/**
* Multiplies <code>this</code> by an integer <code>k</code> using the
* Window NAF method.
* @param k The integer by which <code>this</code> is multiplied.
* @return A new <code>ECPoint</code> which equals <code>this</code>
* multiplied by <code>k</code>.
*/
protected override ECPoint MultiplyPositive(ECPoint p, BigInteger k)
{
// Clamp the window width in the range [2, 16]
int width = System.Math.Max(2, System.Math.Min(16, GetWindowSize(k.BitLength)));
WNafPreCompInfo wnafPreCompInfo = WNafUtilities.Precompute(p, width, true);
ECPoint[] preComp = wnafPreCompInfo.PreComp;
ECPoint[] preCompNeg = wnafPreCompInfo.PreCompNeg;
int[] wnaf = WNafUtilities.GenerateCompactWindowNaf(width, k);
ECPoint R = p.Curve.Infinity;
int i = wnaf.Length;
/*
* NOTE: We try to optimize the first window using the precomputed points to substitute an
* addition for 2 or more doublings.
*/
if (i > 1)
{
int wi = wnaf[--i];
int digit = wi >> 16, zeroes = wi & 0xFFFF;
int n = System.Math.Abs(digit);
ECPoint[] table = digit < 0 ? preCompNeg : preComp;
// Optimization can only be used for values in the lower half of the table
if ((n << 2) < (1 << width))
{
int highest = LongArray.BitLengths[n];
// TODO Get addition/doubling cost ratio from curve and compare to 'scale' to see if worth substituting?
int scale = width - highest;
int lowBits = n ^ (1 << (highest - 1));
int i1 = ((1 << (width - 1)) - 1);
int i2 = (lowBits << scale) + 1;
R = table[i1 >> 1].Add(table[i2 >> 1]);
zeroes -= scale;
//Console.WriteLine("Optimized: 2^" + scale + " * " + n + " = " + i1 + " + " + i2);
}
else
{
R = table[n >> 1];
}
R = R.TimesPow2(zeroes);
}
while (i > 0)
{
int wi = wnaf[--i];
int digit = wi >> 16, zeroes = wi & 0xFFFF;
int n = System.Math.Abs(digit);
ECPoint[] table = digit < 0 ? preCompNeg : preComp;
ECPoint r = table[n >> 1];
R = R.TwicePlus(r);
R = R.TimesPow2(zeroes);
}
return(R);
}