/**
* 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>.
*/
public ECPoint Multiply(ECPoint p, BigInteger k, PreCompInfo preCompInfo)
{
WNafPreCompInfo wnafPreCompInfo;
if ((preCompInfo != null) && (preCompInfo is WNafPreCompInfo))
{
wnafPreCompInfo = (WNafPreCompInfo)preCompInfo;
}
else
{
// Ignore empty PreCompInfo or PreCompInfo of incorrect type
wnafPreCompInfo = new WNafPreCompInfo();
}
// floor(log2(k))
int m = k.BitLength;
// width of the Window NAF
sbyte width;
// Required length of precomputation array
int reqPreCompLen;
// Determine optimal width and corresponding length of precomputation
// array based on literature values
if (m < 13)
{
width = 2;
reqPreCompLen = 1;
}
else
{
if (m < 41)
{
width = 3;
reqPreCompLen = 2;
}
else
{
if (m < 121)
{
width = 4;
reqPreCompLen = 4;
}
else
{
if (m < 337)
{
width = 5;
reqPreCompLen = 8;
}
else
{
if (m < 897)
{
width = 6;
reqPreCompLen = 16;
}
else
{
if (m < 2305)
{
width = 7;
reqPreCompLen = 32;
}
else
{
width = 8;
reqPreCompLen = 127;
}
}
}
}
}
}
// The length of the precomputation array
int preCompLen = 1;
ECPoint[] preComp = wnafPreCompInfo.GetPreComp();
ECPoint twiceP = wnafPreCompInfo.GetTwiceP();
// Check if the precomputed ECPoints already exist
if (preComp == null)
{
// Precomputation must be performed from scratch, create an empty
// precomputation array of desired length
preComp = new ECPoint[]{ p };
}
else
{
// Take the already precomputed ECPoints to start with
preCompLen = preComp.Length;
}
if (twiceP == null)
{
// Compute twice(p)
twiceP = p.Twice();
}
if (preCompLen < reqPreCompLen)
{
// Precomputation array must be made bigger, copy existing preComp
// array into the larger new preComp array
ECPoint[] oldPreComp = preComp;
preComp = new ECPoint[reqPreCompLen];
Array.Copy(oldPreComp, 0, preComp, 0, preCompLen);
for (int i = preCompLen; i < reqPreCompLen; i++)
{
// Compute the new ECPoints for the precomputation array.
// The values 1, 3, 5, ..., 2^(width-1)-1 times p are
// computed
preComp[i] = twiceP.Add(preComp[i - 1]);
}
}
// Compute the Window NAF of the desired width
sbyte[] wnaf = WindowNaf(width, k);
int l = wnaf.Length;
// Apply the Window NAF to p using the precomputed ECPoint values.
ECPoint q = p.Curve.Infinity;
for (int i = l - 1; i >= 0; i--)
{
q = q.Twice();
if (wnaf[i] != 0)
{
if (wnaf[i] > 0)
{
q = q.Add(preComp[(wnaf[i] - 1)/2]);
}
else
{
// wnaf[i] < 0
q = q.Subtract(preComp[(-wnaf[i] - 1)/2]);
}
}
}
// Set PreCompInfo in ECPoint, such that it is available for next
// multiplication.
wnafPreCompInfo.SetPreComp(preComp);
wnafPreCompInfo.SetTwiceP(twiceP);
p.SetPreCompInfo(wnafPreCompInfo);
return q;
}