private static GroupElementP3 P1ToP3(ref GroupElementP1 p) => new GroupElementP3
{
X = FieldElementOperations.Multiplication(ref p.X, ref p.T),
Y = FieldElementOperations.Multiplication(ref p.Y, ref p.Z),
Z = FieldElementOperations.Multiplication(ref p.Z, ref p.T),
T = FieldElementOperations.Multiplication(ref p.X, ref p.Y)
};
private static GroupElementP1 Madd(ref GroupElementP3 p, ref GroupElementP4 q)
{
var t0 = FieldElementOperations.Add(ref p.Z, ref p.Z); /* D = 2*Z1 */
var r = new GroupElementP1();
/* YpX1 = Y1+X1 */
r.X = FieldElementOperations.Add(ref p.Y, ref p.X);
/* YmX1 = Y1-X1 */
r.Y = FieldElementOperations.Sub(ref p.Y, ref p.X);
/* A = YpX1*ypx2 */
r.Z = FieldElementOperations.Multiplication(ref r.X, ref q.YplusX);
/* B = YmX1*ymx2 */
r.Y = FieldElementOperations.Multiplication(ref r.Y, ref q.YminusX);
/* C = xy2d2*T1 */
r.T = FieldElementOperations.Multiplication(ref q.XY2D, ref p.T);
/* X3 = A-B */
r.X = FieldElementOperations.Sub(ref r.Z, ref r.Y);
/* Y3 = A+B */
r.Y = FieldElementOperations.Add(ref r.Z, ref r.Y);
/* Z3 = D+C */
r.Z = FieldElementOperations.Add(ref t0, ref r.T);
/* T3 = D-C */
r.T = FieldElementOperations.Sub(ref t0, ref r.T);
return(r);
}
private static GroupElementP1 P2ToP1(ref GroupElementP2 p)
{
var r = new GroupElementP1();
/* XX=X1^2 */
r.X = FieldElementOperations.Squared(ref p.X);
/* YY=Y1^2 */
r.Z = FieldElementOperations.Squared(ref p.Y);
/* B=2*Z1^2 */
r.T = FieldElementOperations.DoubleSquare(ref p.Z);
/* A=X1+Y1 */
r.Y = FieldElementOperations.Add(ref p.X, ref p.Y);
/* AA=A^2 */
var t0 = FieldElementOperations.Squared(ref r.Y);
/* Y3=YY+XX */
r.Y = FieldElementOperations.Add(ref r.Z, ref r.X);
/* Z3=YY-XX */
r.Z = FieldElementOperations.Sub(ref r.Z, ref r.X);
/* X3=AA-Y3 */
r.X = FieldElementOperations.Sub(ref t0, ref r.Y);
/* T3=B-Z3 */
r.T = FieldElementOperations.Sub(ref r.T, ref r.Z);
return(r);
}
