import { deepStrictEqual, throws } from 'assert'; import { should } from 'micro-should'; import * as fc from 'fast-check'; import * as mod from '@noble/curves/modular'; import { randomBytes } from '@noble/hashes/utils'; // Generic tests for all curves in package import { secp192r1 } from '../lib/p192.js'; import { secp224r1 } from '../lib/p224.js'; import { secp256r1 } from '../lib/p256.js'; import { secp384r1 } from '../lib/p384.js'; import { secp521r1 } from '../lib/p521.js'; import { secp256k1 } from '../lib/secp256k1.js'; import { ed25519, ed25519ctx, ed25519ph } from '../lib/ed25519.js'; import { ed448, ed448ph } from '../lib/ed448.js'; import { starkCurve } from '../lib/stark.js'; import { pallas, vesta } from '../lib/pasta.js'; import { bn254 } from '../lib/bn.js'; import { jubjub } from '../lib/jubjub.js'; // prettier-ignore const CURVES = { secp192r1, secp224r1, secp256r1, secp384r1, secp521r1, secp256k1, ed25519, ed25519ctx, ed25519ph, ed448, ed448ph, starkCurve, pallas, vesta, bn254, jubjub, }; const NUM_RUNS = 5; const getXY = (p) => ({ x: p.x, y: p.y }); function equal(a, b, comment) { deepStrictEqual(a.equals(b), true, `eq(${comment})`); if (a.toAffine && b.toAffine) { deepStrictEqual(getXY(a.toAffine()), getXY(b.toAffine()), `eqToAffine(${comment})`); } else if (!a.toAffine && !b.toAffine) { // Already affine deepStrictEqual(getXY(a), getXY(b), `eqAffine(${comment})`); } else throw new Error('Different point types'); } for (const name in CURVES) { const C = CURVES[name]; const CURVE_ORDER = C.CURVE.n; const FC_BIGINT = fc.bigInt(1n + 1n, CURVE_ORDER - 1n); // Check that curve doesn't accept points from other curves const O = name === 'secp256k1' ? secp256r1 : secp256k1; const POINTS = {}; const OTHER_POINTS = {}; for (const name of ['Point', 'JacobianPoint', 'ExtendedPoint', 'ProjectivePoint']) { POINTS[name] = C[name]; OTHER_POINTS[name] = O[name]; } for (const pointName in POINTS) { const p = POINTS[pointName]; const o = OTHER_POINTS[pointName]; if (!p) continue; const G = [p.ZERO, p.BASE]; for (let i = 2; i < 10; i++) G.push(G[1].multiply(i)); // Here we check basic group laws, to verify that points works as group should(`${name}/${pointName}/Basic group laws (zero)`, () => { equal(G[0].double(), G[0], '(0*G).double() = 0'); equal(G[0].add(G[0]), G[0], '0*G + 0*G = 0'); equal(G[0].subtract(G[0]), G[0], '0*G - 0*G = 0'); equal(G[0].negate(), G[0], '-0 = 0'); for (let i = 0; i < G.length; i++) { const p = G[i]; equal(p, p.add(G[0]), `${i}*G + 0 = ${i}*G`); equal(G[0].multiply(i + 1), G[0], `${i + 1}*0 = 0`); } }); should(`${name}/${pointName}/Basic group laws (one)`, () => { equal(G[1].double(), G[2], '(1*G).double() = 2*G'); equal(G[1].subtract(G[1]), G[0], '1*G - 1*G = 0'); equal(G[1].add(G[1]), G[2], '1*G + 1*G = 2*G'); }); should(`${name}/${pointName}/Basic group laws (sanity tests)`, () => { equal(G[2].double(), G[4], `(2*G).double() = 4*G`); equal(G[2].add(G[2]), G[4], `2*G + 2*G = 4*G`); equal(G[7].add(G[3].negate()), G[4], `7*G - 3*G = 4*G`); }); should(`${name}/${pointName}/Basic group laws (addition commutativity)`, () => { equal(G[4].add(G[3]), G[3].add(G[4]), `4*G + 3*G = 3*G + 4*G`); equal(G[4].add(G[3]), G[3].add(G[2]).add(G[2]), `4*G + 3*G = 3*G + 2*G + 2*G`); }); should(`${name}/${pointName}/Basic group laws (double)`, () => { equal(G[3].double(), G[6], '(3*G).double() = 6*G'); }); should(`${name}/${pointName}/Basic group laws (multiply)`, () => { equal(G[2].multiply(3), G[6], '(2*G).multiply(3) = 6*G'); }); should(`${name}/${pointName}/Basic group laws (same point addition)`, () => { equal(G[3].add(G[3]), G[6], `3*G + 3*G = 6*G`); }); should(`${name}/${pointName}/Basic group laws (same point (negative) addition)`, () => { equal(G[3].add(G[3].negate()), G[0], '3*G + (- 3*G) = 0*G'); equal(G[3].subtract(G[3]), G[0], '3*G - 3*G = 0*G'); }); should(`${name}/${pointName}/Basic group laws (curve