// ec-function: Y^2 = X^3 + a*X + b 'modulo' P
//P = {Xp, Yp}; Q = {Xq, Yq}
//ADD: S = (Yp - Yq) / (Xp - Xq)
// RESULT = {Xr = S * S - Xp - Xq; Yr = S(Xp - Xr) - Yp}
//DUB: S = (3 * Xp * Xp + a) / (2 * Yp)
// RESULT = {Xr = S * S - 2 * Xp ; Yr = S(Xp - Xr) - Yp}
public void GetDouble(ref OwnECPoint p)
{ //return: 2 * p
if (p.IsInfinity)
{
return;
}
if (IsZero(p.Y))
{
p.SetInfinity();
return;
}
Let(S1, p.X);
SquareModP(S1); AddScaledModP(S1, S1, 2);
AddModP(S1, A);
Let(S2, p.Y);
AddModP(S2, S2);
this.RemodFriendlyPrime(S1);
this.RemodFriendlyPrime(S2);
AsmX64Operations.DivideModuloPrime(S1, S2, P, N);
Let(R1, S1);
SquareModP(S1);
SubScaledModP(S1, p.X, 2); //S1 = Rx = S * S - 2 * Px
SubtractModP(p.X, S1, S2); //S2 = Px - Rx
MultiplyModP(S2, R1);
SubModP(S2, p.Y); //S2 = S(Px - Rx) - Py
p.SetFrom(S1, S2, false);
}
public void Add(ref OwnECPoint p, OwnECPoint q, bool subtract = false)
{ //returns: P + Q
if (p.IsInfinity || q.IsInfinity)
{
if (!q.IsInfinity)
{
p.SetFrom(q.X, q.Y, q.IsInfinity);
if (subtract)
{
SubtractModP(P, p.Y, p.Y);
}
}
return;
}
SubtractModP(p.X, q.X, S2); //s2 = Px - Qx
if (subtract)
{ //s1 = Py - Qy; in case of subtract real Q.Y is -Q.Y so we add the value modulo P.
AdditionModP(p.Y, q.Y, S1); //s1 = Py - Qy
}
else
{
SubtractModP(p.Y, q.Y, S1);
}
if (IsZero(S2))
{ //Px == Qx
if (IsZero(S1))
{ // P == Q
GetDouble(ref p);
return;
}
p.SetInfinity();
return;
}
this.RemodFriendlyPrime(S1);
this.RemodFriendlyPrime(S2);
AsmX64Operations.DivideModuloPrime(S1, S2, P, N); //S = s1 = s1 / s2 'modulo' P.
Let(R1, S1);
SquareModP(S1);
SubModP(S1, p.X);
SubModP(S1, q.X); //s1 = Result.x = S * S - Px - Qx
SubtractModP(p.X, S1, S2); //s2 = Px - Rx
MultiplyModP(S2, R1);
SubModP(S2, p.Y); //s2 = S(Px - Rx) - Py
p.SetFrom(S1, S2, false);
}