// Multiplication using strassen algorithm
public static SL2 MulStrassen(SL2 a, SL2 b)
{
GF127[] t = new GF127[7];
t[0] = (a[0][0] + a[1][1]) * (b[0][0] + b[1][1]); // t[0] == (a11 + a22) * (b11 + b22)
t[1] = (a[1][0] + a[1][1]) * b[0][0]; // t[1] == (a21 + a22) * b11
t[2] = (b[0][1] + b[1][1]) * a[0][0]; // t[2] == (b12 + b22) * a11
t[3] = (b[1][0] + b[0][0]) * a[1][1]; // t[3] == (b21 + b11) * a22
t[4] = (a[0][0] + a[0][1]) * b[1][1]; // t[4] == (a11 + a12) * b22
t[5] = (a[1][0] + a[0][0]) * (b[0][0] + b[0][1]); // t[5] == (a21 + a11) * (b11 + b12)
t[6] = (a[0][1] + a[1][1]) * (b[1][0] + b[1][1]); // t[6] == (a12 + a22) * (b21 + b22)
SL2 r = new SL2();
r[0][1] = t[2] + t[4]; // r12 == a11*b12 + a11*b22 + a11*b22 + a12*b22 == a11*b12 + a12*b22
r[1][0] = t[1] + t[3]; // r21 == a21*b11 + a22*b11 + a22*b21 + a22*b11 == a21*b11 + a22*b21
// r11 == (a11*b11 + a22*b11` + a11*b22` + a22*b22`) + (a22*b21` + a22*b11`) + (a11*b22` + a12*b22`) + (a12*b21 + a22*b21` + a12*b22` + a22*b22`)
// == a11*b11 + a12*b21
r[0][0] = t[0] + t[3] + t[4] + t[6];
// r22 == (a11*b11` + a22*b11` + a11*b22` + a22*b22) + (a21*b11` + a22*b11`) + (a11*b12` + a11*b22`) + (a21*b11` + a11*b11` + a21*b12 + a11*b12`)
// == a21*b12 + a22*b22
r[1][1] = t[0] + t[1] + t[2] + t[5];
return(r);
}
public SL2 FromByteArray(byte[] data)
{
if (data.Length != 64)
{
throw new ArgumentException();
}
this[0][0] = new GF127().FromByteArray(data[0..16]);
// MulB() returns this*B, B = {{x, x+1}, {1, 1}}
public SL2 MulB()
{
var r = new SL2();
r[0][0] = GF127.Mul10(this[0][0]) + this[0][1]; // r11 == t11*x + t12
r[0][1] = GF127.Mul10(this[0][0]) + this[0][0] + this[0][1]; // r12 == t11*x + t11 + t12
r[1][0] = GF127.Mul10(this[1][0]) + this[1][1]; // r21 == t21*x + t22
r[1][1] = GF127.Mul10(this[1][0]) + this[1][0] + this[1][1]; // r22 == t21*x + t21 + t22
return(r);
}
// Inv() returns inverse of a in SL2(GF(2^127))
public static SL2 Inv(SL2 a)
{
GF127[] t = new GF127[2];
t[0] = a[0][0] * a[1][1] + a[0][1] * a[1][0]; //
t[1] = GF127.Inv(t[0]);
SL2 r = new SL2();
r[1][1] = t[1] * a[0][0];
r[0][1] = t[1] * a[0][1];
r[1][0] = t[1] * a[1][0];
r[0][0] = t[1] * a[1][1];
return(r);
}
public SL2(GF127 g00, GF127 g01, GF127 g10, GF127 g11)
: this(new GF127[][] { new[] { g00, g01 }, new[] { g10, g11 } })
{
}