ecdsa.js

var assert = require('assert')
var createHmac = require('create-hmac')
var typeForce = require('typeforce')

var BigInteger = require('bigi')
var ECSignature = require('./ecsignature')

var ZERO = new Buffer([0])
var ONE = new Buffer([1])

// https://tools.ietf.org/html/rfc6979#section-3.2
function deterministicGenerateK (curve, hash, d, checkSig) {
  typeForce('Buffer', hash)
  typeForce('BigInteger', d)
  typeForce('Function', checkSig)

  // sanity check
  assert.equal(hash.length, 32, 'Hash must be 256 bit')

  var x = d.toBuffer(32)
  var k = new Buffer(32)
  var v = new Buffer(32)

  // Step A, ignored as hash already provided
  // Step B
  v.fill(1)

  // Step C
  k.fill(0)

  // Step D
  k = createHmac('sha256', k)
    .update(v)
    .update(ZERO)
    .update(x)
    .update(hash)
    .digest()

  // Step E
  v = createHmac('sha256', k).update(v).digest()

  // Step F
  k = createHmac('sha256', k)
    .update(v)
    .update(ONE)
    .update(x)
    .update(hash)
    .digest()

  // Step G
  v = createHmac('sha256', k).update(v).digest()

  // Step H1/H2a, ignored as tlen === qlen (256 bit)
  // Step H2b
  v = createHmac('sha256', k).update(v).digest()

  var T = BigInteger.fromBuffer(v)

  // Step H3, repeat until T is within the interval [1, n - 1] and is suitable for ECDSA
  while ((T.signum() <= 0) || (T.compareTo(curve.n) >= 0) || !checkSig(T)) {
    k = createHmac('sha256', k)
      .update(v)
      .update(ZERO)
      .digest()

    v = createHmac('sha256', k).update(v).digest()

    // Step H1/H2a, again, ignored as tlen === qlen (256 bit)
    // Step H2b again
    v = createHmac('sha256', k).update(v).digest()
    T = BigInteger.fromBuffer(v)
  }

  return T
}

function sign (curve, hash, d) {
  typeForce('Curve', curve)
  typeForce('Buffer', hash)
  typeForce('BigInteger', d)

  var e = BigInteger.fromBuffer(hash)
  var n = curve.n
  var G = curve.G

  var r, s
  deterministicGenerateK(curve, hash, d, function (k) {
    var Q = G.multiply(k)

    if (curve.isInfinity(Q)) return false

    r = Q.affineX.mod(n)
    if (r.signum() === 0) return false

    s = k.modInverse(n).multiply(e.add(d.multiply(r))).mod(n)
    if (s.signum() === 0) return false

    return true
  })

  var N_OVER_TWO = n.shiftRight(1)

  // enforce low S values, see bip62: 'low s values in signatures'
  if (s.compareTo(N_OVER_TWO) > 0) {
    s = n.subtract(s)
  }

  return new ECSignature(r, s)
}

function verify (curve, hash, signature, Q) {
  typeForce('Curve', curve)
  typeForce('Buffer', hash)
  typeForce('ECSignature', signature)
  typeForce('Point', Q)

  var n = curve.n
  var G = curve.G

  var r = signature.r
  var s = signature.s

  // 1.4.1 Enforce r and s are both integers in the interval [1, n − 1]
  if (r.signum() <= 0 || r.compareTo(n) >= 0) return false
  if (s.signum() <= 0 || s.compareTo(n) >= 0) return false

  // 1.4.2 H = Hash(M), already done by the user
  // 1.4.3 e = H
  var e = BigInteger.fromBuffer(hash)

  // Compute s^-1
  var sInv = s.modInverse(n)

  // 1.4.4 Compute u1 = es^−1 mod n
  //               u2 = rs^−1 mod n
  var u1 = e.multiply(sInv).mod(n)
  var u2 = r.multiply(sInv).mod(n)

  // 1.4.5 Compute R = (xR, yR)
  //               R = u1G + u2Q
  var R = G.multiplyTwo(u1, Q, u2)

  // 1.4.5 (cont.) Enforce R is not at infinity
  if (curve.isInfinity(R)) return false

  // 1.4.6 Convert the field element R.x to an integer
  var xR = R.affineX

  // 1.4.7 Set v = xR mod n
  var v = xR.mod(n)

  // 1.4.8 If v = r, output "valid", and if v != r, output "invalid"
  return v.equals(r)
}

/**
  * 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
  */
function recoverPubKey (curve, e, signature, i) {
  typeForce('Curve', curve)
  typeForce('BigInteger', e)
  typeForce('ECSignature', signature)
  typeForce('Number', i)
  assert.strictEqual(i & 3, i, 'Recovery param is more than two bits')

  var n = curve.n
  var G = curve.G

  var r = signature.r
  var s = signature.s

  assert(r.signum() > 0 && r.compareTo(n) < 0, 'Invalid r value')
  assert(s.signum() > 0 && s.compareTo(n) < 0, 'Invalid s value')

  // A set LSB signifies that the y-coordinate is odd
  var isYOdd = i & 1

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

  // 1.1 Let x = r + jn
  var x = isSecondKey ? r.add(n) : r
  var R = curve.pointFromX(isYOdd, x)

  // 1.4 Check that nR is at infinity
  var nR = R.multiply(n)
  assert(curve.isInfinity(nR), 'nR is not a valid curve point')

  // Compute r^-1
  var rInv = r.modInverse(n)

  // Compute -e from e
  var eNeg = e.negate().mod(n)

  // 1.6.1 Compute Q = r^-1 (sR -  eG)
  //               Q = r^-1 (sR + -eG)
  var Q = R.multiplyTwo(s, G, eNeg).multiply(rInv)

  curve.validate(Q)

  return Q
}

/**
  * 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.
  */
function calcPubKeyRecoveryParam (curve, e, signature, Q) {
  typeForce('Curve', curve)
  typeForce('BigInteger', e)
  typeForce('ECSignature', signature)
  typeForce('Point', Q)

  for (var i = 0; i < 4; i++) {
    var Qprime = recoverPubKey(curve, e, signature, i)

    // 1.6.2 Verify Q
    if (Qprime.equals(Q)) {
      return i
    }
  }

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

module.exports = {
  calcPubKeyRecoveryParam: calcPubKeyRecoveryParam,
  deterministicGenerateK: deterministicGenerateK,
  recoverPubKey: recoverPubKey,
  sign: sign,
  verify: verify
}