montgomery: add randomPrivateKey. Add ecdh benchmark.

README.md

@@ -66,10 +66,6 @@ secp256k1.verify(sig, msg, pub) === true;
 
 const privHex = '46c930bc7bb4db7f55da20798697421b98c4175a52c630294d75a84b9c126236';
 const pub2 = secp256k1.getPublicKey(privHex); // keys & other inputs can be Uint8Array-s or hex strings
-
-// Follows hash-to-curve specification to encode arbitrary hashes to EC points
-import { hashToCurve, encodeToCurve } from '@noble/curves/secp256k1';
-hashToCurve('0102abcd');
 ```
 
 All curves:
@@ -180,10 +176,9 @@ const signatures3 = privateKeys.map((p, i) => bls.sign(messages[i], p));
 const aggSignature3 = bls.aggregateSignatures(signatures3);
 const isValid3 = bls.verifyBatch(aggSignature3, messages, publicKeys);
 console.log({ publicKeys, signatures3, aggSignature3, isValid3 });
+// bls.pairing(PointG1, PointG2) // pairings
 
-// Pairings
-// bls.pairing(PointG1, PointG2)
-// Also, check out hash-to-curve examples below.
+// hash-to-curve examples can be seen below
 ```
 
 ## Abstract API
@@ -482,9 +477,11 @@ Every curve has exported `hashToCurve` and `encodeToCurve` methods:
 ```ts
 import { hashToCurve, encodeToCurve } from '@noble/curves/secp256k1';
 import { randomBytes } from '@noble/hashes/utils';
+hashToCurve('0102abcd');
 console.log(hashToCurve(randomBytes()));
 console.log(encodeToCurve(randomBytes()));
 
+
 import { bls12_381 } from '@noble/curves/bls12-381';
 bls12_381.G1.hashToCurve(randomBytes(), { DST: 'another' });
 bls12_381.G2.hashToCurve(randomBytes(), { DST: 'custom' });
@@ -674,6 +671,14 @@ pedersen x 884 ops/sec @ 1ms/op
 poseidon x 8,598 ops/sec @ 116μs/op
 verify x 528 ops/sec @ 1ms/op
 
+ecdh
+├─x25519 x 1,337 ops/sec @ 747μs/op
+├─secp256k1 x 461 ops/sec @ 2ms/op
+├─P256 x 441 ops/sec @ 2ms/op
+├─P384 x 179 ops/sec @ 5ms/op
+├─P521 x 93 ops/sec @ 10ms/op
+└─x448 x 496 ops/sec @ 2ms/op
+
 bls12-381
 init x 32 ops/sec @ 30ms/op
 getPublicKey 1-bit x 858 ops/sec @ 1ms/op

benchmark/ecdh.js

@@ -0,0 +1,19 @@
+import { run, mark, compare, utils } from 'micro-bmark';
+import { generateData } from './_shared.js';
+import { secp256k1 } from '../secp256k1.js';
+import { P256 } from '../p256.js';
+import { P384 } from '../p384.js';
+import { P521 } from '../p521.js';
+import { x25519 } from '../ed25519.js';
+import { x448 } from '../ed448.js';
+
+run(async () => {
+  const curves = { x25519, secp256k1, P256, P384, P521, x448 };
+  const fns = {};
+  for (let [k, c] of Object.entries(curves)) {
+    const pubB = c.getPublicKey(c.utils.randomPrivateKey());
+    const privA = c.utils.randomPrivateKey();
+    fns[k] = () => c.getSharedSecret(privA, pubB);
+  }
+  await compare('ecdh', 1000, fns);
+});

package.json

@@ -12,7 +12,7 @@
     "*.d.ts.map"
   ],
   "scripts": {
-    "bench": "cd benchmark; node secp256k1.js; node curves.js; node stark.js; node bls.js",
+    "bench": "cd benchmark; node secp256k1.js; node curves.js; node ecdh.js; node stark.js; node bls.js",
     "build": "tsc && tsc -p tsconfig.esm.json",
     "build:release": "rollup -c rollup.config.js",
     "lint": "prettier --check 'src/**/*.{js,ts}' 'test/*.js'",

src/abstract/montgomery.ts

@@ -16,12 +16,14 @@ export type CurveType = {
   powPminus2?: (x: bigint) => bigint;
   xyToU?: (x: bigint, y: bigint) => bigint;
   Gu: bigint;
+  randomBytes?: (bytesLength?: number) => Uint8Array;
 };
 export type CurveFn = {
   scalarMult: (scalar: Hex, u: Hex) => Uint8Array;
   scalarMultBase: (scalar: Hex) => Uint8Array;
   getSharedSecret: (privateKeyA: Hex, publicKeyB: Hex) => Uint8Array;
   getPublicKey: (privateKey: Hex) => Uint8Array;
+  utils: { randomPrivateKey: () => Uint8Array; };
   GuBytes: Uint8Array;
 };
 
@@ -181,6 +183,7 @@ export function montgomery(curveDef: CurveType): CurveFn {
     scalarMultBase,
     getSharedSecret: (privateKey: Hex, publicKey: Hex) => scalarMult(privateKey, publicKey),
     getPublicKey: (privateKey: Hex): Uint8Array => scalarMultBase(privateKey),
+    utils: { randomPrivateKey: () => CURVE.randomBytes!(CURVE.nByteLength) },
     GuBytes: GuBytes,
   };
 }

src/ed25519.ts

@@ -149,6 +149,7 @@ export const x25519 = montgomery({
     return mod(pow2(pow_p_5_8, BigInt(3), P) * b2, P);
   },
   adjustScalarBytes,
+  randomBytes,
 });
 
 // Hash To Curve Elligator2 Map (NOTE: different from ristretto255 elligator)

src/ed448.ts

@@ -134,6 +134,7 @@ export const x448 = montgomery({
     return mod(Pminus3 * x, P); // Pminus3 * x = Pminus2
   },
   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)