bitcoinjs-lib/src/ecdsa.js

var sec = require('./jsbn/sec');
var util = require('./util');
var SecureRandom = require('./jsbn/rng');
var BigInteger = require('./jsbn/jsbn');

var ECPointFp = require('./jsbn/ec').ECPointFp;

var rng = new SecureRandom();
var ecparams = sec("secp256k1");
var P_OVER_FOUR = null;

function implShamirsTrick(P, k, Q, l)
{
  var m = Math.max(k.bitLength(), l.bitLength());
  var Z = P.add2D(Q);
  var R = P.curve.getInfinity();

  for (var i = m - 1; i >= 0; --i) {
    R = R.twice2D();

    R.z = BigInteger.ONE;

    if (k.testBit(i)) {
      if (l.testBit(i)) {
        R = R.add2D(Z);
      } else {
        R = R.add2D(P);
      }
    } else {
      if (l.testBit(i)) {
        R = R.add2D(Q);
      }
    }
  }

  return R;
};

var ECDSA = {
  getBigRandom: function (limit) {
    return new BigInteger(limit.bitLength(), rng)
      .mod(limit.subtract(BigInteger.ONE))
      .add(BigInteger.ONE)
    ;
  },
  sign: function (hash, priv) {
    var d = priv;
    var n = ecparams.getN();
    var e = BigInteger.fromByteArrayUnsigned(hash);

    do {
      var k = ECDSA.getBigRandom(n);
      var G = ecparams.getG();
      var Q = G.multiply(k);
      var r = Q.getX().toBigInteger().mod(n);
    } while (r.compareTo(BigInteger.ZERO) <= 0);

    var s = k.modInverse(n).multiply(e.add(d.multiply(r))).mod(n);

    return ECDSA.serializeSig(r, s);
  },

  verify: function (hash, sig, pubkey) {
    var r,s;
    if (util.isArray(sig)) {
      var obj = ECDSA.parseSig(sig);
      r = obj.r;
      s = obj.s;
    } else if ("object" === typeof sig && sig.r && sig.s) {
      r = sig.r;
      s = sig.s;
    } else {
      throw new Error("Invalid value for signature");
    }

    var Q;
    if (pubkey instanceof ECPointFp) {
      Q = pubkey;
    } else if (util.isArray(pubkey)) {
      Q = ECPointFp.decodeFrom(ecparams.getCurve(), pubkey);
    } else {
      throw new Error("Invalid format for pubkey value, must be byte array or ECPointFp");
    }
    var e = BigInteger.fromByteArrayUnsigned(hash);

    return ECDSA.verifyRaw(e, r, s, Q);
  },

  verifyRaw: function (e, r, s, Q) {
    var n = ecparams.getN();
    var G = ecparams.getG();

    if (r.compareTo(BigInteger.ONE) < 0 ||
        r.compareTo(n) >= 0)
      return false;

    if (s.compareTo(BigInteger.ONE) < 0 ||
        s.compareTo(n) >= 0)
      return false;

    var c = s.modInverse(n);

    var u1 = e.multiply(c).mod(n);
    var u2 = r.multiply(c).mod(n);

    // TODO(!!!): For some reason Shamir's trick isn't working with
    // signed message verification!? Probably an implementation
    // error!
    //var point = implShamirsTrick(G, u1, Q, u2);
    var point = G.multiply(u1).add(Q.multiply(u2));

    var v = point.getX().toBigInteger().mod(n);

    return v.equals(r);
  },

  /**
   * Serialize a signature into DER format.
   *
   * Takes two BigIntegers representing r and s and returns a byte array.
   */
  serializeSig: function (r, s) {
    var rBa = r.toByteArraySigned();
    var sBa = s.toByteArraySigned();

    var sequence = [];
    sequence.push(0x02); // INTEGER
    sequence.push(rBa.length);
    sequence = sequence.concat(rBa);

    sequence.push(0x02); // INTEGER
    sequence.push(sBa.length);
    sequence = sequence.concat(sBa);

    sequence.unshift(sequence.length);
    sequence.unshift(0x30); // SEQUENCE

    return sequence;
  },

  /**
   * Parses a byte array containing a DER-encoded signature.
   *
   * This function will return an object of the form:
   *
   * {
   *   r: BigInteger,
   *   s: BigInteger
   * }
   */
  parseSig: function (sig) {
    var cursor;
    if (sig[0] != 0x30)
      throw new Error("Signature not a valid DERSequence");

    cursor = 2;
    if (sig[cursor] != 0x02)
      throw new Error("First element in signature must be a DERInteger");;
    var rBa = sig.slice(cursor+2, cursor+2+sig[cursor+1]);

    cursor += 2+sig[cursor+1];
    if (sig[cursor] != 0x02)
      throw new Error("Second element in signature must be a DERInteger");
    var sBa = sig.slice(cursor+2, cursor+2+sig[cursor+1]);

    cursor += 2+sig[cursor+1];

