//return: P * factor on the elliptic curves domain.
public OwnECPoint MultiplyWithEndomorphism(OwnECPoint p, ulong[] factor)
{
OwnECPoint result;
if (!this.SupportsEndomorphism)
{
result = this.Multiply(p, factor);
return(result);
}
BigInteger lambda = W1ModOrder.ToBigInteger();
BigInteger k = factor.ToBigInteger(), k1, k2;
SplitKToHalfBits(k, lambda, out k1, out k2);
OwnECPoint q = p.Copy();
MultiplyModP(q.X, W1ModP);
//OwnECPoint test1 = Multiply(p, W1ModOrder);
//bool testok = test1.ToString() == q.ToString();
//if (!testok)
//{
// Debugger.Break();
//}
result = DualMultiply(p, k1, q, k2);
return(result);
}
public OwnECPoint Negative(OwnECPoint point)
{
OwnECPoint result = point.Copy();
SubtractModP(this.P, result.Y, result.Y);
return(result);
}
//return: P * factor on the elliptic curves domain.
public OwnECPoint MultiplyReference(OwnECPoint p, ulong[] factor)
{
int high = HighBit(factor);
if (high < 0)
{
return(new OwnECPoint(p.X, p.Y, true));
}
OwnECPoint result = p.Copy();
for (int i = high; --i >= 0;)
{
GetDouble(ref result);
if ((factor[i >> 6] & (1UL << (i & 63))) != 0)
{
Add(ref result, p);
}
}
RemodFriendlyPrime(result.X);
RemodFriendlyPrime(result.Y);
return(result);
}
//return: P * factor on the elliptic curves domain.
public OwnECPoint DualMultiply(OwnECPoint p1, BigInteger k1, OwnECPoint p2, BigInteger k2)
{
if (k1 < 0)
{
p1 = Negative(p1);
k1 = -k1;
}
if (k2 < 0)
{
p2 = Negative(p2);
k2 = -k2;
}
BigInteger exp1 = k1 ^ (k1 * 3);
BigInteger exp2 = k2 ^ (k2 * 3);
BigInteger max = BigInteger.Max(exp1, exp2);
int high = max <= 0 ? 0 : 1 + (int)Math.Ceiling(BigInteger.Log(max, 2));
JacobianECPoint x = new JacobianECPoint(p1.X, p1.Y, true);
OwnECPoint cacheAdd = p1.Copy();
OwnECPoint cacheSub = p1.Copy();
Add(ref cacheAdd, p2);
Subtract(ref cacheSub, p2);
BigInteger bit = BigInteger.One << high;
for (int i = high; --i >= 0; bit >>= 1)
{
GetDouble(ref x);
if ((exp1 & bit) != 0 && (exp2 & bit) != 0)
{
int branch = ((k1 & bit) != 0 ? 0 : 1) + ((k2 & bit) != 0 ? 0 : 2);
switch (branch)
{
case 0: Subtract(ref x, cacheAdd); break;
case 1: Add(ref x, cacheSub); break;
case 2: Subtract(ref x, cacheSub); break;
case 3: Add(ref x, cacheAdd); break;
}
continue;
}
if ((exp1 & bit) != 0)
{
if ((k1 & bit) != 0)
{
Subtract(ref x, p1);
}
else
{
Add(ref x, p1);
}
continue;
}
if ((exp2 & bit) != 0)
{
if ((k2 & bit) != 0)
{
Subtract(ref x, p2);
}
else
{
Add(ref x, p2);
}
continue;
}
}
OwnECPoint result = x.ToECPoint(this);
return(result);
}