Double and Add algorithm

Very much like the fast powering algorithm - binary expansion can be used to calculate Q= nP fast.
ex n=947 = 2^9+2^8+2^7+2^5+2^4+2^1+2^0

which means that 947P = P+2P+16P+32P+128P+256P+512P. Thats 9 doublings and 6 additions, much better than 946 additions....
if we allow subtraction as well (ternary expansion) its even better.

want to calculate nP?

algorithm:

1. input point P from E(Fp) and n>=1
2. set Q=P and R=Ø (point at infinity)
3. loop while n>0{
     if n = 1 (mod2) set R= R+Q
     set Q=2Q and n=n/2 (floor)}
4.return R (which equals nP)

I've now posted working sourcecode available at http://christelbach.com
(source code contained in master thesis)

for instance this:
//double and add algorithm

private BigInteger[] calculatenP(BigInteger x, BigInteger y, BigInteger n, BigInteger A, BigInteger modp)
{
BigInteger[] Q = { x, y };
BigInteger[] R = { 0, 0 };
while (n > 0)
{
   BigInteger t = BigInteger.ModPow(n, 1, 2); 
   if ((t) == 1)
   {
   R = addPoints(Q[0], Q[1], R[0], R[1], modp);
   } 
   Q = doublePoints(Q[0], Q[1], A, modp);
   n = n / 2;
}
BigInteger[] resPoint = { R[0], R[1] };
return resPoint;
}

Look in the pdf file for the methods addPoints() and doublePoints()