ecdsa: opt for shiftRight, pow and square

In the given situations, these offer better readability, or in the case
of shiftRight, a substantial performance increase.

src/ec.js

@@ -170,9 +170,9 @@ function pointFpTwice() {
     // x3 = 2 * y1 * z1 * (w^2 - 8 * x1 * y1^2 * z1)
     var x3 = w.square().subtract(x1.shiftLeft(3).multiply(y1sqz1)).shiftLeft(1).multiply(y1z1).mod(this.curve.q);
     // y3 = 4 * y1^2 * z1 * (3 * w * x1 - 2 * y1^2 * z1) - w^3
-    var y3 = w.multiply(THREE).multiply(x1).subtract(y1sqz1.shiftLeft(1)).shiftLeft(2).multiply(y1sqz1).subtract(w.square().multiply(w)).mod(this.curve.q);
+    var y3 = w.multiply(THREE).multiply(x1).subtract(y1sqz1.shiftLeft(1)).shiftLeft(2).multiply(y1sqz1).subtract(w.pow(3)).mod(this.curve.q);
     // z3 = 8 * (y1 * z1)^3
-    var z3 = y1z1.square().multiply(y1z1).shiftLeft(3).mod(this.curve.q);
+    var z3 = y1z1.pow(3).shiftLeft(3).mod(this.curve.q);
 
     return new ECPointFp(this.curve, this.curve.fromBigInteger(x3), this.curve.fromBigInteger(y3), z3);
 }
@@ -348,7 +348,7 @@ ECPointFp.decodeFrom = function (curve, buffer) {
     }
 
     // Convert x to point
-    var alpha = x.square().multiply(x).add(SEVEN).mod(p)
+    var alpha = x.pow(3).add(SEVEN).mod(p)
     var beta = alpha.modPow(curve.P_OVER_FOUR, p)
 
     // If beta is even, but y isn't, or vice versa, then convert it,
@@ -440,10 +440,9 @@ ECPointFp.prototype.isOnCurve = function () {
   var y = this.getY().toBigInteger();
   var a = this.curve.getA().toBigInteger();
   var b = this.curve.getB().toBigInteger();
-  var n = this.curve.getQ();
-  var lhs = y.multiply(y).mod(n);
-  var rhs = x.multiply(x).multiply(x)
-    .add(a.multiply(x)).add(b).mod(n);
+  var p = this.curve.getQ()
+  var lhs = y.square().mod(p)
+  var rhs = x.pow(3).add(a.multiply(x)).add(b).mod(p)
   return lhs.equals(rhs);
 };
 

src/ecdsa.js

@@ -73,7 +73,7 @@ var ecdsa = {
     var s = k.modInverse(n).multiply(e.add(D.multiply(r))).mod(n)
     assert.notEqual(s.signum(), 0, 'Invalid S value')
 
-    var N_OVER_TWO = n.divide(BigInteger.valueOf(2))
+    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) {
@@ -263,7 +263,7 @@ var ecdsa = {
     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 alpha = x.pow(3).add(a.multiply(x)).add(b).mod(p)
     var beta = alpha.modPow(curve.P_OVER_FOUR, p)
 
     // If beta is even, but y isn't, or vice versa, then convert it,

test/ecdsa.js

@@ -59,7 +59,8 @@ describe('ecdsa', function() {
       var psig = ecdsa.parseSig(signature)
 
       // See BIP62 for more information
-      assert(psig.s.compareTo(ecparams.getN().divide(BigInteger.valueOf(2))) <= 0)
+      var N_OVER_TWO = ecparams.getN().shiftRight(1)
+      assert(psig.s.compareTo(N_OVER_TWO) <= 0)
     })
   })