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@ -4,269 +4,269 @@ var crypto = require('./crypto') |
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var BigInteger = require('bigi') |
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var ECPointFp = require('./ec').ECPointFp |
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function deterministicGenerateK(ecparams, hash, D) { |
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assert(Buffer.isBuffer(hash), 'Hash must be a Buffer, not ' + hash) |
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assert.equal(hash.length, 32, 'Hash must be 256 bit') |
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assert(D instanceof BigInteger, 'Private key must be a BigInteger') |
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var x = D.toBuffer(32) |
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var k = new Buffer(32) |
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var v = new Buffer(32) |
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k.fill(0) |
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v.fill(1) |
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k = crypto.HmacSHA256(Buffer.concat([v, new Buffer([0]), x, hash]), k) |
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v = crypto.HmacSHA256(v, k) |
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k = crypto.HmacSHA256(Buffer.concat([v, new Buffer([1]), x, hash]), k) |
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v = crypto.HmacSHA256(v, k) |
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v = crypto.HmacSHA256(v, k) |
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var n = ecparams.getN() |
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var kB = BigInteger.fromBuffer(v).mod(n) |
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assert(kB.compareTo(BigInteger.ONE) > 0, 'Invalid k value') |
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assert(kB.compareTo(ecparams.getN()) < 0, 'Invalid k value') |
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return kB |
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} |
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function deterministicGenerateK(ecparams, hash, D) { |
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assert(Buffer.isBuffer(hash), 'Hash must be a Buffer, not ' + hash) |
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assert.equal(hash.length, 32, 'Hash must be 256 bit') |
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assert(D instanceof BigInteger, 'Private key must be a BigInteger') |
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var x = D.toBuffer(32) |
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var k = new Buffer(32) |
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var v = new Buffer(32) |
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k.fill(0) |
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v.fill(1) |
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k = crypto.HmacSHA256(Buffer.concat([v, new Buffer([0]), x, hash]), k) |
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v = crypto.HmacSHA256(v, k) |
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k = crypto.HmacSHA256(Buffer.concat([v, new Buffer([1]), x, hash]), k) |
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v = crypto.HmacSHA256(v, k) |
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v = crypto.HmacSHA256(v, k) |
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var n = ecparams.getN() |
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var kB = BigInteger.fromBuffer(v).mod(n) |
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assert(kB.compareTo(BigInteger.ONE) > 0, 'Invalid k value') |
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assert(kB.compareTo(ecparams.getN()) < 0, 'Invalid k value') |
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return kB |
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} |
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function sign(ecparams, hash, D) { |
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var k = deterministicGenerateK(ecparams, hash, D) |
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function sign(ecparams, hash, D) { |
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var k = deterministicGenerateK(ecparams, hash, D) |
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var n = ecparams.getN() |
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var G = ecparams.getG() |
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var Q = G.multiply(k) |
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var e = BigInteger.fromBuffer(hash) |
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var n = ecparams.getN() |
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var G = ecparams.getG() |
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var Q = G.multiply(k) |
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var e = BigInteger.fromBuffer(hash) |
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var r = Q.getX().toBigInteger().mod(n) |
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assert.notEqual(r.signum(), 0, 'Invalid R value') |
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var r = Q.getX().toBigInteger().mod(n) |
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assert.notEqual(r.signum(), 0, 'Invalid R value') |
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var s = k.modInverse(n).multiply(e.add(D.multiply(r))).mod(n) |
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assert.notEqual(s.signum(), 0, 'Invalid S value') |
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var s = k.modInverse(n).multiply(e.add(D.multiply(r))).mod(n) |
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assert.notEqual(s.signum(), 0, 'Invalid S value') |
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var N_OVER_TWO = n.shiftRight(1) |
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var N_OVER_TWO = n.shiftRight(1) |
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// enforce low S values, see bip62: 'low s values in signatures'
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if (s.compareTo(N_OVER_TWO) > 0) { |
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s = n.subtract(s) |
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} |
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return {r: r, s: s} |
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// enforce low S values, see bip62: 'low s values in signatures'
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if (s.compareTo(N_OVER_TWO) > 0) { |
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s = n.subtract(s) |
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} |
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function verify(ecparams, hash, r, s, Q) { |
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var e = BigInteger.fromBuffer(hash) |
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return {r: r, s: s} |
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} |
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return verifyRaw(ecparams, e, r, s, Q) |
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} |
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function verify(ecparams, hash, r, s, Q) { |
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var e = BigInteger.fromBuffer(hash) |
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function verifyRaw(ecparams, e, r, s, Q) { |
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var n = ecparams.getN() |
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var G = ecparams.getG() |
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return verifyRaw(ecparams, e, r, s, Q) |
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} |
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if (r.compareTo(BigInteger.ONE) < 0 || r.compareTo(n) >= 0) { |
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return false |
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} |
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function verifyRaw(ecparams, e, r, s, Q) { |
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var n = ecparams.getN() |
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var G = ecparams.getG() |
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if (s.compareTo(BigInteger.ONE) < 0 || s.compareTo(n) >= 0) { |
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return false |
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} |
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if (r.compareTo(BigInteger.ONE) < 0 || r.compareTo(n) >= 0) { |
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return false |
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} |
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if (s.compareTo(BigInteger.ONE) < 0 || s.compareTo(n) >= 0) { |
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return false |
