diff --git a/lib/ecdsa.js b/lib/ecdsa.js
index 38b0ce9..552cd7f 100644
--- a/lib/ecdsa.js
+++ b/lib/ecdsa.js
@@ -1,5 +1,5 @@
-var bn = require('./bn');
-var point = require('./point');
+var BN = require('./bn');
+var Point = require('./point');
 var Signature = require('./signature');
 var Key = require('./key');
 var Privkey = require('./privkey');
@@ -15,29 +15,93 @@ var ECDSA = function ECDSA(hash, key, sig, k) {
   this.k = k;
 };
 
+ECDSA.prototype.calci = function() {
+  for (var i = 0; i < 4; i++) {
+    this.sig.i = i;
+    try {
+      var Qprime = this.sig2pubkey();
+    } catch (e) {
+      console.log(e);
+      continue;
+    }
+
+    if (Qprime.point.eq(this.key.pubkey.point)) {
+      return this;
+    }
+  }
+
+  this.sig.i = undefined;
+  throw new Error('Unable to find valid recovery factor');
+};
+
 ECDSA.prototype.fromString = function(str) {
   var obj = JSON.parse(str);
   if (obj.hash)
     this.hash = new Buffer(obj.hash, 'hex');
   if (obj.key)
-    this.key = (new Key()).fromString(obj.key);
+    this.key = Key().fromString(obj.key);
   if (obj.sig)
-    this.sig = (new Signature()).fromString(obj.sig);
+    this.sig = Signature().fromString(obj.sig);
   if (obj.k)
-    this.k = bn(obj.k, 10);
+    this.k = BN(obj.k, 10);
   return this;
 };
 
 ECDSA.prototype.randomK = function() {
-  var N = point.getN();
+  var N = Point.getN();
   var k;
   do {
-    k = bn.fromBuffer(Random.getRandomBuffer(32));
+    k = BN().fromBuffer(Random.getRandomBuffer(32));
   } while (!(k.lt(N) && k.gt(0)));
   this.k = k;
   return this;
 };
 
+ECDSA.prototype.sig2pubkey = function() {
+  var i = this.sig.i;
+  if (!(i === 0 || i === 1 || i === 2 || i === 3))
+    throw new Error('signature: i must be equal to 0, 1, 2, or 3');
+
+  var e = BN().fromBuffer(this.hash);
+  var r = this.sig.r;
+  var s = this.sig.s;
+
+  // 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;
+
+  var n = Point.getN();
+  var G = Point.getG();
+
+  // 1.1 Let x = r + jn
+  var x = isSecondKey ? r.add(n) : r;
+  var R = Point.fromX(isYOdd, x);
+
+  // 1.4 Check that nR is at infinity
+  var nR = R.mul(n);
+
+  if (!nR.isInfinity())
+    throw new Error('nR is not a valid curve point');
+
+  // Compute -e from e
+  var eNeg = e.neg().mod(n);
+
+  // 1.6.1 Compute Q = r^-1 (sR - eG)
+  // Q = r^-1 (sR + -eG)
+  var rInv = r.invm(n);
+
+  //var Q = R.multiplyTwo(s, G, eNeg).mul(rInv);
+  var Q = R.mul(s).add(G.mul(eNeg)).mul(rInv);
+
+  var pubkey = new Pubkey(Q);
+  pubkey.validate();
+
+  return pubkey;
+};
+
 ECDSA.prototype.sigError = function() {
   if (!Buffer.isBuffer(this.hash) || this.hash.length !== 32)
     return 'Invalid hash';
@@ -46,21 +110,21 @@ ECDSA.prototype.sigError = function() {
     this.key.pubkey.validate();
   } catch (e) {
     return 'Invalid pubkey: ' + e;
-  };
+  }
 
   var r = this.sig.r;
   var s = this.sig.s;
-  if (!(r.gt(0) && r.lt(point.getN()))
-   || !(s.gt(0) && s.lt(point.getN())))
+  if (!(r.gt(0) && r.lt(Point.getN()))
+   || !(s.gt(0) && s.lt(Point.getN())))
     return 'r and s not in range';
 
-  var e = bn.fromBuffer(this.hash);
-  var n = point.getN();
+  var e = BN().fromBuffer(this.hash);
+  var n = Point.getN();
   var sinv = s.invm(n);
   var u1 = sinv.mul(e).mod(n);
   var u2 = sinv.mul(r).mod(n);
 
-  var p = point.getG().mulAdd(u1, this.key.pubkey.point, u2);
+  var p = Point.getG().mulAdd(u1, this.key.pubkey.point, u2);
   if (p.isInfinity())
     return 'p is infinity';
 
@@ -79,9 +143,9 @@ ECDSA.prototype.sign = function() {
   if (!hash || !privkey || !k || !d)
     throw new Error('ecdsa: invalid parameters');
 
