diff --git a/src/ecdsa.js b/src/ecdsa.js
index cb1013c..5303c0b 100644
--- a/src/ecdsa.js
+++ b/src/ecdsa.js
@@ -205,7 +205,7 @@ var ecdsa = {
    *
    * http://www.secg.org/download/aid-780/sec1-v2.pdf
    */
-  recoverPubKey: function (r, s, hash, i) {
+  recoverPubKey: function (e, r, s, i) {
     assert.strictEqual(i & 3, i, 'The recovery param is more than two bits')
 
     // A set LSB signifies that the y-coordinate is odd
@@ -243,15 +243,16 @@ var ecdsa = {
     var R = new ECPointFp(curve, curve.fromBigInteger(x), curve.fromBigInteger(y))
     R.validate()
 
-    // 1.5 Compute e from M
-    var e = BigInteger.fromBuffer(hash)
+    // 1.5 Compute -e from e
     var eNeg = e.negate().mod(n)
 
-    // 1.6 Compute Q = r^-1 (sR - eG)
+    // 1.6 Compute Q = r^-1 (sR -  eG)
+    //             Q = r^-1 (sR + -eG)
     var rInv = r.modInverse(n)
-    var Q = R.multiplyTwo(s, G, eNeg).multiply(rInv)
 
+    var Q = R.multiplyTwo(s, G, eNeg).multiply(rInv)
     Q.validate()
+
     if (!ecdsa.verifyRaw(e, r, s, Q)) {
       throw new Error("Pubkey recovery unsuccessful")
     }
@@ -270,16 +271,16 @@ var ecdsa = {
    * This function simply tries all four cases and returns the value
    * that resulted in a successful pubkey recovery.
    */
-  calcPubKeyRecoveryParam: function (origPubKey, r, s, hash) {
+  calcPubKeyRecoveryParam: function (e, r, s, Q) {
     for (var i = 0; i < 4; i++) {
-      var pubKey = ecdsa.recoverPubKey(r, s, hash, i)
+      var Qprime = ecdsa.recoverPubKey(e, r, s, i)
 
-      if (pubKey.equals(origPubKey)) {
+      if (Qprime.equals(Q)) {
         return i
       }
     }
 
-    throw new Error("Unable to find valid recovery factor")
+    throw new Error('Unable to find valid recovery factor')
   }
 }
 
diff --git a/src/message.js b/src/message.js
index b7d545b..1feaa31 100644
--- a/src/message.js
+++ b/src/message.js
@@ -1,5 +1,6 @@
 /// Implements Bitcoin's feature for signing arbitrary messages.
 var Address = require('./address')
+var BigInteger = require('bigi')
 var bufferutils = require('./bufferutils')
 var crypto = require('./crypto')
 var ecdsa = require('./ecdsa')
@@ -25,7 +26,8 @@ function sign(key, message, network) {
 
   var hash = magicHash(message, network)
   var sig = ecdsa.parseSig(key.sign(hash))
-  var i = ecdsa.calcPubKeyRecoveryParam(key.pub.Q, sig.r, sig.s, hash)
+  var e = BigInteger.fromBuffer(hash)
+  var i = ecdsa.calcPubKeyRecoveryParam(e, sig.r, sig.s, key.pub.Q)
 
   return ecdsa.serializeSigCompact(sig.r, sig.s, i, key.pub.compressed)
 }
@@ -40,7 +42,8 @@ function verify(address, compactSig, message, network) {
 
   var hash = magicHash(message, network)
   var sig = ecdsa.parseSigCompact(compactSig)
-  var Q = ecdsa.recoverPubKey(sig.r, sig.s, hash, sig.i)
+  var e = BigInteger.fromBuffer(hash)
+  var Q = ecdsa.recoverPubKey(e, sig.r, sig.s, sig.i)
 
   var pubKey = new ECPubKey(Q, sig.compressed)
   return pubKey.getAddress(address.version).toString() === address.toString()
diff --git a/test/ecdsa.js b/test/ecdsa.js
index 9decb27..ad9806d 100644
--- a/test/ecdsa.js
+++ b/test/ecdsa.js
@@ -32,8 +32,9 @@ describe('ecdsa', function() {
 
       var obj = ecdsa.parseSigCompact(signature)
       var hash = message.magicHash('1111', networks.bitcoin)
+      var e = BigInteger.fromBuffer(hash)
 
-      var pubKey = new ECPubKey(ecdsa.recoverPubKey(obj.r, obj.s, hash, obj.i))
+      var pubKey = new ECPubKey(ecdsa.recoverPubKey(e, obj.r, obj.s, obj.i))
 
       assert.equal(pubKey.toHex(), '02e8fcf4d749b35879bc1f3b14b49e67ab7301da3558c5a9b74a54f1e6339c334c')
     })