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 FieldElement CalculateLadderStep(byte[] n, ref FieldElement p, int noffset = 0)
{
var e = new byte[32];
uint i;
FieldElement x1;
FieldElement x2;
FieldElement z2;
FieldElement x3;
FieldElement z3;
int pos;
uint swap;
for (i = 0; i < 32; ++i)
{
e[i] = n[noffset + i];
}
ClampOperation.Clamp(e, 0);
x1 = p;
x2 = FieldElementOperations.Set1();
z2 = FieldElementOperations.Set0();
x3 = x1;
z3 = FieldElementOperations.Set1();
swap = 0;
for (pos = 254; pos >= 0; --pos)
{
var b = (uint)(e[pos / 8] >> (pos & 7));
b &= 1;
swap ^= b;
FieldElementOperations.Swap(ref x2, ref x3, swap);
FieldElementOperations.Swap(ref z2, ref z3, swap);
swap = b;
/* D = X3-Z3 */
var tmp0 = FieldElementOperations.Sub(ref x3, ref z3);
/* B = X2-Z2 */
var tmp1 = FieldElementOperations.Sub(ref x2, ref z2);
/* A = X2+Z2 */
x2 = FieldElementOperations.Add(ref x2, ref z2);
/* C = X3+Z3 */
z2 = FieldElementOperations.Add(ref x3, ref z3);
/* DA = D*A */
z3 = FieldElementOperations.Multiplication(ref tmp0, ref x2);
/* CB = C*B */
z2 = FieldElementOperations.Multiplication(ref z2, ref tmp1);
/* BB = B^2 */
tmp0 = FieldElementOperations.Squared(ref tmp1);
/* AA = A^2 */
tmp1 = FieldElementOperations.Squared(ref x2);
/* t0 = DA+CB */
x3 = FieldElementOperations.Add(ref z3, ref z2);
/* t1 = DA-CB */
z2 = FieldElementOperations.Sub(ref z3, ref z2);
/* X4 = AA*BB */
x2 = FieldElementOperations.Multiplication(ref tmp1, ref tmp0);
/* E = AA-BB */
tmp1 = FieldElementOperations.Sub(ref tmp1, ref tmp0);
/* t2 = t1^2 */
z2 = FieldElementOperations.Squared(ref z2);
/* t3 = a24*E */
z3 = FieldElementOperations.Multiply121666(ref tmp1);
/* X5 = t0^2 */
x3 = FieldElementOperations.Squared(ref x3);
/* t4 = BB+t3 */
tmp0 = FieldElementOperations.Add(ref tmp0, ref z3);
/* Z5 = X1*t2 */
z3 = FieldElementOperations.Multiplication(ref x1, ref z2);
/* Z4 = E*t4 */
z2 = FieldElementOperations.Multiplication(ref tmp1, ref tmp0);
}
FieldElementOperations.Swap(ref x2, ref x3, swap);
FieldElementOperations.Swap(ref z2, ref z3, swap);
z2 = FieldElementOperations.Invert(ref z2);
x2 = FieldElementOperations.Multiplication(ref x2, ref z2);
var q = x2;
Array.Clear(e, 0, e.Length);
return(q);
}