edwards: change API. Add options.strict, context. Add edwardsToMontgomery

src/abstract/edwards.ts

@@ -18,7 +18,7 @@ export type CurveType = BasicCurve<bigint> & {
   adjustScalarBytes?: (bytes: Uint8Array) => Uint8Array; // clears bits to get valid field elemtn
   domain?: (data: Uint8Array, ctx: Uint8Array, phflag: boolean) => Uint8Array; // Used for hashing
   uvRatio?: (u: bigint, v: bigint) => { isValid: boolean; value: bigint }; // Ratio √(u/v)
-  preHash?: FHash; // RFC 8032 pre-hashing of messages to sign() / verify()
+  prehash?: FHash; // RFC 8032 pre-hashing of messages to sign() / verify()
   mapToCurve?: (scalar: bigint[]) => AffinePoint<bigint>; // for hash-to-curve standard
 };
 
@@ -90,7 +90,15 @@ export type CurveFn = {
 // It is not generic twisted curve for now, but ed25519/ed448 generic implementation
 export function twistedEdwards(curveDef: CurveType): CurveFn {
   const CURVE = validateOpts(curveDef) as ReturnType<typeof validateOpts>;
-  const { Fp, n: CURVE_ORDER, preHash, hash: cHash, randomBytes, nByteLength, h: cofactor } = CURVE;
+  const {
+    Fp,
+    n: CURVE_ORDER,
+    prehash: preHash,
+    hash: cHash,
+    randomBytes,
+    nByteLength,
+    h: cofactor,
+  } = CURVE;
   const MASK = _2n ** BigInt(nByteLength * 8);
   const modP = Fp.create; // Function overrides
 
@@ -423,29 +431,30 @@ export function twistedEdwards(curveDef: CurveType): CurveFn {
   }
 
   /** Signs message with privateKey. RFC8032 5.1.6 */
-  function sign(msg: Hex, privKey: Hex, context?: Hex): Uint8Array {
+  function sign(msg: Hex, privKey: Hex, options: { context?: Hex } = {}): Uint8Array {
     msg = ensureBytes('message', msg);
     if (preHash) msg = preHash(msg); // for ed25519ph etc.
     const { prefix, scalar, pointBytes } = getExtendedPublicKey(privKey);
-    const r = hashDomainToScalar(context, prefix, msg); // r = dom2(F, C) || prefix || PH(M)
+    const r = hashDomainToScalar(options.context, prefix, msg); // r = dom2(F, C) || prefix || PH(M)
     const R = G.multiply(r).toRawBytes(); // R = rG
-    const k = hashDomainToScalar(context, R, pointBytes, msg); // R || A || PH(M)
+    const k = hashDomainToScalar(options.context, R, pointBytes, msg); // R || A || PH(M)
     const s = modN(r + k * scalar); // S = (r + k * s) mod L
     assertGE0(s); // 0 <= s < l
     const res = ut.concatBytes(R, ut.numberToBytesLE(s, Fp.BYTES));
     return ensureBytes('result', res, nByteLength * 2); // 64-byte signature
   }
 
-  function verify(sig: Hex, msg: Hex, publicKey: Hex, context?: Hex): boolean {
+  const verifyOpts: { context?: Hex; strict?: boolean } = { strict: false };
+  function verify(sig: Hex, msg: Hex, publicKey: Hex, options = verifyOpts): boolean {
     const len = Fp.BYTES; // Verifies EdDSA signature against message and public key. RFC8032 5.1.7.
     sig = ensureBytes('signature', sig, 2 * len); // An extended group equation is checked.
     msg = ensureBytes('message', msg); // ZIP215 compliant, which means not fully RFC8032 compliant.
     if (preHash) msg = preHash(msg); // for ed25519ph, etc
     const A = Point.fromHex(publicKey, false); // Check for s bounds, hex validity
-    const R = Point.fromHex(sig.slice(0, len), false); // 0 <= R < 2^256: ZIP215 R can be >= P
+    const R = Point.fromHex(sig.slice(0, len), options.strict); // R <P (RFC8032) or <2^256 (ZIP215)
     const s = ut.bytesToNumberLE(sig.slice(len, 2 * len));
     const SB = G.multiplyUnsafe(s); // 0 <= s < l is done inside
-    const k = hashDomainToScalar(context, R.toRawBytes(), A.toRawBytes(), msg);
+    const k = hashDomainToScalar(options.context, R.toRawBytes(), A.toRawBytes(), msg);
     const RkA = R.add(A.multiplyUnsafe(k));
     // [8][S]B = [8]R + [8][k]A'
     return RkA.subtract(SB).clearCofactor().equals(Point.ZERO);

src/ed25519.ts

@@ -95,7 +95,7 @@ export const ED25519_TORSION_SUBGROUP = [
 
 const Fp = Field(ED25519_P, undefined, true);
 
-const ED25519_DEF = {
+const ed25519Defaults = {
   // Param: a
   a: BigInt(-1),
   // Equal to -121665/121666 over finite field.
@@ -120,7 +120,7 @@ const ED25519_DEF = {
   uvRatio,
 } as const;
 