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} |
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var c = s.modInverse(n) |
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var u1 = e.multiply(c).mod(n) |
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var u2 = r.multiply(c).mod(n) |
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var c = s.modInverse(n) |
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var u1 = e.multiply(c).mod(n) |
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var u2 = r.multiply(c).mod(n) |
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var point = G.multiplyTwo(u1, Q, u2) |
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var v = point.getX().toBigInteger().mod(n) |
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var point = G.multiplyTwo(u1, Q, u2) |
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var v = point.getX().toBigInteger().mod(n) |
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return v.equals(r) |
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} |
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return v.equals(r) |
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} |
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/** |
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* Serialize a signature into DER format. |
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* |
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* Takes two BigIntegers representing r and s and returns a byte array. |
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*/ |
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function serializeSig(r, s) { |
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var rBa = r.toByteArraySigned() |
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var sBa = s.toByteArraySigned() |
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/** |
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* Serialize a signature into DER format. |
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* |
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* Takes two BigIntegers representing r and s and returns a byte array. |
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*/ |
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function serializeSig(r, s) { |
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var rBa = r.toByteArraySigned() |
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var sBa = s.toByteArraySigned() |
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var sequence = [] |
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sequence.push(0x02); // INTEGER
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sequence.push(rBa.length) |
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sequence = sequence.concat(rBa) |
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var sequence = [] |
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sequence.push(0x02); // INTEGER
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sequence.push(rBa.length) |
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sequence = sequence.concat(rBa) |
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sequence.push(0x02); // INTEGER
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sequence.push(sBa.length) |
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sequence = sequence.concat(sBa) |
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sequence.push(0x02); // INTEGER
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sequence.push(sBa.length) |
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sequence = sequence.concat(sBa) |
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sequence.unshift(sequence.length) |
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sequence.unshift(0x30); // SEQUENCE
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sequence.unshift(sequence.length) |
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sequence.unshift(0x30); // SEQUENCE
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return sequence |
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} |
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return sequence |
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} |
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/** |
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* Parses a buffer containing a DER-encoded signature. |
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* |
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* This function will return an object of the form: |
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* |
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* { |
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* r: BigInteger, |
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* s: BigInteger |
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* } |
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*/ |
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function parseSig(buffer) { |
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assert.equal(buffer.readUInt8(0), 0x30, 'Not a DER sequence') |
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assert.equal(buffer.readUInt8(1), buffer.length - 2, 'Invalid sequence length') |
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assert.equal(buffer.readUInt8(2), 0x02, 'Expected DER integer') |
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var rLen = buffer.readUInt8(3) |
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var rB = buffer.slice(4, 4 + rLen) |
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var offset = 4 + rLen |
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assert.equal(buffer.readUInt8(offset), 0x02, 'Expected a 2nd DER integer') |
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var sLen = buffer.readUInt8(1 + offset) |
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var sB = buffer.slice(2 + offset) |
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return { |
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r: BigInteger.fromByteArraySigned(rB), |
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s: BigInteger.fromByteArraySigned(sB) |
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} |
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/** |
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* Parses a buffer containing a DER-encoded signature. |
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* |
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* This function will return an object of the form: |
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* |
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* { |
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* r: BigInteger, |
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* s: BigInteger |
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* } |
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*/ |
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function parseSig(buffer) { |
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assert.equal(buffer.readUInt8(0), 0x30, 'Not a DER sequence') |
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assert.equal(buffer.readUInt8(1), buffer.length - 2, 'Invalid sequence length') |
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assert.equal(buffer.readUInt8(2), 0x02, 'Expected DER integer') |
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var rLen = buffer.readUInt8(3) |
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var rB = buffer.slice(4, 4 + rLen) |
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var offset = 4 + rLen |
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assert.equal(buffer.readUInt8(offset), 0x02, 'Expected a 2nd DER integer') |
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var sLen = buffer.readUInt8(1 + offset) |
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var sB = buffer.slice(2 + offset) |
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return { |
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r: BigInteger.fromByteArraySigned(rB), |
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s: BigInteger.fromByteArraySigned(sB) |
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} |
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} |
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function serializeSigCompact(r, s, i, compressed) { |
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if (compressed) { |
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i += 4 |
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} |
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function serializeSigCompact(r, s, i, compressed) { |
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if (compressed) { |
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i += 4 |
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} |
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i += 27 |
