'u' coordinate of curve25519 point.
+
+    NOTE: jubjub will need full mapping, for now only Point -> U is enough
+    */
+  function _UfromPoint(p: Point): Uint8Array {
+    if (!(p instanceof Point)) throw new Error('Wrong point');
+    const { y } = p;
+    const u = modP((y + _1n) * mod.invert(_1n - y, P));
+    return numberToBytesLE(u, montgomeryBytes);
+  }
+  const UfromPoint = CURVE.UfromPoint || _UfromPoint;
+
+  const BASE_POINT_U = CURVE.basePointU || bytesToHex(UfromPoint(Point.BASE));
+  // Multiply point u by scalar
+  function scalarMult(u: Hex, scalar: Hex): Uint8Array {
+    const pointU = decodeUCoordinate(u);
+    const _scalar = decodeScalar(scalar);
+    const pu = montgomeryLadder(pointU, _scalar);
+    // The result was not contributory
+    // https://cr.yp.to/ecdh.html#validate
+    if (pu === _0n) throw new Error('Invalid private or public key received');
+    return encodeUCoordinate(pu);
+  }
+  // Multiply base point by scalar
+  const scalarMultBase = (scalar: Hex): Uint8Array =>
+    montgomeryCurve.scalarMult(montgomeryCurve.BASE_POINT_U, scalar);
+
+  const montgomeryCurve = {
+    BASE_POINT_U,
+    UfromPoint,
+    // NOTE: we can get 'y' coordinate from 'u', but Point.fromHex also wants 'x' coordinate oddity flag, and we cannot get 'x' without knowing 'v'
+    // Need to add generic conversion between twisted edwards and complimentary curve for JubJub
+    scalarMult,
+    scalarMultBase,
+    // NOTE: these function work on complimentary montgomery curve
+    getSharedSecret: (privateKey: Hex, publicKey: Hex) => scalarMult(publicKey, privateKey),
+    getPublicKey: (privateKey: Hex): Uint8Array => scalarMultBase(privateKey),
+  };
+
+  /**
+   * Calculates X25519 DH shared secret from ed25519 private & public keys.
+   * Curve25519 used in X25519 consumes private keys as-is, while ed25519 hashes them with sha512.
+   * Which means we will need to normalize ed25519 seeds to "hashed repr".
+   * @param privateKey ed25519 private key
+   * @param publicKey ed25519 public key
+   * @returns X25519 shared key
+   */
+  function getSharedSecret(privateKey: PrivKey, publicKey: Hex): Uint8Array {
+    const { head } = getExtendedPublicKey(privateKey);
+    const u = montgomeryCurve.UfromPoint(Point.fromHex(publicKey));
+    return montgomeryCurve.getSharedSecret(head, u);
+  }
+
   const utils = {
     getExtendedPublicKey,
     mod: modP,
@@ -661,12 +867,7 @@ export function twistedEdwards(curveDef: CurveType): CurveFn {
      * @param hash hash output from sha512, or a similar function
      * @returns valid private scalar
      */
-    hashToPrivateScalar: (hash: Hex): bigint => {
-      hash = ensureBytes(hash);
-      if (hash.length < 40 || hash.length > 1024)
-        throw new Error('Expected 40-1024 bytes of private key as per FIPS 186');
-      return mod.mod(bytesToNumberLE(hash), CURVE_ORDER - _1n) + _1n;
-    },
+    hashToPrivateScalar: (hash: Hex): bigint => hashToPrivateScalar(hash, CURVE_ORDER, true),
 
     /**
      * ed25519 private keys are uniform 32-bit strings. We do not need to check for
@@ -690,6 +891,8 @@ export function twistedEdwards(curveDef: CurveType): CurveFn {
 
   return {
     CURVE,
+    montgomeryCurve,
+    getSharedSecret,
     ExtendedPoint,
     Point,
     Signature,

src/modular.ts

@@ -99,7 +99,6 @@ export function legendre(num: bigint, fieldPrime: bigint): bigint {
 
