Do real secp256k1 point->curve checking

src/types.d.ts

@@ -1,6 +1,7 @@
 /// <reference types="node" />
 export declare const typeforce: any;
 export declare function isPoint(p: Buffer | number | undefined | null): boolean;
+export declare function isXOnlyPoint(p: Buffer | number | undefined | null): boolean;
 export declare function UInt31(value: number): boolean;
 export declare function BIP32Path(value: string): boolean;
 export declare namespace BIP32Path {

src/types.js

@@ -1,30 +1,79 @@
 'use strict';
 Object.defineProperty(exports, '__esModule', { value: true });
-exports.oneOf = exports.Null = exports.BufferN = exports.Function = exports.UInt32 = exports.UInt8 = exports.tuple = exports.maybe = exports.Hex = exports.Buffer = exports.String = exports.Boolean = exports.Array = exports.Number = exports.Hash256bit = exports.Hash160bit = exports.Buffer256bit = exports.Network = exports.ECPoint = exports.Satoshi = exports.Signer = exports.BIP32Path = exports.UInt31 = exports.isPoint = exports.typeforce = void 0;
+exports.oneOf = exports.Null = exports.BufferN = exports.Function = exports.UInt32 = exports.UInt8 = exports.tuple = exports.maybe = exports.Hex = exports.Buffer = exports.String = exports.Boolean = exports.Array = exports.Number = exports.Hash256bit = exports.Hash160bit = exports.Buffer256bit = exports.Network = exports.ECPoint = exports.Satoshi = exports.Signer = exports.BIP32Path = exports.UInt31 = exports.isXOnlyPoint = exports.isPoint = exports.typeforce = void 0;
 const buffer_1 = require('buffer');
 exports.typeforce = require('typeforce');
-const ZERO32 = buffer_1.Buffer.alloc(32, 0);
-const EC_P = buffer_1.Buffer.from(
-  'fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f',
-  'hex',
+const BN_ZERO = BigInt(0);
+// Bitcoin uses the secp256k1 curve, whose parameters can be found on
+// page 13, section 2.4.1, of https://www.secg.org/sec2-v2.pdf
+const EC_P = BigInt(
+  `0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f`,
 );
+// The short Weierstrass form curve equation simplifes to y^2 = x^3 + 7.
+function secp256k1Right(x) {
+  const EC_B = BigInt(7);
+  const x2 = (x * x) % EC_P;
+  const x3 = (x2 * x) % EC_P;
+  return (x3 + EC_B) % EC_P;
+}
+// For prime P, the Jacobi Symbol of 'a' is 1 if and only if 'a' is a quadratic
+// residue mod P, ie. there exists a value 'x' for whom x^2 = a.
+function jacobiSymbol(a) {
+  // Idea from noble-secp256k1, to be nice to bad JS parsers
+  const _1n = BigInt(1);
+  const _2n = BigInt(2);
+  const _3n = BigInt(3);
+  const _5n = BigInt(5);
+  const _7n = BigInt(7);
+  if (a === BN_ZERO) return 0;
+  let p = EC_P;
+  let sign = 1;
+  // This algorithm is fairly heavily optimized, so don't simplify it w/o benchmarking
+  for (;;) {
+    let and3;
+    // Handle runs of zeros efficiently w/o flipping sign each time
+    for (and3 = a & _3n; and3 === BN_ZERO; a >>= _2n, and3 = a & _3n);
+    // If there's one more zero, shift it off and flip the sign
+    if (and3 === _2n) {
+      a >>= _1n;
+      const pand7 = p & _7n;
+      if (pand7 === _3n || pand7 === _5n) sign = -sign;
+    }
+    if (a === _1n) break;
+    if ((_3n & a) === _3n && (_3n & p) === _3n) sign = -sign;
+    [a, p] = [p % a, a];
+  }
+  return sign > 0 ? 1 : -1;
+}
 function isPoint(p) {
   if (!buffer_1.Buffer.isBuffer(p)) return false;
   if (p.length < 33) return false;
   const t = p[0];
-  const x = p.slice(1, 33);
-  if (x.compare(ZERO32) === 0) return false;
-  if (x.compare(EC_P) >= 0) return false;
-  if ((t === 0x02 || t === 0x03) && p.length === 33) {
-    return true;
+  if (p.length === 33) {
+    return (t === 0x02 || t === 0x03) && isXOnlyPoint(p.slice(1));
   }
-  const y = p.slice(33);
-  if (y.compare(ZERO32) === 0) return false;
-  if (y.compare(EC_P) >= 0) return false;
-  if (t === 0x04 && p.length === 65) return true;
-  return false;
+  if (t !== 0x04 || p.length !== 65) return false;
+  const x = BigInt(`0x${p.slice(1, 33).toString('hex')}`);
+  if (x === BN_ZERO) return false;
+  if (x >= EC_P) return false;
+  const y = BigInt(`0x${p.slice(33).toString('hex')}`);
+  if (y === BN_ZERO) return false;
+  if (y >= EC_P) return false;
+  const left = (y * y) % EC_P;
+  const right = secp256k1Right(x);
+  return left === right;
 }
 exports.isPoint = isPoint;
+function isXOnlyPoint(p) {
+  if (!buffer_1.Buffer.isBuffer(p)) return false;
+  if (p.length !== 32) return false;
+  const x = BigInt(`0x${p.toString('hex')}`);
+  if (x === BN_ZERO) return false;
+  if (x >= EC_P) return false;
+  const y2 = secp256k1Right(x);
+  return jacobiSymbol(y2) === 1; // If sqrt(y^2) exists, x is on the curve.
+}
+exports.isXOnlyPoint = isXOnlyPoint;
 const UINT31_MAX = Math.pow(2, 31) - 1;
 function UInt31(value) {
   return exports.typeforce.UInt32(value) && value <= UINT31_MAX;

