public static void Invert(ulong[] x, ulong[] z)
{
if (Nat192.IsZero64(x))
{
throw new InvalidOperationException();
}
// Itoh-Tsujii inversion
ulong[] t0 = Nat192.Create64();
ulong[] t1 = Nat192.Create64();
Square(x, t0);
Multiply(t0, x, t0);
SquareN(t0, 2, t1);
Multiply(t1, t0, t1);
SquareN(t1, 4, t0);
Multiply(t0, t1, t0);
SquareN(t0, 8, t1);
Multiply(t1, t0, t1);
SquareN(t1, 16, t0);
Multiply(t0, t1, t0);
SquareN(t0, 32, t1);
Multiply(t1, t0, t1);
Square(t1, t1);
Multiply(t1, x, t1);
SquareN(t1, 65, t0);
Multiply(t0, t1, t0);
Square(t0, z);
}
public override ECFieldElement SquarePow(int pow)
{
if (pow < 1)
return this;
ulong[] z = Nat192.Create64();
SecT163Field.SquareN(x, pow, z);
return new SecT163FieldElement(z);
}
public override ECFieldElement SquarePow(int pow)
{
if (pow < 1)
{
return(this);
}
ulong[] z = Nat192.Create64();
SecT131Field.SquareN(x, pow, z);
return(new SecT131FieldElement(z));
}
public override ECFieldElement SquarePlusProduct(ECFieldElement x, ECFieldElement y)
{
ulong[] array = this.x;
ulong[] array2 = ((SecT163FieldElement)x).x;
ulong[] y2 = ((SecT163FieldElement)y).x;
ulong[] array3 = Nat192.CreateExt64();
SecT163Field.SquareAddToExt(array, array3);
SecT163Field.MultiplyAddToExt(array2, y2, array3);
ulong[] z = Nat192.Create64();
SecT163Field.Reduce(array3, z);
return(new SecT163FieldElement(z));
}
public override ECFieldElement SquarePlusProduct(ECFieldElement x, ECFieldElement y)
{
ulong[] ax = this.x;
ulong[] xx = ((SecT163FieldElement)x).x, yx = ((SecT163FieldElement)y).x;
ulong[] tt = Nat192.CreateExt64();
SecT163Field.SquareAddToExt(ax, tt);
SecT163Field.MultiplyAddToExt(xx, yx, tt);
ulong[] z = Nat192.Create64();
SecT163Field.Reduce(tt, z);
return new SecT163FieldElement(z);
}
public override ECFieldElement MultiplyPlusProduct(ECFieldElement b, ECFieldElement x, ECFieldElement y)
{
ulong[] ax = this.x, bx = ((SecT131FieldElement)b).x;
ulong[] xx = ((SecT131FieldElement)x).x, yx = ((SecT131FieldElement)y).x;
ulong[] tt = Nat.Create64(5);
SecT131Field.MultiplyAddToExt(ax, bx, tt);
SecT131Field.MultiplyAddToExt(xx, yx, tt);
ulong[] z = Nat192.Create64();
SecT131Field.Reduce(tt, z);
return(new SecT131FieldElement(z));
}
public override ECPoint LookupVar(int index)
{
ulong[] x = Nat192.Create64(), y = Nat192.Create64();
int pos = index * SECT163R1_FE_LONGS * 2;
for (int j = 0; j < SECT163R1_FE_LONGS; ++j)
{
x[j] = m_table[pos + j];
y[j] = m_table[pos + SECT163R1_FE_LONGS + j];
}
return(CreatePoint(x, y));
}
public override ECFieldElement MultiplyPlusProduct(ECFieldElement b, ECFieldElement x, ECFieldElement y)
{
ulong[] array = this.x;
ulong[] y2 = ((SecT131FieldElement)b).x;
ulong[] array2 = ((SecT131FieldElement)x).x;
ulong[] y3 = ((SecT131FieldElement)y).x;
ulong[] array3 = Nat.Create64(5);
SecT131Field.MultiplyAddToExt(array, y2, array3);
SecT131Field.MultiplyAddToExt(array2, y3, array3);
ulong[] z = Nat192.Create64();
