Implement ElligatorSwift

src/secp256k1.ts

@@ -1,7 +1,7 @@
 /*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
 import { sha256 } from '@noble/hashes/sha256';
 import { randomBytes } from '@noble/hashes/utils';
-import { Field, mod, pow2 } from './abstract/modular.js';
+import { Field, mod, pow2, FpIsSquare } from './abstract/modular.js';
 import { ProjPointType as PointType, mapToCurveSimpleSWU } from './abstract/weierstrass.js';
 import type { Hex, PrivKey } from './abstract/utils.js';
 import { bytesToNumberBE, concatBytes, ensureBytes, numberToBytesBE } from './abstract/utils.js';
@@ -272,3 +272,129 @@ const htf = /* @__PURE__ */ (() =>
   ))();
 export const hashToCurve = /* @__PURE__ */ (() => htf.hashToCurve)();
 export const encodeToCurve = /* @__PURE__ */ (() => htf.encodeToCurve)();
+
+// ElligatorSwift: Schnorr-like x-only ECDH with public keys indistinguishable
+// from uniformly random bytes.
+// https://github.com/bitcoin/bips/blob/master/bip-0324.mediawiki,
+// https://github.com/bitcoin/bitcoin/blob/master/src/secp256k1/doc/ellswift.md
+// SwiftEC: Shallue-van de Woestijne Indifferentiable Function to Elliptic Curves.
+// https://eprint.iacr.org/2022/759.pdf
+//
+// Curve25519 & P-521 are incompatible with SwiftEC. Differences from SwiftEC:
+// - undefined inputs are remapped
+// - y-parity is encoded in u/t values
+const MINUS_3_SQRT = Fp.sqrt(Fp.create(BigInt(-3)));
+const _3n = BigInt(3);
+const _4n = BigInt(4);
+const _7n = BigInt(7);
+const isSquare = FpIsSquare(Fp);
+const isValidX = (x: bigint) => isSquare(Fp.add(Fp.mul(Fp.mul(x, x), x), _7n));
+const trySqrt = (x: bigint): bigint | void => {
+  try {
+    return Fp.sqrt(x);
+  } catch (_e) {}
+};
+
+export const elligatorSwift = /* @__PURE__ */ {
+  // (internal stuff, exported for tests only): decode(u, _inv(x, u)) = x
+  _inv: (x: bigint, u: bigint, ellCase: number): bigint | void => {
+    if (!Number.isSafeInteger(ellCase) || ellCase < 0 || ellCase > 7)
+      throw new Error(`elligatorSwift._inv: wrong case=${ellCase}`);
+    let v: bigint, s: bigint;
+    // Most rejections happens in 3 condition (in comments, ~33% each)
+    const u2 = Fp.mul(u, u); // u**2
+    const u3 = Fp.mul(u2, u); // u**3
+    if ((ellCase & 2) === 0) {
+      if (isValidX(Fp.sub(Fp.neg(x), u))) return; // [1 condition]
+      v = x;
+      s = Fp.div(Fp.neg(Fp.add(u3, _7n)), Fp.add(Fp.add(u2, Fp.mul(u, v)), Fp.mul(v, v))); // = -(u**3 + 7) / (u**2 + u*v + v**2)
+    } else {
+      s = Fp.sub(x, u); // x - u
+      if (Fp.is0(s)) return;
+      const t0 = Fp.add(u3, _7n); // (u**3 + 7)
+      const t1 = Fp.mul(Fp.mul(_3n, s), u2); // 3 * s * u**2
+      // r = (-s * (4 * (u**3 + 7) + 3 * s * u**2)).sqrt()
+      const r = trySqrt(Fp.mul(Fp.neg(s), Fp.add(Fp.mul(_4n, t0), t1)));
+      if (r === undefined) return; // [2 condition]
+      if (ellCase & 1 && Fp.is0(r)) return;
+      v = Fp.div(Fp.add(Fp.neg(u), Fp.div(r, s)), _2n); // v = (-u + r / s) / 2
+    }
+    const w = trySqrt(s);
+    if (w === undefined) return; // [3 condition]
+    const last = ellCase & 5; // ellCase = 0..8, last = 0,1,4,5
+    const t0 = last & 1 ? Fp.add(_1n, MINUS_3_SQRT) : Fp.sub(_1n, MINUS_3_SQRT);
+    const w0 = last === 0 || last === 5 ? Fp.neg(w) : w; // -w | w
+    // w0 * (u * t0 / 2 + v)