-export const ed25519 = twistedEdwards(ED25519_DEF);
+export const ed25519 = twistedEdwards(ed25519Defaults);
 function ed25519_domain(data: Uint8Array, ctx: Uint8Array, phflag: boolean) {
   if (ctx.length > 255) throw new Error('Context is too big');
   return concatBytes(
@@ -130,11 +130,11 @@ function ed25519_domain(data: Uint8Array, ctx: Uint8Array, phflag: boolean) {
     data
   );
 }
-export const ed25519ctx = twistedEdwards({ ...ED25519_DEF, domain: ed25519_domain });
+export const ed25519ctx = twistedEdwards({ ...ed25519Defaults, domain: ed25519_domain });
 export const ed25519ph = twistedEdwards({
-  ...ED25519_DEF,
+  ...ed25519Defaults,
   domain: ed25519_domain,
-  preHash: sha512,
+  prehash: sha512,
 });
 
 export const x25519 = montgomery({
@@ -153,6 +153,20 @@ export const x25519 = montgomery({
   randomBytes,
 });
 
+/**
+ * Converts ed25519 public key to x25519 public key. Uses formula:
+ * * `(u, v) = ((1+y)/(1-y), sqrt(-486664)*u/x)`
+ * * `(x, y) = (sqrt(-486664)*u/v, (u-1)/(u+1))`
+ * @example
+ *   const aPub = ed25519.getPublicKey(utils.randomPrivateKey());
+ *   x25519.getSharedSecret(edwardsToMontgomery(aPub), edwardsToMontgomery(someonesPub))
+ */
+export function edwardsToMontgomery(edwardsPub: Hex): Uint8Array {
+  const { y } = ed25519.ExtendedPoint.fromHex(edwardsPub);
+  const _1n = BigInt(1);
+  return Fp.toBytes(Fp.create((y - _1n) * Fp.inv(y + _1n)));
+}
+
 // Hash To Curve Elligator2 Map (NOTE: different from ristretto255 elligator)
 // NOTE: very important part is usage of FpSqrtEven for ELL2_C1_EDWARDS, since
 // SageMath returns different root first and everything falls apart

src/ed448.ts

@@ -120,7 +120,7 @@ const ED448_DEF = {
 
 export const ed448 = twistedEdwards(ED448_DEF);
 // NOTE: there is no ed448ctx, since ed448 supports ctx by default
-export const ed448ph = twistedEdwards({ ...ED448_DEF, preHash: shake256_64 });
+export const ed448ph = twistedEdwards({ ...ED448_DEF, prehash: shake256_64 });
 
 export const x448 = montgomery({
   a: BigInt(156326),
@@ -136,22 +136,22 @@ export const x448 = montgomery({
   },
   adjustScalarBytes,
   randomBytes,
-  // The 4-isogeny maps between the Montgomery curve and this Edwards
-  // curve are:
-  //   (u, v) = (y^2/x^2, (2 - x^2 - y^2)*y/x^3)
-  //   (x, y) = (4*v*(u^2 - 1)/(u^4 - 2*u^2 + 4*v^2 + 1),
-  //             -(u^5 - 2*u^3 - 4*u*v^2 + u)/
-  //             (u^5 - 2*u^2*v^2 - 2*u^3 - 2*v^2 + u))
-  // xyToU: (p: PointType) => {
-  //   const P = ed448P;
-  //   const { x, y } = p;
-  //   if (x === _0n) throw new Error(`Point with x=0 doesn't have mapping`);
-  //   const invX = invert(x * x, P); // x^2
-  //   const u = mod(y * y * invX, P); // (y^2/x^2)
-  //   return numberToBytesLE(u, 56);
-  // },
 });
 
+/**
+ * Converts edwards448 public key to x448 public key. Uses formula:
+ * * `(u, v) = ((y-1)/(y+1), sqrt(156324)*u/x)`
+ * * `(x, y) = (sqrt(156324)*u/v, (1+u)/(1-u))`
+ * @example
+ *   const aPub = ed448.getPublicKey(utils.randomPrivateKey());
+ *   x448.getSharedSecret(edwardsToMontgomery(aPub), edwardsToMontgomery(someonesPub))
+ */
+export function edwardsToMontgomery(edwardsPub: string | Uint8Array): Uint8Array {
+  const { y } = ed448.ExtendedPoint.fromHex(edwardsPub);
+  const _1n = BigInt(1);
+  return Fp.toBytes(Fp.create((y - _1n) * Fp.inv(y + _1n)));
+}
+
 // Hash To Curve Elligator2 Map
 const ELL2_C1 = (Fp.ORDER - BigInt(3)) / BigInt(4); // 1. c1 = (q - 3) / 4         # Integer arithmetic
 const ELL2_J = BigInt(156326);

test/ed25519-addons.test.js

@@ -62,8 +62,14 @@ describe('RFC8032ctx', () => {
     const v = VECTORS_RFC8032_CTX[i];
     should(`${i}`, () => {
       deepStrictEqual(hex(ed25519ctx.getPublicKey(v.secretKey)), v.publicKey);
-      deepStrictEqual(hex(ed25519ctx.sign(v.message, v.secretKey, v.context)), v.signature);
+      deepStrictEqual(
-      deepStrictEqual(ed25519ctx.verify(v.signature, v.message, v.publicKey, v.context), true);
+        hex(ed25519ctx.sign(v.message, v.secretKey, { context: v.context })),
+        v.signature
+      );
+      deepStrictEqual(
+        ed25519ctx.verify(v.signature, v.message, v.publicKey, { context: v.context }),
+        true
+      );
     });
   }
 });
@@ -93,14 +99,7 @@ describe('RFC8032ph', () => {
 });
 