order)`, () => { equal(G[1].multiply(CURVE_ORDER - 1n).add(G[1]), G[0], '(N-1)*G + G = 0'); equal(G[1].multiply(CURVE_ORDER - 1n).add(G[2]), G[1], '(N-1)*G + 2*G = 1*G'); equal(G[1].multiply(CURVE_ORDER - 2n).add(G[2]), G[0], '(N-2)*G + 2*G = 0'); const half = CURVE_ORDER / 2n; const carry = CURVE_ORDER % 2n === 1n ? G[1] : G[0]; equal(G[1].multiply(half).double().add(carry), G[0], '((N/2) * G).double() = 0'); }); should(`${name}/${pointName}/Basic group laws (inversion)`, () => { const a = 1234n; const b = 5678n; const c = a * b; equal(G[1].multiply(a).multiply(b), G[1].multiply(c), 'a*b*G = c*G'); const inv = mod.invert(b, CURVE_ORDER); equal(G[1].multiply(c).multiply(inv), G[1].multiply(a), 'c*G * (1/b)*G = a*G'); }); should(`${name}/${pointName}/Basic group laws (multiply, rand)`, () => fc.assert( fc.property(FC_BIGINT, FC_BIGINT, (a, b) => { const c = mod.mod(a + b, CURVE_ORDER); if (c === CURVE_ORDER || c < 1n) return; const pA = G[1].multiply(a); const pB = G[1].multiply(b); const pC = G[1].multiply(c); equal(pA.add(pB), pB.add(pA), `pA + pB = pB + pA`); equal(pA.add(pB), pC, `pA + pB = pC`); }), { numRuns: NUM_RUNS } ) ); should(`${name}/${pointName}/Basic group laws (multiply2, rand)`, () => fc.assert( fc.property(FC_BIGINT, FC_BIGINT, (a, b) => { const c = mod.mod(a * b, CURVE_ORDER); const pA = G[1].multiply(a); const pB = G[1].multiply(b); equal(pA.multiply(b), pB.multiply(a), `b*pA = a*pB`); equal(pA.multiply(b), G[1].multiply(c), `b*pA = c*G`); }), { numRuns: NUM_RUNS } ) ); for (const op of ['add', 'subtract']) { should(`${name}/${pointName}/${op} type check`, () => { throws(() => G[1][op](0), '0'); throws(() => G[1][op](0n), '0n'); G[1][op](G[2]); throws(() => G[1][op](CURVE_ORDER), 'CURVE_ORDER'); throws(() => G[1][op](123.456), '123.456'); throws(() => G[1][op](true), 'true'); throws(() => G[1][op]('1'), "'1'"); throws(() => G[1][op]({ x: 1n, y: 1n, z: 1n, t: 1n }), '{ x: 1n, y: 1n, z: 1n, t: 1n }'); throws(() => G[1][op](new Uint8Array([])), 'ui8a([])'); throws(() => G[1][op](new Uint8Array([0])), 'ui8a([0])'); throws(() => G[1][op](new Uint8Array([1])), 'ui8a([1])'); throws(() => G[1][op](new Uint8Array(4096).fill(1)), 'ui8a(4096*[1])'); if (G[1].toAffine) throws(() => G[1][op](C.Point.BASE), `Point ${op} ${pointName}`); throws(() => G[1][op](o.BASE), `${op}/other curve point`); }); } should(`${name}/${pointName}/equals type check`, () => { throws(() => G[1].equals(0), '0'); throws(() => G[1].equals(0n), '0n'); deepStrictEqual(G[1].equals(G[2]), false, '1*G != 2*G'); deepStrictEqual(G[1].equals(G[1]), true, '1*G == 1*G'); deepStrictEqual(G[2].equals(G[2]), true, '2*G == 2*G'); throws(() => G[1].equals(CURVE_ORDER), 'CURVE_ORDER'); throws(() => G[1].equals(123.456), '123.456'); throws(() => G[1].equals(true), 'true'); throws(() => G[1].equals('1'), "'1'"); throws(() => G[1].equals({ x: 1n, y: 1n, z: 1n, t: 1n }), '{ x: 1n, y: 1n, z: 1n, t: 1n }'); throws(() => G[1].equals(new Uint8Array([])), 'ui8a([])'); throws(() => G[1].equals(new Uint8Array([0])), 'ui8a([0])'); throws(() => G[1].equals(new Uint8Array([1])), 'ui8a([1])'); throws(() => G[1].equals(new Uint8Array(4096).fill(1)), 'ui8a(4096*[1])'); if (G[1].toAffine) throws(() => G[1].equals(C.Point.BASE), `Point.equals(${pointName})`); throws(() => G[1].equals(o.BASE), 'other curve point'); }); for (const op of ['multiply', 'multiplyUnsafe']) { if (!p.BASE[op]) continue; should(`${name}/${pointName}/${op} type check`, () => { if (op !