test/fixtures/crypto.json

@@ -40,4 +40,4 @@
       "result": "71ae15bad52efcecf4c9f672bfbded68a4adb8258f1b95f0d06aefdb5ebd14e9"
     }
   ]
-}
+}

test/fixtures/types.json

@@ -0,0 +1,58 @@
+{
+  "isPoint": [
+    {
+      "hex": "0400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+      "expected": false
+    },
+    {
+      "hex": "04ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
+      "expected": false
+    },
+    {
+      "hex": "044289801366bcee6172b771cf5a7f13aaecd237a0b9a1ff9d769cabc2e6b70a34cec320a0565fb7caf11b1ca2f445f9b7b012dda5718b3cface369ee3a034ded6",
+      "expected": true
+    },
+    {
+      "hex": "044289801366bcee6172b771cf5a7f13aaecd237a0b9a1ff9d769cabc2e6b70a34cec320a0565fb7caf11b1ca2f445f9b7b012dda5718b3cface369ee3a034ded0",
+      "expected": false
+    },
+    {
+      "hex": "04ff",
+      "expected": false
+    }
+  ],
+  "isXOnlyPoint": [
+    {
+      "hex": "ff",
+      "expected": false
+    },
+    {
+      "hex": "79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f8179800",
+      "expected": false
+    },
+    {
+      "hex": "79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798",
+      "expected": true
+    },
+    {
+      "hex": "fffffffffffffffffffffffffffffffffffffffffffffffffffffffeeffffc2e",
+      "expected": true
+    },
+    {
+      "hex": "f9308a019258c31049344f85f89d5229b531c845836f99b08601f113bce036f9",
+      "expected": true
+    },
+    {
+      "hex": "0000000000000000000000000000000000000000000000000000000000000001",
+      "expected": true
+    },
+    {
+      "hex": "0000000000000000000000000000000000000000000000000000000000000000",
+      "expected": false
+    },
+    {
+      "hex": "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f",
+      "expected": false
+    }
+  ]
+}

test/types.spec.ts

@@ -2,6 +2,7 @@ import * as assert from 'assert';
 import { describe, it } from 'mocha';
 import * as types from '../src/types';
 const typeforce = require('typeforce');
+import * as fixtures from './fixtures/types.json';
 
 describe('types', () => {
   describe('Buffer Hash160/Hash256', () => {
@@ -91,4 +92,32 @@ describe('types', () => {
       assert.equal(toJsonValue, '"BIP32 derivation path"');
     });
   });
+
+  describe('isPoint (uncompressed)', () => {
+    fixtures.isPoint.forEach(f => {
+      it(`returns ${f.expected} for isPoint(${f.hex})`, () => {
+        const bytes = Buffer.from(f.hex, 'hex');
+        assert.strictEqual(types.isPoint(bytes), f.expected);
+      });
+    });
+  });
+
+  describe('isPoint (compressed) + isXOnlyPoint', () => {
+    fixtures.isXOnlyPoint.forEach(f => {
+      it(`returns ${f.expected} for isPoint(02${f.hex})`, () => {
+        const bytes = Buffer.from(`02${f.hex}`, 'hex');
+        assert.strictEqual(types.isPoint(bytes), f.expected);
+      });
+
+      it(`returns ${f.expected} for isPoint(03${f.hex})`, () => {
+        const bytes = Buffer.from(`03${f.hex}`, 'hex');
+        assert.strictEqual(types.isPoint(bytes), f.expected);
+      });
+
+      it(`returns ${f.expected} for isXOnlyPoint(${f.hex})`, () => {
+        const bytes = Buffer.from(f.hex, 'hex');
+        assert.strictEqual(types.isXOnlyPoint(bytes), f.expected);
+      });
+    });
+  });
 });

ts_src/types.ts

@@ -1,28 +1,85 @@
 import { Buffer as NBuffer } from 'buffer';
 export const typeforce = require('typeforce');
 