    //if (cursor != sig.length)
    //  throw new Error("Extra bytes in signature");

    var r = BigInteger.fromByteArrayUnsigned(rBa);
    var s = BigInteger.fromByteArrayUnsigned(sBa);

    return {r: r, s: s};
  },

  parseSigCompact: function (sig) {
    if (sig.length !== 65) {
      throw new Error("Signature has the wrong length");
    }

    // Signature is prefixed with a type byte storing three bits of
    // information.
    var i = sig[0] - 27;
    if (i < 0 || i > 7) {
      throw new Error("Invalid signature type");
    }

    var n = ecparams.getN();
    var r = BigInteger.fromByteArrayUnsigned(sig.slice(1, 33)).mod(n);
    var s = BigInteger.fromByteArrayUnsigned(sig.slice(33, 65)).mod(n);

    return {r: r, s: s, i: i};
  },

  /**
   * Recover a public key from a signature.
   *
   * See SEC 1: Elliptic Curve Cryptography, section 4.1.6, "Public
   * Key Recovery Operation".
   *
   * http://www.secg.org/download/aid-780/sec1-v2.pdf
   */
  recoverPubKey: function (r, s, hash, i) {
    // The recovery parameter i has two bits.
    i = i & 3;

    // The less significant bit specifies whether the y coordinate
    // of the compressed point is even or not.
    var isYEven = i & 1;

    // The more significant bit specifies whether we should use the
    // first or second candidate key.
    var isSecondKey = i >> 1;

    var n = ecparams.getN();
    var G = ecparams.getG();
    var curve = ecparams.getCurve();
    var p = curve.getQ();
    var a = curve.getA().toBigInteger();
    var b = curve.getB().toBigInteger();

    // We precalculate (p + 1) / 4 where p is if the field order
    if (!P_OVER_FOUR) {
      P_OVER_FOUR = p.add(BigInteger.ONE).divide(BigInteger.valueOf(4));
    }

    // 1.1 Compute x
    var x = isSecondKey ? r.add(n) : r;

    // 1.3 Convert x to point
    var alpha = x.multiply(x).multiply(x).add(a.multiply(x)).add(b).mod(p);
    var beta = alpha.modPow(P_OVER_FOUR, p);

    var xorOdd = beta.isEven() ? (i % 2) : ((i+1) % 2);
    // If beta is even, but y isn't or vice versa, then convert it,
    // otherwise we're done and y == beta.
    var y = (beta.isEven() ? !isYEven : isYEven) ? beta : p.subtract(beta);

    // 1.4 Check that nR is at infinity
    var R = new ECPointFp(curve,
                          curve.fromBigInteger(x),
                          curve.fromBigInteger(y));
    R.validate();

    // 1.5 Compute e from M
    var e = BigInteger.fromByteArrayUnsigned(hash);
    var eNeg = BigInteger.ZERO.subtract(e).mod(n);

    // 1.6 Compute Q = r^-1 (sR - eG)
    var rInv = r.modInverse(n);
    var Q = implShamirsTrick(R, s, G, eNeg).multiply(rInv);

    Q.validate();
    if (!ECDSA.verifyRaw(e, r, s, Q)) {
      throw new Error("Pubkey recovery unsuccessful");
    }

    // TODO (shtylman) this is stupid because this file and eckey
    // have circular dependencies
    var ECKey = require('./eckey');
    var pubKey = ECKey();
    pubKey.pub = Q;
    return pubKey;
  },

  /**
   * Calculate pubkey extraction parameter.
   *
   * When extracting a pubkey from a signature, we have to
   * distinguish four different cases. Rather than putting this
   * burden on the verifier, Bitcoin includes a 2-bit value with the
   * signature.
   *
   * This function simply tries all four cases and returns the value
   * that resulted in a successful pubkey recovery.
   */
  calcPubkeyRecoveryParam: function (address, r, s, hash)
  {
    for (var i = 0; i < 4; i++) {
      var pubkey = ECDSA.recoverPubKey(r, s, hash, i);
      if (pubkey.getBitcoinAddress().toString() == address) {
        return i;
      }
    }

    throw new Error("Unable to find valid recovery factor");
  }
};

module.exports = ECDSA;