== 'multiplyUnsafe') { throws(() => G[1][op](0), '0'); throws(() => G[1][op](0n), '0n'); } G[1][op](1n); G[1][op](CURVE_ORDER - 1n); throws(() => G[1][op](G[2]), 'G[2]'); throws(() => G[1][op](CURVE_ORDER), 'CURVE_ORDER'); throws(() => G[1][op](CURVE_ORDER + 1n), 'CURVE_ORDER+1'); throws(() => G[1][op](123.456), '123.456'); throws(() => G[1][op](true), 'true'); throws(() => G[1][op]('1'), '1'); throws(() => G[1][op](new Uint8Array([])), 'ui8a([])'); throws(() => G[1][op](new Uint8Array([0])), 'ui8a([0])'); throws(() => G[1][op](new Uint8Array([1])), 'ui8a([1])'); throws(() => G[1][op](new Uint8Array(4096).fill(1)), 'ui8a(4096*[1])'); throws(() => G[1][op](o.BASE), 'other curve point'); }); } // Complex point (Extended/Jacobian/Projective?) if (p.BASE.toAffine) { should(`${name}/${pointName}/toAffine()`, () => { equal(p.ZERO.toAffine(), C.Point.ZERO, `0 = 0`); equal(p.BASE.toAffine(), C.Point.BASE, `1 = 1`); }); } if (p.fromAffine) { should(`${name}/${pointName}/fromAffine()`, () => { equal(p.ZERO, p.fromAffine(C.Point.ZERO), `0 = 0`); equal(p.BASE, p.fromAffine(C.Point.BASE), `1 = 1`); }); } // toHex/fromHex (if available) if (p.fromHex && p.BASE.toHex) { should(`${name}/${pointName}/fromHex(toHex()) roundtrip`, () => { fc.assert( fc.property(FC_BIGINT, (x) => { const hex = p.BASE.multiply(x).toHex(); deepStrictEqual(p.fromHex(hex).toHex(), hex); }) ); }); } } // Generic complex things (getPublicKey/sign/verify/getSharedSecret) should(`${name}/getPublicKey type check`, () => { throws(() => C.getPublicKey(0), '0'); throws(() => C.getPublicKey(0n), '0n'); throws(() => C.getPublicKey(false), 'false'); throws(() => C.getPublicKey(123.456), '123.456'); throws(() => C.getPublicKey(true), 'true'); throws(() => C.getPublicKey(''), "''"); // NOTE: passes because of disabled hex padding checks for starknet, maybe enable? //throws(() => C.getPublicKey('1'), "'1'"); throws(() => C.getPublicKey('key'), "'key'"); throws(() => C.getPublicKey(new Uint8Array([]))); throws(() => C.getPublicKey(new Uint8Array([0]))); throws(() => C.getPublicKey(new Uint8Array([1]))); throws(() => C.getPublicKey(new Uint8Array(4096).fill(1))); }); should(`${name}.verify()/should verify random signatures`, () => fc.assert( fc.property(fc.hexaString({ minLength: 64, maxLength: 64 }), (msg) => { const priv = C.utils.randomPrivateKey(); const pub = C.getPublicKey(priv); const sig = C.sign(msg, priv); deepStrictEqual(C.verify(sig, msg, pub), true); }), { numRuns: NUM_RUNS } ) ); should(`${name}.sign()/edge cases`, () => { throws(() => C.sign()); throws(() => C.sign('')); }); should(`${name}.verify()/should not verify signature with wrong hash`, () => { const MSG = '01'.repeat(32); const PRIV_KEY = 0x2n; const WRONG_MSG = '11'.repeat(32); const signature = C.sign(MSG, PRIV_KEY); const publicKey = C.getPublicKey(PRIV_KEY); deepStrictEqual(C.verify(signature, WRONG_MSG, publicKey), false); }); // NOTE: fails for ed, because of empty message. Since we convert it to scalar, // need to check what other implementations do. Empty message != new Uint8Array([0]), but what scalar should be in that case? // should(`${name}/should not verify signature with wrong message`, () => { // fc.assert( // fc.property( // fc.array(fc.integer({ min: 0x00, max: 0xff })), // fc.array(fc.integer({ min: 0x00, max: 0xff })), // (bytes, wrongBytes) => { // const privKey = C.utils.randomPrivateKey(); // const message = new Uint8Array(bytes); // const wrongMessage = new Uint8Array(wrongBytes); // const publicKey = C.getPublicKey(privKey); // const signature = C.sign(message, privKey); // deepStrictEqual( // C.verify(signature, wrongMessage, publicKey), // bytes.toString() === wrongBytes.toString() // ); // } // ), // { numRuns: NUM_RUNS } // ); // }); if (C.getSharedSecret) { should(`${name}/getSharedSecret() should be commutative`, () => { for (let i = 0; i < NUM_RUNS; i++) { const asec = C.utils.randomPrivateKey(); const apub = C.getPublicKey(asec); const bsec = C.utils.randomPrivateKey(); const bpub = C.getPublicKey(bsec); try { deepStrictEqual(C.getSharedSecret(asec, bpub), C.getSharedSecret(bsec, apub)); } catch (error) { console.error('not commutative', { asec, apub, bsec, bpub }); throw error; } } }); } } // ESM is broken. import url from 'url'; if (import.meta.url === url.pathToFileURL(process.argv[1]).href) { should.run(); }