SecT131Field.Reduce(array3, z);
return(new SecT131FieldElement(z));
}
public static void Invert(ulong[] x, ulong[] z)
{
if (Nat192.IsZero64(x))
{
throw new InvalidOperationException();
}
// Itoh-Tsujii inversion with bases { 2, 3 }
ulong[] t0 = Nat192.Create64();
ulong[] t1 = Nat192.Create64();
Square(x, t0);
// 3 | 162
SquareN(t0, 1, t1);
Multiply(t0, t1, t0);
SquareN(t1, 1, t1);
Multiply(t0, t1, t0);
// 3 | 54
SquareN(t0, 3, t1);
Multiply(t0, t1, t0);
SquareN(t1, 3, t1);
Multiply(t0, t1, t0);
// 3 | 18
SquareN(t0, 9, t1);
Multiply(t0, t1, t0);
SquareN(t1, 9, t1);
Multiply(t0, t1, t0);
// 3 | 6
SquareN(t0, 27, t1);
Multiply(t0, t1, t0);
SquareN(t1, 27, t1);
Multiply(t0, t1, t0);
// 2 | 2
SquareN(t0, 81, t1);
Multiply(t0, t1, z);
}
public virtual ECPoint Lookup(int index)
{
ulong[] x = Nat192.Create64(), y = Nat192.Create64();
int pos = 0;
for (int i = 0; i < m_size; ++i)
{
ulong MASK = (ulong)(long)(((i ^ index) - 1) >> 31);
for (int j = 0; j < SECT163R1_FE_LONGS; ++j)
{
x[j] ^= m_table[pos + j] & MASK;
y[j] ^= m_table[pos + SECT163R1_FE_LONGS + j] & MASK;
}
pos += (SECT163R1_FE_LONGS * 2);
}
return(m_outer.CreateRawPoint(new SecT163FieldElement(x), new SecT163FieldElement(y), false));
}
public override ECPoint Lookup(int index)
{
ulong[] x = Nat192.Create64(), y = Nat192.Create64();
int pos = 0;
for (int i = 0; i < m_size; ++i)
{
ulong MASK = (ulong)(long)(((i ^ index) - 1) >> 31);
for (int j = 0; j < SECT163R1_FE_LONGS; ++j)
{
x[j] ^= m_table[pos + j] & MASK;
y[j] ^= m_table[pos + SECT163R1_FE_LONGS + j] & MASK;
}
pos += (SECT163R1_FE_LONGS * 2);
}
return(CreatePoint(x, y));
}
public static void Sqrt(ulong[] x, ulong[] z)
{
ulong[] odd = Nat192.Create64();
ulong u0, u1;
u0 = Interleave.Unshuffle(x[0]); u1 = Interleave.Unshuffle(x[1]);
ulong e0 = (u0 & 0x00000000FFFFFFFFUL) | (u1 << 32);
odd[0] = (u0 >> 32) | (u1 & 0xFFFFFFFF00000000UL);
u0 = Interleave.Unshuffle(x[2]);
ulong e1 = (u0 & 0x00000000FFFFFFFFUL);
odd[1] = (u0 >> 32);
Multiply(odd, ROOT_Z, z);
z[0] ^= e0;
z[1] ^= e1;
}
public override ECFieldElement Multiply(ECFieldElement b)
{
ulong[] z = Nat192.Create64();
SecT131Field.Multiply(x, ((SecT131FieldElement)b).x, z);
return(new SecT131FieldElement(z));
}
public override ECFieldElement AddOne()
{
ulong[] z = Nat192.Create64();
SecT131Field.AddOne(x, z);
return(new SecT131FieldElement(z));
}
public SecT131FieldElement()
{
this.x = Nat192.Create64();
}
public SecT163FieldElement()
{
x = Nat192.Create64();
}
public override ECFieldElement Add(ECFieldElement b)
{
ulong[] z = Nat192.Create64();
SecT163Field.Add(x, ((SecT163FieldElement)b).x, z);
return new SecT163FieldElement(z);
}
public override ECFieldElement Sqrt()
{
ulong[] z = Nat192.Create64();
SecT163Field.Sqrt(x, z);
return new SecT163FieldElement(z);
}
public override ECFieldElement HalfTrace()
{
ulong[] z = Nat192.Create64();
SecT163Field.HalfTrace(x, z);
return new SecT163FieldElement(z);
}
