public static PointEdwardsProjective operator +(PointEdwardsProjective P, PointEdwardsProjective Q)//10M + 1S + 1*a + 1*d + 7add
{
BigInteger A, B, C, D, E, F, G, x, y, z;
if (Q.z == 1)
{
B = P.z * P.z;
C = P.x * Q.x;
D = P.y * Q.y;
E = P.E.b * C * D;
F = B - E;
G = B + E;
x = (P.z * F * ((P.x + P.y) * (Q.x + Q.y) - C - D)) % P.E.n;
y = (P.z * G * (D - P.E.a * C)) % P.E.n;
z = (F * G) % P.E.n;
return(new PointEdwardsProjective(x, y, z, P.E));
}
A = P.z * Q.z;
B = A * A;
C = P.x * Q.x;
D = P.y * Q.y;
E = P.E.b * C * D;
F = B - E;
G = B + E;
x = (A * F * ((P.x + P.y) * (Q.x + Q.y) - C - D)) % P.E.n;
y = (A * G * (D - P.E.a * C)) % P.E.n;
z = (F * G) % P.E.n;
return(new PointEdwardsProjective(x, y, z, P.E));
}
public static PointEdwardsInverted operator +(PointEdwardsInverted P, PointEdwardsInverted Q)//9M + 1S + 1*a + 1*d + 7add
{
BigInteger A, B, C, D, E, F, G, H, I, x, y, z;
if (Q.z == 1)
{
B = P.E.b * P.z * P.z;
C = P.x * Q.x;
D = P.y * Q.y;
E = C * D;
H = C - P.E.a * D;
I = (P.x + P.y) * (Q.x + Q.y) - C - D;
x = ((E + B) * H) % P.E.n;
y = ((E - B) * I) % P.E.n;
z = (P.z * H * I) % P.E.n;
return(new PointEdwardsInverted(x, y, z, P.E));
}
A = P.z * Q.z;
B = P.E.b * A * A;
C = P.x * Q.x;
D = P.y * Q.y;
E = C * D;
H = C - P.E.a * D;
I = (P.x + P.y) * (Q.x + Q.y) - C - D;
x = ((E + B) * H) % P.E.n;
y = ((E - B) * I) % P.E.n;
z = (A * H * I) % P.E.n;
return(new PointEdwardsInverted(x, y, z, P.E));
}
public PointEdwardsProjective(BigInteger x, BigInteger y, EllipticCurveEdwards E)
{
this.x = x;
this.y = y;
this.z = 1;
this.E = E;
}
public PointEdwardsInverted(BigInteger x, BigInteger y, BigInteger z, EllipticCurveEdwards E)
{
this.x = x;
this.y = y;
this.z = z;
this.E = E;
}
public PointEdwardsInverted(BigInteger x, BigInteger y, EllipticCurveEdwards E)
{
this.x = Algorithms.Invert(x, E.n);
this.y = Algorithms.Invert(y, E.n);
this.z = 1;
this.E = E;
}
public static PointEdwardsExtended operator +(PointEdwardsExtended P, PointEdwardsExtended Q)//9M + 1*a + 7add
{
BigInteger A, B, C, D, E, F, G, H, I, x, y, z, t;
if (Q.z == 1)
{
A = P.x * Q.x;
B = P.y * Q.y;
C = P.z * Q.t;
D = P.t;
E = D + C;
F = (P.x - P.y) * (Q.x + Q.y) + B - A;
G = B + P.E.a * A;
H = D - C;
x = (E * F) % P.E.n;
y = (G * H) % P.E.n;
t = (E * H) % P.E.n;
z = (F * G) % P.E.n;
return(new PointEdwardsExtended(x, y, z, t, P.E));
}
A = P.x * Q.x;
B = P.y * Q.y;
C = P.z * Q.t;
D = P.t * Q.z;
E = D + C;
F = (P.x - P.y) * (Q.x + Q.y) + B - A;
G = B + P.E.a * A;
H = D - C;
x = (E * F) % P.E.n;
y = (G * H) % P.E.n;
t = (E * H) % P.E.n;
z = (F * G) % P.E.n;
return(new PointEdwardsExtended(x, y, z, t, P.E));
}
public PointEdwardsExtended(BigInteger x, BigInteger y, EllipticCurveEdwards E)
{
this.x = x;
this.y = y;
this.z = 1;
this.t = (x * y) % E.n;
this.E = E;
}
public PointEdwardsExtended(BigInteger x, BigInteger y, BigInteger z, BigInteger t, EllipticCurveEdwards E)
{
this.x = x;
this.y = y;
this.z = z;
this.t = t;
this.E = E;
}
public override bool Equals(Object obj)
{
if (obj == null)
{
return(false);
}
EllipticCurveEdwards E = obj as EllipticCurveEdwards;
return(new EllipticCurveEdwards(this.a, this.b, this.n) == E);
}
}//extended
private static EllipticCurveEdwards GenerateCurve(BigInteger n, out BigInteger x, out BigInteger y, TorsionType type)
{
switch (type)
{
case TorsionType.RandomCurve:
return(EllipticCurveEdwards.GenerateCurveRandom(n, out x, out y));
case TorsionType.Curve12:
return(EllipticCurveEdwards.GenerateCurve12(n, out x, out y));
case TorsionType.Curve2x8:
return(EllipticCurveEdwards.GenerateCurve2x8(n, out x, out y));
case TorsionType.Curve12FromFile:
return(EllipticCurveEdwards.GetCurve(n, out x, out y, "curve12.txt"));
case TorsionType.Curve2x8FromFile:
return(EllipticCurveEdwards.GetCurve(n, out x, out y, "curve2x8.txt"));
default:
return(EllipticCurveEdwards.GenerateCurveRandom(n, out x, out y));
}
}