-  var N = point.getN();
-  var G = point.getG();
-  var e = bn(hash);
+  var N = Point.getN();
+  var G = Point.getG();
+  var e = BN().fromBuffer(hash);
 
   do {
     var Q = G.mul(k);
diff --git a/test/test.ecdsa.js b/test/test.ecdsa.js
index f7db604..0a623a6 100644
--- a/test/test.ecdsa.js
+++ b/test/test.ecdsa.js
@@ -4,7 +4,7 @@ var Key = require('../lib/key');
 var Privkey = require('../lib/privkey');
 var Pubkey = require('../lib/pubkey');
 var Signature = require('../lib/signature');
-var bn = require('../lib/bn');
+var BN = require('../lib/bn');
 var point = require('../lib/point');
 var should = require('chai').should();
 
@@ -17,9 +17,36 @@ describe("ECDSA", function() {
   var ecdsa = new ECDSA();
   ecdsa.hash = Hash.sha256(new Buffer('test data'));
   ecdsa.key = new Key();
-  ecdsa.key.privkey = new Privkey(bn.fromBuffer(new Buffer('fee0a1f7afebf9d2a5a80c0c98a31c709681cce195cbcd06342b517970c0be1e', 'hex')));
-  ecdsa.key.pubkey = new Pubkey(point(bn.fromBuffer(new Buffer('ac242d242d23be966085a2b2b893d989f824e06c9ad0395a8a52f055ba39abb2', 'hex')),
-                                      bn.fromBuffer(new Buffer('4836ab292c105a711ed10fcfd30999c31ff7c02456147747e03e739ad527c380', 'hex'))));
+  ecdsa.key.privkey = new Privkey(BN.fromBuffer(new Buffer('fee0a1f7afebf9d2a5a80c0c98a31c709681cce195cbcd06342b517970c0be1e', 'hex')));
+  ecdsa.key.pubkey = new Pubkey(point(BN.fromBuffer(new Buffer('ac242d242d23be966085a2b2b893d989f824e06c9ad0395a8a52f055ba39abb2', 'hex')),
+                                      BN.fromBuffer(new Buffer('4836ab292c105a711ed10fcfd30999c31ff7c02456147747e03e739ad527c380', 'hex'))));
+
+  describe('#calci', function() {
+    
+    it('should calculate i', function() {
+      ecdsa.randomK();
+      ecdsa.sign();
+      ecdsa.calci();
+      should.exist(ecdsa.sig.i);
+    });
+
+    it('should calulate this known i', function() {
+      var hash = Hash.sha256(new Buffer('some data'));
+      var r = BN('71706645040721865894779025947914615666559616020894583599959600180037551395766', 10);
+      var s = BN('109412465507152403114191008482955798903072313614214706891149785278625167723646', 10);
+      var ecdsa = new ECDSA();
+      ecdsa.key = new Key();
+      ecdsa.key.privkey = Privkey();
+      ecdsa.key.privkey.bn = BN().fromBuffer(Hash.sha256(new Buffer('test')));
+      ecdsa.key.privkey2pubkey();
+      ecdsa.hash = hash;
+      ecdsa.sig = new Signature(r, s);
+
+      ecdsa.calci();
+      ecdsa.sig.i.should.equal(1);
+    });
+
+  });
 
   describe('#fromString', function() {
     
@@ -46,12 +73,24 @@ describe("ECDSA", function() {
     it('should generate a random k that is (almost always) greater than this relatively small number', function() {
       ecdsa.randomK();
       var k1 = ecdsa.k;
-      var k2 = bn(Math.pow(2, 32)).mul(bn(Math.pow(2, 32))).mul(bn(Math.pow(2, 32)));
+      var k2 = BN(Math.pow(2, 32)).mul(BN(Math.pow(2, 32))).mul(BN(Math.pow(2, 32)));
       k2.gt(k1).should.equal(false);
     });
 
   });
 
+  describe('#sig2pubkey', function() {
+
+    it('should calculate the correct public key', function() {
+      ecdsa.k = BN('114860389168127852803919605627759231199925249596762615988727970217268189974335', 10);
+      ecdsa.sign();
+      ecdsa.sig.i = 1;
+      var pubkey = ecdsa.sig2pubkey();
+      pubkey.point.eq(ecdsa.key.pubkey.point).should.equal(true);
+    });
+
+  });
+
   describe('#sigError', function() {
 
     it('should return an error if the hash is invalid', function() {
@@ -73,15 +112,15 @@ describe("ECDSA", function() {
       ecdsa.key = new Key();
       ecdsa.key.pubkey = pk;
       ecdsa.sig = new Signature();
-      ecdsa.sig.r = bn(0);
-      ecdsa.sig.s = bn(0);
+      ecdsa.sig.r = BN(0);
+      ecdsa.sig.s = BN(0);
       ecdsa.sigError().should.equal("r and s not in range");
     });
 
     it('should return an error if the signature is incorrect', function() {
       ecdsa.sig = new Signature();
       ecdsa.sig.fromString('3046022100e9915e6236695f093a4128ac2a956c40ed971531de2f4f41ba05fac7e2bd019c02210094e6a4a769cc7f2a8ab3db696c7cd8d56bcdbfff860a8c81de4bc6a798b90827');
-      ecdsa.sig.r = ecdsa.sig.r.add(bn(1));
+      ecdsa.sig.r = ecdsa.sig.r.add(BN(1));
       ecdsa.sigError().should.equal("Invalid signature");
     });