 /**
  * Calculates square root of a number in a finite field.
- * Used to calculate y - the square root of y².
  */
 export function sqrt(number: bigint, modulo: bigint): bigint {
   const n = number;
@@ -109,6 +108,7 @@ export function sqrt(number: bigint, modulo: bigint): bigint {
   // P = 3 (mod 4)
   // sqrt n = n^((P+1)/4)
   if (P % _4n === _3n) return pow(n, p1div4, P);
+
   // P = 5 (mod 8)
   if (P % _8n === _5n) {
     const n2 = mod(n * _2n, P);

src/utils.ts

@@ -2,6 +2,9 @@
 // Convert between types
 // ---------------------
 
+type Hex = string | Uint8Array;
+import * as mod from './modular.js';
+
 const hexes = Array.from({ length: 256 }, (v, i) => i.toString(16).padStart(2, '0'));
 export function bytesToHex(uint8a: Uint8Array): string {
   if (!(uint8a instanceof Uint8Array)) throw new Error('Expected Uint8Array');
@@ -44,15 +47,19 @@ export function hexToBytes(hex: string): Uint8Array {
 }
 
 // Big Endian
-export function bytesToNumber(bytes: Uint8Array): bigint {
+export function bytesToNumberBE(bytes: Uint8Array): bigint {
   return hexToNumber(bytesToHex(bytes));
 }
+export function bytesToNumberLE(uint8a: Uint8Array): bigint {
+  if (!(uint8a instanceof Uint8Array)) throw new Error('Expected Uint8Array');
+  return BigInt('0x' + bytesToHex(Uint8Array.from(uint8a).reverse()));
+}
 
 export const numberToBytesBE = (n: bigint, len: number) =>
   hexToBytes(n.toString(16).padStart(len * 2, '0'));
 export const numberToBytesLE = (n: bigint, len: number) => numberToBytesBE(n, len).reverse();
 
-export function ensureBytes(hex: string | Uint8Array, expectedLength?: number): Uint8Array {
+export function ensureBytes(hex: Hex, expectedLength?: number): Uint8Array {
   // Uint8Array.from() instead of hash.slice() because node.js Buffer
   // is instance of Uint8Array, and its slice() creates **mutable** copy
   const bytes = hex instanceof Uint8Array ? Uint8Array.from(hex) : hexToBytes(hex);
@@ -82,3 +89,19 @@ export function nLength(n: bigint, nBitLength?: number) {
   const nByteLength = Math.ceil(_nBitLength / 8);
   return { nBitLength: _nBitLength, nByteLength };
 }
+
+/**
+ * Can take (n+8) or more bytes of uniform input e.g. from CSPRNG or KDF
+ * and convert them into private scalar, with the modulo bias being neglible.
+ * As per FIPS 186 B.4.1.
+ * @param hash hash output from sha512, or a similar function
+ * @returns valid private scalar
+ */
+const _1n = BigInt(1);
+export function hashToPrivateScalar(hash: Hex, CURVE_ORDER: bigint, isLE = false): bigint {
+  hash = ensureBytes(hash);
+  if (hash.length < 40 || hash.length > 1024)
+    throw new Error('Expected 40-1024 bytes of private key as per FIPS 186');
+  const num = isLE ? bytesToNumberLE(hash) : bytesToNumberBE(hash);
+  return mod.mod(num, CURVE_ORDER - _1n) + _1n;
+}

src/weierstrass.ts

@@ -12,13 +12,14 @@
 import * as mod from './modular.js';
 import {
   bytesToHex,
-  bytesToNumber,
+  bytesToNumberBE,
   concatBytes,
   ensureBytes,
   hexToBytes,
   hexToNumber,
   numberToHexUnpadded,
   nLength,
+  hashToPrivateScalar,
 } from './utils.js';
 import { wNAF } from './group.js';
 
