public static void ScalarMult(byte[] k, int kOff, byte[] u, int uOff, byte[] r, int rOff)
{
uint[] n = new uint[8]; DecodeScalar(k, kOff, n);
int[] x1 = X25519Field.Create(); X25519Field.Decode(u, uOff, x1);
int[] x2 = X25519Field.Create(); X25519Field.Copy(x1, 0, x2, 0);
int[] z2 = X25519Field.Create(); z2[0] = 1;
int[] x3 = X25519Field.Create(); x3[0] = 1;
int[] z3 = X25519Field.Create();
int[] t1 = X25519Field.Create();
int[] t2 = X25519Field.Create();
Debug.Assert(n[7] >> 30 == 1U);
int bit = 254, swap = 1;
do
{
X25519Field.Apm(x3, z3, t1, x3);
X25519Field.Apm(x2, z2, z3, x2);
X25519Field.Mul(t1, x2, t1);
X25519Field.Mul(x3, z3, x3);
X25519Field.Sqr(z3, z3);
X25519Field.Sqr(x2, x2);
X25519Field.Sub(z3, x2, t2);
X25519Field.Mul(t2, C_A24, z2);
X25519Field.Add(z2, x2, z2);
X25519Field.Mul(z2, t2, z2);
X25519Field.Mul(x2, z3, x2);
X25519Field.Apm(t1, x3, x3, z3);
X25519Field.Sqr(x3, x3);
X25519Field.Sqr(z3, z3);
X25519Field.Mul(z3, x1, z3);
--bit;
int word = bit >> 5, shift = bit & 0x1F;
int kt = (int)(n[word] >> shift) & 1;
swap ^= kt;
X25519Field.CSwap(swap, x2, x3);
X25519Field.CSwap(swap, z2, z3);
swap = kt;
}while (bit >= 3);
Debug.Assert(swap == 0);
for (int i = 0; i < 3; ++i)
{
PointDouble(x2, z2);
}
X25519Field.Inv(z2, z2);
X25519Field.Mul(x2, z2, x2);
X25519Field.Normalize(x2);
X25519Field.Encode(x2, r, rOff);
}
public static void ScalarMultBase(byte[] k, int kOff, byte[] r, int rOff)
{
Precompute();
uint[] n = new uint[8]; DecodeScalar(k, kOff, n);
int[] x0 = X25519Field.Create();
//int[] x1 = X25519Field.Create(); X25519Field.Copy(S_x, 0, x1, 0);
int[] x1 = X25519Field.Create(); x1[0] = 1;
int[] z1 = X25519Field.Create(); z1[0] = 1;
int[] x2 = X25519Field.Create(); X25519Field.Copy(PsubS_x, 0, x2, 0);
int[] z2 = X25519Field.Create(); z2[0] = 1;
int[] A = x1;
int[] B = z1;
int[] C = x0;
int[] D = A;
int[] E = B;
Debug.Assert(n[7] >> 30 == 1U);
int off = 0, bit = 3, swap = 1;
do
{
X25519Field.Copy(precompBase, off, x0, 0);
off += X25519Field.Size;
int word = bit >> 5, shift = bit & 0x1F;
int kt = (int)(n[word] >> shift) & 1;
swap ^= kt;
X25519Field.CSwap(swap, x1, x2);
X25519Field.CSwap(swap, z1, z2);
swap = kt;
X25519Field.Apm(x1, z1, A, B);
X25519Field.Mul(x0, B, C);
X25519Field.Carry(A);
X25519Field.Apm(A, C, D, E);
X25519Field.Sqr(D, D);
X25519Field.Sqr(E, E);
X25519Field.Mul(z2, D, x1);
X25519Field.Mul(x2, E, z1);
}while (++bit < 255);
Debug.Assert(swap == 1);
for (int i = 0; i < 3; ++i)
{
PointDouble(x1, z1);
}
X25519Field.Inv(z1, z1);
X25519Field.Mul(x1, z1, x1);
X25519Field.Normalize(x1);
X25519Field.Encode(x1, r, rOff);
}
private static void PointDouble(int[] x, int[] z)
{
int[] A = X25519Field.Create();
int[] B = X25519Field.Create();
X25519Field.Apm(x, z, A, B);
X25519Field.Sqr(A, A);
X25519Field.Sqr(B, B);
X25519Field.Mul(A, B, x);
X25519Field.Sub(A, B, A);
X25519Field.Mul(A, C_A24, z);
X25519Field.Add(z, B, z);
X25519Field.Mul(z, A, z);
}
public static void ScalarMultBase(byte[] k, int kOff, byte[] r, int rOff)
{
int[] y = X25519Field.Create();
int[] z = X25519Field.Create();
Ed25519.ScalarMultBaseYZ(k, kOff, y, z);
X25519Field.Apm(z, y, y, z);
X25519Field.Inv(z, z);
X25519Field.Mul(y, z, y);
X25519Field.Normalize(y);
X25519Field.Encode(y, r, rOff);
}
public static void Precompute()
{
if (precompBase != null)
{
return;
}
precompBase = new int[X25519Field.Size * 252];
int[] xs = precompBase;
int[] zs = new int[X25519Field.Size * 251];
int[] x = X25519Field.Create(); x[0] = 9;
int[] z = X25519Field.Create(); z[0] = 1;
int[] n = X25519Field.Create();
int[] d = X25519Field.Create();
X25519Field.Apm(x, z, n, d);
int[] c = X25519Field.Create(); X25519Field.Copy(d, 0, c, 0);
int off = 0;
for (;;)
{
X25519Field.Copy(n, 0, xs, off);
if (off == (X25519Field.Size * 251))
{
break;
}
PointDouble(x, z);
X25519Field.Apm(x, z, n, d);
X25519Field.Mul(n, c, n);
X25519Field.Mul(c, d, c);
X25519Field.Copy(d, 0, zs, off);
off += X25519Field.Size;
}
int[] u = X25519Field.Create();
X25519Field.Inv(c, u);
for (;;)
{
X25519Field.Copy(xs, off, x, 0);
X25519Field.Mul(x, u, x);
//X25519Field.Normalize(x);
X25519Field.Copy(x, 0, precompBase, off);
if (off == 0)
{
break;
}
off -= X25519Field.Size;
X25519Field.Copy(zs, off, z, 0);
X25519Field.Mul(u, z, u);
}
}