-const ZERO32 = NBuffer.alloc(32, 0);
-const EC_P = NBuffer.from(
-  'fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f',
-  'hex',
+const BN_ZERO = BigInt(0);
+// Bitcoin uses the secp256k1 curve, whose parameters can be found on
+// page 13, section 2.4.1, of https://www.secg.org/sec2-v2.pdf
+const EC_P = BigInt(
+  `0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f`,
 );
+
+// The short Weierstrass form curve equation simplifes to y^2 = x^3 + 7.
+function secp256k1Right(x: bigint): bigint {
+  const EC_B = BigInt(7);
+  const x2 = (x * x) % EC_P;
+  const x3 = (x2 * x) % EC_P;
+  return (x3 + EC_B) % EC_P;
+}
+
+// For prime P, the Jacobi Symbol of 'a' is 1 if and only if 'a' is a quadratic
+// residue mod P, ie. there exists a value 'x' for whom x^2 = a.
+function jacobiSymbol(a: bigint): -1 | 0 | 1 {
+  // Idea from noble-secp256k1, to be nice to bad JS parsers
+  const _1n = BigInt(1);
+  const _2n = BigInt(2);
+  const _3n = BigInt(3);
+  const _5n = BigInt(5);
+  const _7n = BigInt(7);
+
+  if (a === BN_ZERO) return 0;
+
+  let p = EC_P;
+  let sign = 1;
+  // This algorithm is fairly heavily optimized, so don't simplify it w/o benchmarking
+  for (;;) {
+    let and3;
+    // Handle runs of zeros efficiently w/o flipping sign each time
+    for (and3 = a & _3n; and3 === BN_ZERO; a >>= _2n, and3 = a & _3n);
+    // If there's one more zero, shift it off and flip the sign
+    if (and3 === _2n) {
+      a >>= _1n;
+      const pand7 = p & _7n;
+      if (pand7 === _3n || pand7 === _5n) sign = -sign;
+    }
+    if (a === _1n) break;
+    if ((_3n & a) === _3n && (_3n & p) === _3n) sign = -sign;
+    [a, p] = [p % a, a];
+  }
+  return sign > 0 ? 1 : -1;
+}
+
 export function isPoint(p: Buffer | number | undefined | null): boolean {
   if (!NBuffer.isBuffer(p)) return false;
   if (p.length < 33) return false;
 
   const t = p[0];
-  const x = p.slice(1, 33);
-  if (x.compare(ZERO32) === 0) return false;
-  if (x.compare(EC_P) >= 0) return false;
-  if ((t === 0x02 || t === 0x03) && p.length === 33) {
-    return true;
+  if (p.length === 33) {
+    return (t === 0x02 || t === 0x03) && isXOnlyPoint(p.slice(1));
   }
 
-  const y = p.slice(33);
-  if (y.compare(ZERO32) === 0) return false;
-  if (y.compare(EC_P) >= 0) return false;
-  if (t === 0x04 && p.length === 65) return true;
-  return false;
+  if (t !== 0x04 || p.length !== 65) return false;
+
+  const x = BigInt(`0x${p.slice(1, 33).toString('hex')}`);
+  if (x === BN_ZERO) return false;
+  if (x >= EC_P) return false;
+
+  const y = BigInt(`0x${p.slice(33).toString('hex')}`);
+  if (y === BN_ZERO) return false;
+  if (y >= EC_P) return false;
+
+  const left = (y * y) % EC_P;
+  const right = secp256k1Right(x);
+  return left === right;
+}
+
+export function isXOnlyPoint(p: Buffer | number | undefined | null): boolean {
+  if (!NBuffer.isBuffer(p)) return false;
+  if (p.length !== 32) return false;
+  const x = BigInt(`0x${p.toString('hex')}`);
+  if (x === BN_ZERO) return false;
+  if (x >= EC_P) return false;
+  const y2 = secp256k1Right(x);
+  return jacobiSymbol(y2) === 1; // If sqrt(y^2) exists, x is on the curve.
 }
 
 const UINT31_MAX: number = Math.pow(2, 31) - 1;