+    return Fp.mul(w0, Fp.add(Fp.div(Fp.mul(u, t0), _2n), v));
+  },
+  // Encode public key (point or x coordinate bigint) into 64-byte pseudorandom encoding
+  encode: (x: bigint | PointType<bigint>): Uint8Array => {
+    if (x instanceof secp256k1.ProjectivePoint) x = x.x;
+    if (typeof x !== 'bigint') {
+      throw new Error(
+        'elligatorSwift.encode: wrong public key. Should be Projective point or x coordinate (bigint)'
+      );
+    }
+    // 200k test cycles per keygen: avg=4 max=48
+    // seems too much, but same as for reference implementation
+    while (true) {
+      // random scalar 1..Fp.ORDER
+      const u = Fp.create(Fp.fromBytes(secp256k1.utils.randomPrivateKey()));
+      const ellCase = randomBytes(1)[0] & 7; // [0..8)
+      const t = elligatorSwift._inv(x, u, ellCase);
+      if (!t) continue;
+      return concatBytes(numberToBytesBE(u, 32), numberToBytesBE(t, 32));
+    }
+  },
+  // Decode elligatorSwift point to xonly
+  decode: (data: Hex): Uint8Array => {
+    const _data = ensureBytes('data', data, 64);
+    let u = Fp.create(Fp.fromBytes(_data.subarray(0, 32)));
+    let t = Fp.create(Fp.fromBytes(_data.subarray(32, 64)));
+    if (Fp.is0(u)) u = Fp.create(_1n);
+    if (Fp.is0(t)) t = Fp.create(_1n);
+    const u3 = Fp.mul(Fp.mul(u, u), u); // u**3
+    const u3plus7 = Fp.add(u3, _7n);
+    // u**3 + t**2 + 7 == 0 -> t = 2 * t
+    if (Fp.is0(Fp.add(u3plus7, Fp.mul(t, t)))) t = Fp.add(t, t);
+    // X = (u**3 + 7 - t**2) / (2 * t)
+    const x = Fp.div(Fp.sub(u3plus7, Fp.mul(t, t)), Fp.add(t, t));
+    // Y = (X + t) / (MINUS_3_SQRT * u);
+    const y = Fp.div(Fp.add(x, t), Fp.mul(MINUS_3_SQRT, u));
+    // try different cases
+    let res = Fp.add(u, Fp.mul(Fp.mul(y, y), _4n)); // u + 4 * Y ** 2,
+    if (isValidX(res)) return numberToBytesBE(res, 32);
+    res = Fp.div(Fp.sub(Fp.div(Fp.neg(x), y), u), _2n); // (-X / Y - u) / 2
+    if (isValidX(res)) return numberToBytesBE(res, 32);
+    res = Fp.div(Fp.sub(Fp.div(x, y), u), _2n); // (X / Y - u) / 2
+    if (isValidX(res)) return numberToBytesBE(res, 32);
+    throw new Error('elligatorSwift: cannot decode public key');
+  },
+  // Generate pair (public key, secret key)
+  keygen: () => {
+    const privateKey = secp256k1.utils.randomPrivateKey();
+    const publicKey = elligatorSwift.encode(Point.fromPrivateKey(privateKey));
+    return { privateKey, publicKey };
+  },
+  // Generates shared secret between a pub key and a priv key
+  getSharedSecret: (privateKeyA: Hex, publicKeyB: Hex) => {
+    const pub = elligatorSwift.decode(publicKeyB);
+    const priv = ensureBytes('privKey', privateKeyA, 32);
+    const point = lift_x(Fp.fromBytes(pub));
+    const d = bytesToNumberBE(priv);
+    return numberToBytesBE(point.multiply(d).x, 32);
+  },
+  // BIP324 shared secret
+  getSharedSecretBip324: (
+    privateKeyOurs: Hex,
+    publicKeyTheirs: Hex,
+    publicKeyOurs: Hex,
+    initiating: boolean
+  ) => {
+    const ours = ensureBytes('publicKeyOurs', publicKeyOurs);
+    const theirs = ensureBytes('publicKeyTheirs', publicKeyTheirs);
+    const ecdhPoint = elligatorSwift.getSharedSecret(privateKeyOurs, theirs);
+    const pubs = initiating ? [ours, theirs] : [theirs, ours];
+    return taggedHash('bip324_ellswift_xonly_ecdh', ...pubs, ecdhPoint);
+  },
+};

