Lucas Lehmer optimization

I've been working to optimize the Lucas-Lehmer primality test using C# code (yes I'm doing something with Mersenne primes to calculate perfect numbers. I was wondering it is possible with the current code to make further improvements in speed. I use the System.Numerics.BigInteger class to hold the numbers, perhaps it is not the wisest, we'll see it then.

This code is actually based on the intelligence found on: http://en.wikipedia.org/wiki/Lucas%E2%80%93Lehmer_primality_test

This page (at the timestamp) section, some proof is given to optimize the division away.

The code for the LucasTest is:

public bool LucasLehmerTest(int num)
{
  if (num % 2 == 0)
     return num == 2;
  else
  {
     BigInteger ss = new BigInteger(4);
     for (int i = 3; i <= num; i++)
     {
        ss = KaratsubaSquare(ss) - 2;
        ss = LucasLehmerMod(ss, num);
     }
     return ss == BigInteger.Zero;
  }

}

Edit: Which is faster than using ModPow from the BigInteger class as suggested by Mare Infinitus below. That implementation is:

public bool LucasLehmerTest(int num)
{
  if (num % 2 == 0)
     return num == 2;
  else
  {
     BigInteger m = (BigInteger.One << num) - 1;
     BigInteger ss = new BigInteger(4);
     for (int i = 3; i <= num; i++)
       ss = (BigInteger.ModPow(ss, 2, m) - 2) % m;
     return ss == BigInteger.Zero;
  }

}

The LucasLehmerMod method is implemented as follows:

public BigInteger LucasLehmerMod(BigInteger divident, int divisor)
{
   BigInteger mask = (BigInteger.One << divisor) - 1;  //Mask
   BigInteger remainder = BigInteger.Zero;
   BigInteger temporaryResult = divident;

   do
   {
      remainder = temporaryResult & mask;
      temporaryResult >>= divisor;
      temporaryResul