@@ -131,7 +132,7 @@ function parseDERInt(data: Uint8Array) {
   if (res[0] === 0x00 && res[1] <= 0x7f) {
     throw new DERError('Invalid signature integer: trailing length');
   }
-  return { data: bytesToNumber(res), left: data.subarray(len + 2) };
+  return { data: bytesToNumberBE(res), left: data.subarray(len + 2) };
 }
 
 function parseDERSignature(data: Uint8Array) {
@@ -214,8 +215,8 @@ export interface JacobianPointType {
   double(): JacobianPointType;
   add(other: JacobianPointType): JacobianPointType;
   subtract(other: JacobianPointType): JacobianPointType;
-  multiplyUnsafe(scalar: bigint): JacobianPointType;
   multiply(scalar: number | bigint, affinePoint?: PointType): JacobianPointType;
+  multiplyUnsafe(scalar: bigint): JacobianPointType;
   toAffine(invZ?: bigint): PointType;
 }
 // Static methods
@@ -392,7 +393,7 @@ export function weierstrass(curveDef: CurveType): CurveFn {
       num = hexToNumber(key);
     } else if (key instanceof Uint8Array) {
       if (key.length !== groupLen) throw new Error(`Expected ${groupLen} bytes of private key`);
-      num = bytesToNumber(key);
+      num = bytesToNumberBE(key);
     } else {
       throw new TypeError('Expected valid private key');
     }
@@ -435,7 +436,7 @@ export function weierstrass(curveDef: CurveType): CurveFn {
     const { n, nBitLength } = CURVE;
     const byteLength = hash.length;
     const delta = byteLength * 8 - nBitLength; // size of curve.n (252 bits)
-    let h = bytesToNumber(hash);
+    let h = bytesToNumberBE(hash);
     if (delta > 0) h = h >> BigInt(delta);
     if (!truncateOnly && h >= n) h -= n;
     return h;
@@ -720,7 +721,7 @@ export function weierstrass(curveDef: CurveType): CurveFn {
      */
     private static fromCompressedHex(bytes: Uint8Array) {
       const P = CURVE.P;
-      const x = bytesToNumber(bytes.subarray(1));
+      const x = bytesToNumberBE(bytes.subarray(1));
       if (!isValidFieldElement(x)) throw new Error('Point is not on curve');
       const y2 = weierstrassEquation(x); // y² = x³ + ax + b
       let y = sqrtModCurve(y2, P); // y = y² ^ (p+1)/4
@@ -734,8 +735,8 @@ export function weierstrass(curveDef: CurveType): CurveFn {
     }
 
     private static fromUncompressedHex(bytes: Uint8Array) {
-      const x = bytesToNumber(bytes.subarray(1, fieldLen + 1));
-      const y = bytesToNumber(bytes.subarray(fieldLen + 1, 2 * fieldLen + 1));
+      const x = bytesToNumberBE(bytes.subarray(1, fieldLen + 1));
+      const y = bytesToNumberBE(bytes.subarray(fieldLen + 1, 2 * fieldLen + 1));
       const point = new Point(x, y);
       point.assertValidity();
       return point;
@@ -962,15 +963,7 @@ export function weierstrass(curveDef: CurveType): CurveFn {
      * @param hash hash output from sha512, or a similar function
      * @returns valid private key
      */
-    hashToPrivateKey: (hash: Hex): Uint8Array => {
-      hash = ensureBytes(hash);
-      const minLen = fieldLen + 8;
-      if (hash.length < minLen || hash.length > 1024) {
-        throw new Error(`Expected ${minLen}-1024 bytes of private key as per FIPS 186`);
-      }
-      const num = mod.mod(bytesToNumber(hash), CURVE_ORDER - _1n) + _1n;
-      return numToField(num);
-    },
+    hashToPrivateKey: (hash: Hex): Uint8Array => numToField(hashToPrivateScalar(hash, CURVE_ORDER)),
 
     // Takes curve order + 64 bits from CSPRNG
     // so that modulo bias is neglible, matches FIPS 186 B.4.1.
@@ -1035,7 +1028,7 @@ export function weierstrass(curveDef: CurveType): CurveFn {
   // RFC6979 methods
   function bits2int(bytes: Uint8Array) {
     const slice = bytes.length > fieldLen ? bytes.slice(0, fieldLen) : bytes;
-    return bytesToNumber(slice);
+    return bytesToNumberBE(slice);
   }
   function bits2octets(bytes: Uint8Array): Uint8Array {
     const z1 = bits2int(bytes);