test/index.test.js

@@ -9,6 +9,7 @@ import './ed25519.test.js';
 import './ed25519-addons.test.js';
 import './secp256k1.test.js';
 import './secp256k1-schnorr.test.js';
+import './secp256k1-bip-0324.test.js';
 import './jubjub.test.js';
 import './hash-to-curve.test.js';
 import './poseidon.test.js';

test/secp256k1-bip-0324.test.js

@@ -0,0 +1,122 @@
+import { deepStrictEqual } from 'assert';
+import { should, describe } from 'micro-should';
+import * as fs from 'fs';
+import {
+  hexToBytes,
+  hexToNumber,
+  concatBytes,
+  bytesToHex as toHex,
+} from '../esm/abstract/utils.js';
+// Generic tests for all curves in package
+import { secp256k1, elligatorSwift } from '../esm/secp256k1.js';
+// ESM is broken.
+import { dirname } from 'path';
+import { fileURLToPath } from 'url';
+export const __dirname = dirname(fileURLToPath(import.meta.url));
+
+// https://eprint.iacr.org/2022/759
+
+const parseCSV = (path) => {
+  const data = fs.readFileSync(`${__dirname}/vectors/secp256k1/${path}`, 'utf8');
+  const lines = data.split('\n').filter((i) => !!i);
+  const rows = lines.map((i) => i.trim().split(','));
+  const lengths = new Set(rows.map((i) => i.length));
+  if (lengths.size !== 1) throw new Error('wrong dimensions');
+  if (rows.length < 2) throw new Error('wrong rows length');
+  const [head, ...rest] = rows;
+  return rest.map((row) => Object.fromEntries(row.map((cell, j) => [head[j], cell])));
+};
+
+describe('ElligatorSwift', () => {
+  should('packet_encoding_test_vectors', () => {
+    for (const t of parseCSV('bip-0324/packet_encoding_test_vectors.csv')) {
+      const inPriv = hexToNumber(t['in_priv_ours']);
+      const pubX = secp256k1.ProjectivePoint.BASE.multiply(inPriv)
+        .x.toString(16)
+        .padStart(2 * 32, '0');
+      deepStrictEqual(pubX, t['mid_x_ours']);
+
+      const bytesOurs = hexToBytes(t['in_ellswift_ours']);
+      const decoded = elligatorSwift.decode(bytesOurs);
+      deepStrictEqual(toHex(decoded), t['mid_x_ours']);
+
+      const bytesTheirs = hexToBytes(t['in_ellswift_theirs']);
+      deepStrictEqual(toHex(elligatorSwift.decode(bytesTheirs)), t['mid_x_theirs']);
+
+      const xShared = elligatorSwift.getSharedSecret(t['in_priv_ours'], bytesTheirs);
+      deepStrictEqual(toHex(xShared), t['mid_x_shared']);
+
+      const sharedSecret = elligatorSwift.getSharedSecretBip324(
+        t['in_priv_ours'],
+        t['in_ellswift_theirs'],
+        t['in_ellswift_ours'],
+        t['in_initiating'] === '1'
+      );
+      deepStrictEqual(toHex(sharedSecret), t['mid_shared_secret']);
+    }
+  });
+
+  should('xswiftec_inv_test_vectors', () => {
+    for (const t of parseCSV('bip-0324/xswiftec_inv_test_vectors.csv')) {
+      const Fp = secp256k1.CURVE.Fp;
+      const u = Fp.create(Fp.fromBytes(hexToBytes(t['u'])));
+      const x = Fp.create(Fp.fromBytes(hexToBytes(t['x'])));
+      for (let c = 0; c < 8; c++) {
+        const name = `case${c}_t`;
+        const ret = elligatorSwift._inv(x, u, c);
+        if (!ret) deepStrictEqual(t[name], '', 'empty case');
+        else {
+          deepStrictEqual(toHex(Fp.toBytes(ret)), t[name], 'real case');
+          deepStrictEqual(
+            elligatorSwift.decode(concatBytes(Fp.toBytes(u), Fp.toBytes(ret))),
+            Fp.toBytes(x)
+          );
+        }
+      }
+    }
+  });
+
+  should('ellswift_decode_test_vectors', () => {
+    for (const t of parseCSV('bip-0324/ellswift_decode_test_vectors.csv')) {
+      deepStrictEqual(toHex(elligatorSwift.decode(t['ellswift'])), t['x']);
+    }
+  });
+  should('Example', () => {
+    // random, so test more.
+    for (let i = 0; i < 100; i++) {
+      const alice = elligatorSwift.keygen();
+      const bob = elligatorSwift.keygen();
+      // ECDH
+      const sharedAlice = elligatorSwift.getSharedSecret(alice.privateKey, bob.publicKey);
+      const sharedBob = elligatorSwift.getSharedSecret(bob.privateKey, alice.publicKey);
+      deepStrictEqual(sharedAlice, sharedBob);
+      // ECDH BIP324
+      const sharedAlice2 = elligatorSwift.getSharedSecretBip324(
+        alice.privateKey,
+        bob.publicKey,
+        alice.publicKey,
+        true
+      );
+      const sharedBob2 = elligatorSwift.getSharedSecretBip324(
+        bob.privateKey,
+        alice.publicKey,
+        bob.publicKey,
+        false
+      );
+      deepStrictEqual(sharedAlice2, sharedBob2);
+      // pubKey decoding
+      for (const k of [alice, bob]) {
+        deepStrictEqual(
+          toHex(elligatorSwift.decode(k.publicKey)),
+          toHex(secp256k1.getPublicKey(k.privateKey, true).subarray(1))
+        );
+      }
+    }
+  });
+});
+
+// ESM is broken.
+import url from 'url';
+if (import.meta.url === url.pathToFileURL(process.argv[1]).href) {
+  should.run();
+}