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i += 27 |
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var buffer = new Buffer(65) |
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buffer.writeUInt8(i, 0) |
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r.toBuffer(32).copy(buffer, 1) |
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s.toBuffer(32).copy(buffer, 33) |
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var buffer = new Buffer(65) |
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buffer.writeUInt8(i, 0) |
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r.toBuffer(32).copy(buffer, 1) |
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s.toBuffer(32).copy(buffer, 33) |
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return buffer |
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} |
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return buffer |
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} |
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function parseSigCompact(buffer) { |
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assert.equal(buffer.length, 65, 'Invalid signature length') |
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var i = buffer.readUInt8(0) - 27 |
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function parseSigCompact(buffer) { |
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assert.equal(buffer.length, 65, 'Invalid signature length') |
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var i = buffer.readUInt8(0) - 27 |
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// At most 3 bits
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assert.equal(i, i & 7, 'Invalid signature type') |
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var compressed = !!(i & 4) |
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// At most 3 bits
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assert.equal(i, i & 7, 'Invalid signature type') |
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var compressed = !!(i & 4) |
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// Recovery param only
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i = i & 3 |
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// Recovery param only
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i = i & 3 |
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var r = BigInteger.fromBuffer(buffer.slice(1, 33)) |
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var s = BigInteger.fromBuffer(buffer.slice(33)) |
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var r = BigInteger.fromBuffer(buffer.slice(1, 33)) |
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var s = BigInteger.fromBuffer(buffer.slice(33)) |
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return { |
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r: r, |
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s: s, |
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i: i, |
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compressed: compressed |
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} |
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return { |
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r: r, |
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s: s, |
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i: i, |
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compressed: compressed |
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} |
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} |
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/** |
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* Recover a public key from a signature. |
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* |
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* See SEC 1: Elliptic Curve Cryptography, section 4.1.6, "Public |
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* Key Recovery Operation". |
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* |
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* http://www.secg.org/download/aid-780/sec1-v2.pdf
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*/ |
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function recoverPubKey(ecparams, e, r, s, i) { |
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assert.strictEqual(i & 3, i, 'The recovery param is more than two bits') |
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// A set LSB signifies that the y-coordinate is odd
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// By reduction, the y-coordinate is even if it is clear
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var isYEven = !(i & 1) |
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// The more significant bit specifies whether we should use the
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// first or second candidate key.
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var isSecondKey = i >> 1 |
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var n = ecparams.getN() |
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var G = ecparams.getG() |
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var curve = ecparams.getCurve() |
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var p = curve.getQ() |
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var a = curve.getA().toBigInteger() |
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var b = curve.getB().toBigInteger() |
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// We precalculate (p + 1) / 4 where p is the field order
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if (!curve.P_OVER_FOUR) { |
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curve.P_OVER_FOUR = p.add(BigInteger.ONE).shiftRight(2) |
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} |
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// 1.1 Compute x
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var x = isSecondKey ? r.add(n) : r |
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/** |
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* Recover a public key from a signature. |
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* |
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* See SEC 1: Elliptic Curve Cryptography, section 4.1.6, "Public |
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* Key Recovery Operation". |
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* |
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* http://www.secg.org/download/aid-780/sec1-v2.pdf
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*/ |
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function recoverPubKey(ecparams, e, r, s, i) { |
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assert.strictEqual(i & 3, i, 'The recovery param is more than two bits') |
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// A set LSB signifies that the y-coordinate is odd
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// By reduction, the y-coordinate is even if it is clear
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var isYEven = !(i & 1) |
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// The more significant bit specifies whether we should use the
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// first or second candidate key.
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var isSecondKey = i >> 1 |
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var n = ecparams.getN() |
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var G = ecparams.getG() |
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var curve = ecparams.getCurve() |
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var p = curve.getQ() |
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var a = curve.getA().toBigInteger() |
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var b = curve.getB().toBigInteger() |
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// We precalculate (p + 1) / 4 where p is the field order
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if (!curve.P_OVER_FOUR) { |
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curve.P_OVER_FOUR = p.add(BigInteger.ONE).shiftRight(2) |
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} |
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// 1.3 Convert x to point
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var alpha = x.pow(3).add(a.multiply(x)).add(b).mod(p) |
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var beta = alpha.modPow(curve.P_OVER_FOUR, p) |
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// 1.1 Compute x
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var x = isSecondKey ? r.add(n) : r |
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// If beta is even, but y isn't, or vice versa, then convert it,
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// otherwise we're done and y == beta.
