private static void PointAddPrecomp(PointPrecomp p, PointAccum r)
{
int[] A = X25519Field.Create();
int[] B = X25519Field.Create();
int[] C = X25519Field.Create();
int[] E = r.u;
int[] F = X25519Field.Create();
int[] G = X25519Field.Create();
int[] H = r.v;
X25519Field.Apm(r.y, r.x, B, A);
X25519Field.Mul(A, p.ymx_h, A);
X25519Field.Mul(B, p.ypx_h, B);
X25519Field.Mul(r.u, r.v, C);
X25519Field.Mul(C, p.xyd, C);
X25519Field.Apm(B, A, H, E);
X25519Field.Apm(r.z, C, G, F);
X25519Field.Carry(G);
X25519Field.Mul(E, F, r.x);
X25519Field.Mul(G, H, r.y);
X25519Field.Mul(F, G, r.z);
}
private static void PointAddVar(bool negate, PointExt p, PointExt q, PointExt r)
{
int[] A = X25519Field.Create();
int[] B = X25519Field.Create();
int[] C = X25519Field.Create();
int[] D = X25519Field.Create();
int[] E = X25519Field.Create();
int[] F = X25519Field.Create();
int[] G = X25519Field.Create();
int[] H = X25519Field.Create();
int[] c, d, f, g;
if (negate)
{
c = D; d = C; f = G; g = F;
}
else
{
c = C; d = D; f = F; g = G;
}
X25519Field.Apm(p.y, p.x, B, A);
X25519Field.Apm(q.y, q.x, d, c);
X25519Field.Mul(A, C, A);
X25519Field.Mul(B, D, B);
X25519Field.Mul(p.t, q.t, C);
X25519Field.Mul(C, C_d2, C);
X25519Field.Mul(p.z, q.z, D);
X25519Field.Add(D, D, D);
X25519Field.Apm(B, A, H, E);
X25519Field.Apm(D, C, g, f);
X25519Field.Carry(g);
X25519Field.Mul(E, F, r.x);
X25519Field.Mul(G, H, r.y);
X25519Field.Mul(F, G, r.z);
X25519Field.Mul(E, H, r.t);
}
private static void PointDouble(PointAccum r)
{
int[] A = X25519Field.Create();
int[] B = X25519Field.Create();
int[] C = X25519Field.Create();
int[] E = r.u;
int[] F = X25519Field.Create();
int[] G = X25519Field.Create();
int[] H = r.v;
X25519Field.Sqr(r.x, A);
X25519Field.Sqr(r.y, B);
X25519Field.Sqr(r.z, C);
X25519Field.Add(C, C, C);
X25519Field.Apm(A, B, H, G);
X25519Field.Add(r.x, r.y, E);
X25519Field.Sqr(E, E);
X25519Field.Sub(H, E, E);
X25519Field.Add(C, G, F);
X25519Field.Carry(F);
X25519Field.Mul(E, F, r.x);
X25519Field.Mul(G, H, r.y);
X25519Field.Mul(F, G, r.z);
}
public static void Precompute()
{
lock (precompLock)
{
if (precompBase != null)
{
return;
}
// Precomputed table for the base point in verification ladder
{
PointExt b = new PointExt();
X25519Field.Copy(B_x, 0, b.x, 0);
X25519Field.Copy(B_y, 0, b.y, 0);
PointExtendXY(b);
precompBaseTable = PointPrecompVar(b, 1 << (WnafWidthBase - 2));
}
PointAccum p = new PointAccum();
X25519Field.Copy(B_x, 0, p.x, 0);
X25519Field.Copy(B_y, 0, p.y, 0);
PointExtendXY(p);
precompBase = new int[PrecompBlocks * PrecompPoints * 3 * X25519Field.Size];
int off = 0;
for (int b = 0; b < PrecompBlocks; ++b)
{
PointExt[] ds = new PointExt[PrecompTeeth];
PointExt sum = new PointExt();
PointSetNeutral(sum);
for (int t = 0; t < PrecompTeeth; ++t)
{
PointExt q = PointCopy(p);
PointAddVar(true, sum, q, sum);
PointDouble(p);
ds[t] = PointCopy(p);
if (b + t != PrecompBlocks + PrecompTeeth - 2)
{
for (int s = 1; s < PrecompSpacing; ++s)
{
PointDouble(p);
}
}
}
PointExt[] points = new PointExt[PrecompPoints];
int k = 0;
points[k++] = sum;
for (int t = 0; t < (PrecompTeeth - 1); ++t)
{
int size = 1 << t;
for (int j = 0; j < size; ++j, ++k)
{
PointAddVar(false, points[k - size], ds[t], points[k] = new PointExt());
}
}
Debug.Assert(k == PrecompPoints);
for (int i = 0; i < PrecompPoints; ++i)
{
PointExt q = points[i];
int[] x = X25519Field.Create();
int[] y = X25519Field.Create();
X25519Field.Add(q.z, q.z, x);
// TODO[ed25519] Batch inversion
X25519Field.Inv(x, y);
X25519Field.Mul(q.x, y, x);
X25519Field.Mul(q.y, y, y);
PointPrecomp r = new PointPrecomp();
X25519Field.Apm(y, x, r.ypx_h, r.ymx_h);
X25519Field.Mul(x, y, r.xyd);
X25519Field.Mul(r.xyd, C_d4, r.xyd);
X25519Field.Normalize(r.ypx_h);
X25519Field.Normalize(r.ymx_h);
//X25519Field.Normalize(r.xyd);
X25519Field.Copy(r.ypx_h, 0, precompBase, off); off += X25519Field.Size;
X25519Field.Copy(r.ymx_h, 0, precompBase, off); off += X25519Field.Size;
X25519Field.Copy(r.xyd, 0, precompBase, off); off += X25519Field.Size;
}
}
Debug.Assert(off == precompBase.Length);
}
}