 // x25519
-should('X25519 base point', () => {
+describe('RFC7748 X25519 ECDH', () => {
-  const { y } = ed25519ph.ExtendedPoint.BASE;
-  const { Fp } = ed25519ph.CURVE;
-  const u = Fp.create((y + 1n) * Fp.inv(1n - y));
-  deepStrictEqual(numberToBytesLE(u, 32), x25519.GuBytes);
-});
-
-describe('RFC7748', () => {
   const rfc7748Mul = [
     {
       scalar: 'a546e36bf0527c9d3b16154b82465edd62144c0ac1fc5a18506a2244ba449ac4',
@@ -127,7 +126,7 @@ describe('RFC7748', () => {
   ];
   for (let i = 0; i < rfc7748Iter.length; i++) {
     const { scalar, iters } = rfc7748Iter[i];
-    should(`scalarMult iteration (${i})`, () => {
+    should(`scalarMult iteration x${iters}`, () => {
       let k = x25519.GuBytes;
       for (let i = 0, u = k; i < iters; i++) [k, u] = [x25519.scalarMult(k, u), k];
       deepStrictEqual(hex(k), scalar);
@@ -145,10 +144,16 @@ describe('RFC7748', () => {
     deepStrictEqual(hex(x25519.scalarMult(alicePrivate, bobPublic)), shared);
     deepStrictEqual(hex(x25519.scalarMult(bobPrivate, alicePublic)), shared);
   });
-});
+
-describe('Wycheproof', () => {
+  should('base point', () => {
+    const { y } = ed25519ph.ExtendedPoint.BASE;
+    const { Fp } = ed25519ph.CURVE;
+    const u = Fp.create((y + 1n) * Fp.inv(1n - y));
+    deepStrictEqual(numberToBytesLE(u, 32), x25519.GuBytes);
+  });
+
   const group = x25519vectors.testGroups[0];
-  should(`X25519`, () => {
+  should('wycheproof', () => {
     for (let i = 0; i < group.tests.length; i++) {
       const v = group.tests[i];
       const comment = `(${i}, ${v.result}) ${v.comment}`;

test/ed448.test.js

@@ -513,8 +513,11 @@ describe('ed448', () => {
       const v = VECTORS_RFC8032_CTX[i];
       should(`${i}`, () => {
         deepStrictEqual(hex(ed.getPublicKey(v.secretKey)), v.publicKey);
-        deepStrictEqual(hex(ed.sign(v.message, v.secretKey, v.context)), v.signature);
+        deepStrictEqual(hex(ed.sign(v.message, v.secretKey, { context: v.context })), v.signature);
-        deepStrictEqual(ed.verify(v.signature, v.message, v.publicKey, v.context), true);
+        deepStrictEqual(
+          ed.verify(v.signature, v.message, v.publicKey, { context: v.context }),
+          true
+        );
       });
     }
   });
@@ -559,8 +562,14 @@ describe('ed448', () => {
       const v = VECTORS_RFC8032_PH[i];
       should(`${i}`, () => {
         deepStrictEqual(hex(ed448ph.getPublicKey(v.secretKey)), v.publicKey);
-        deepStrictEqual(hex(ed448ph.sign(v.message, v.secretKey, v.context)), v.signature);
+        deepStrictEqual(
-        deepStrictEqual(ed448ph.verify(v.signature, v.message, v.publicKey, v.context), true);
+          hex(ed448ph.sign(v.message, v.secretKey, { context: v.context })),
+          v.signature
+        );
+        deepStrictEqual(
+          ed448ph.verify(v.signature, v.message, v.publicKey, { context: v.context }),
+          true
+        );
       });
     }
   });
@@ -661,9 +670,8 @@ describe('ed448', () => {
       deepStrictEqual(hex(x448.scalarMult(bobPrivate, alicePublic)), shared);
     });
 
-    describe('wycheproof', () => {
+    should('wycheproof', () => {
       const group = x448vectors.testGroups[0];
-      should(`X448`, () => {
       for (let i = 0; i < group.tests.length; i++) {
         const v = group.tests[i];
         const index = `(${i}, ${v.result}) ${v.comment}`;
@@ -689,7 +697,6 @@ describe('ed448', () => {
         } else throw new Error('unknown test result');
       }
     });
-    });
 
     should('have proper base point', () => {
       const { x, y } = Point.BASE;