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var y = (beta.isEven() ^ isYEven) ? p.subtract(beta) : beta |
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// 1.3 Convert x to point
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var alpha = x.pow(3).add(a.multiply(x)).add(b).mod(p) |
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var beta = alpha.modPow(curve.P_OVER_FOUR, p) |
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// 1.4 Check that nR isn't at infinity
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var R = new ECPointFp(curve, curve.fromBigInteger(x), curve.fromBigInteger(y)) |
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R.validate() |
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// If beta is even, but y isn't, or vice versa, then convert it,
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// otherwise we're done and y == beta.
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var y = (beta.isEven() ^ isYEven) ? p.subtract(beta) : beta |
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// 1.5 Compute -e from e
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var eNeg = e.negate().mod(n) |
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// 1.4 Check that nR isn't at infinity
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var R = new ECPointFp(curve, curve.fromBigInteger(x), curve.fromBigInteger(y)) |
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R.validate() |
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// 1.6 Compute Q = r^-1 (sR - eG)
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// Q = r^-1 (sR + -eG)
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var rInv = r.modInverse(n) |
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// 1.5 Compute -e from e
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var eNeg = e.negate().mod(n) |
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var Q = R.multiplyTwo(s, G, eNeg).multiply(rInv) |
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Q.validate() |
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// 1.6 Compute Q = r^-1 (sR - eG)
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// Q = r^-1 (sR + -eG)
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var rInv = r.modInverse(n) |
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if (!verifyRaw(ecparams, e, r, s, Q)) { |
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throw new Error("Pubkey recovery unsuccessful") |
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} |
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var Q = R.multiplyTwo(s, G, eNeg).multiply(rInv) |
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Q.validate() |
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return Q |
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if (!verifyRaw(ecparams, e, r, s, Q)) { |
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throw new Error("Pubkey recovery unsuccessful") |
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} |
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/** |
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* Calculate pubkey extraction parameter. |
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* |
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* When extracting a pubkey from a signature, we have to |
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* distinguish four different cases. Rather than putting this |
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* burden on the verifier, Bitcoin includes a 2-bit value with the |
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* signature. |
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* |
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* This function simply tries all four cases and returns the value |
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* that resulted in a successful pubkey recovery. |
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*/ |
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function calcPubKeyRecoveryParam(ecparams, e, r, s, Q) { |
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for (var i = 0; i < 4; i++) { |
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var Qprime = recoverPubKey(ecparams, e, r, s, i) |
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if (Qprime.equals(Q)) { |
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return i |
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} |
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} |
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return Q |
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} |
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throw new Error('Unable to find valid recovery factor') |
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/** |
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* Calculate pubkey extraction parameter. |
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* |
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|
* When extracting a pubkey from a signature, we have to |
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|
* distinguish four different cases. Rather than putting this |
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* burden on the verifier, Bitcoin includes a 2-bit value with the |
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|
* signature. |
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* |
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* This function simply tries all four cases and returns the value |
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* that resulted in a successful pubkey recovery. |
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*/ |
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function calcPubKeyRecoveryParam(ecparams, e, r, s, Q) { |
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for (var i = 0; i < 4; i++) { |
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var Qprime = recoverPubKey(ecparams, e, r, s, i) |
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if (Qprime.equals(Q)) { |
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return i |
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} |
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} |
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throw new Error('Unable to find valid recovery factor') |
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} |
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module.exports = { |
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calcPubKeyRecoveryParam: calcPubKeyRecoveryParam, |
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deterministicGenerateK: deterministicGenerateK, |
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recoverPubKey: recoverPubKey, |
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sign: sign, |
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verify: verify, |
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verifyRaw: verifyRaw, |
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serializeSig: serializeSig, |
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parseSig: parseSig, |
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serializeSigCompact: serializeSigCompact, |
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parseSigCompact: parseSigCompact |
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calcPubKeyRecoveryParam: calcPubKeyRecoveryParam, |
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deterministicGenerateK: deterministicGenerateK, |
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recoverPubKey: recoverPubKey, |
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sign: sign, |
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verify: verify, |
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verifyRaw: verifyRaw, |
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serializeSig: serializeSig, |
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parseSig: parseSig, |
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serializeSigCompact: serializeSigCompact, |
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parseSigCompact: parseSigCompact |
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} |
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Daniel Cousens
11 years ago