/**
* return a sqrt root - the routine verifies that the calculation returns the right value - if
* none exists it returns null.
*/
public override ECFieldElement Sqrt()
{
// Raise this element to the exponent 2^382 - 2^126 - 2^94 + 2^30
uint[] x1 = this.x;
if (Nat.IsZero(12, x1) || Nat.IsOne(12, x1))
return this;
uint[] t1 = Nat.Create(12);
uint[] t2 = Nat.Create(12);
uint[] t3 = Nat.Create(12);
uint[] t4 = Nat.Create(12);
SecP384R1Field.Square(x1, t1);
SecP384R1Field.Multiply(t1, x1, t1);
SecP384R1Field.SquareN(t1, 2, t2);
SecP384R1Field.Multiply(t2, t1, t2);
SecP384R1Field.Square(t2, t2);
SecP384R1Field.Multiply(t2, x1, t2);
SecP384R1Field.SquareN(t2, 5, t3);
SecP384R1Field.Multiply(t3, t2, t3);
SecP384R1Field.SquareN(t3, 5, t4);
SecP384R1Field.Multiply(t4, t2, t4);
SecP384R1Field.SquareN(t4, 15, t2);
SecP384R1Field.Multiply(t2, t4, t2);
SecP384R1Field.SquareN(t2, 2, t3);
SecP384R1Field.Multiply(t1, t3, t1);
SecP384R1Field.SquareN(t3, 28, t3);
SecP384R1Field.Multiply(t2, t3, t2);
SecP384R1Field.SquareN(t2, 60, t3);
SecP384R1Field.Multiply(t3, t2, t3);
uint[] r = t2;
SecP384R1Field.SquareN(t3, 120, r);
SecP384R1Field.Multiply(r, t3, r);
SecP384R1Field.SquareN(r, 15, r);
SecP384R1Field.Multiply(r, t4, r);
SecP384R1Field.SquareN(r, 33, r);
SecP384R1Field.Multiply(r, t1, r);
SecP384R1Field.SquareN(r, 64, r);
SecP384R1Field.Multiply(r, x1, r);
SecP384R1Field.SquareN(r, 30, t1);
SecP384R1Field.Square(t1, t2);
return Nat.Eq(12, x1, t2) ? new SecP384R1FieldElement(t1) : null;
}
public virtual bool Equals(SecP384R1FieldElement other)
{
if (this == other)
return true;
if (null == other)
return false;
return Nat.Eq(12, x, other.x);
}
public static uint[] FromBigInteger(BigInteger x)
{
uint[] numArray = Nat.FromBigInteger(0x209, x);
if (Nat.Eq(0x11, numArray, P))
{
Nat.Zero(0x11, numArray);
}
return(numArray);
}
public static uint[] FromBigInteger(BigInteger x)
{
uint[] z = Nat.FromBigInteger(521, x);
if (Nat.Eq(17, z, P))
{
Nat.Zero(17, z);
}
return(z);
}
public static uint[] FromBigInteger(BigInteger x)
{
uint[] array = Nat.FromBigInteger(521, x);
if (Nat.Eq(17, array, P))
{
Nat.Zero(17, array);
}
return(array);
}
public static void AddOne(uint[] x, uint[] z)
{
uint c = Nat.Inc(16, x, z) + x[16];
if (c > P16 || (c == P16 && Nat.Eq(16, z, P)))
{
c += Nat.Inc(16, z);
c &= P16;
}
z[16] = c;
}
public static void AddOne(uint[] x, uint[] z)
{
uint num = Nat.Inc(16, x, z) + x[16];
if (num > 511u || (num == 511u && Nat.Eq(16, z, SecP521R1Field.P)))
{
num += Nat.Inc(16, z);
num &= 511u;
}
z[16] = num;
}
public static void AddOne(uint[] x, uint[] z)
{
uint num = Nat.Inc(16, x, z) + x[16];
if (num > 511 || (num == 511 && Nat.Eq(16, z, P)))
{
num += Nat.Inc(16, z);
num &= 0x1FF;
}
z[16] = num;
}
public static void AddOne(uint[] x, uint[] z)
{
uint num = Nat.Inc(0x10, x, z) + x[0x10];
if ((num > 0x1ff) || ((num == 0x1ff) && Nat.Eq(0x10, z, P)))
{
num += Nat.Inc(0x10, z);
num &= 0x1ff;
}
z[0x10] = num;
}
public static void Reduce23(uint[] z)
{
uint z16 = z[16];
uint c = Nat.AddWordTo(16, z16 >> 9, z) + (z16 & P16);
if (c > P16 || (c == P16 && Nat.Eq(16, z, P)))
{
c += Nat.Inc(16, z);
c &= P16;
}
z[16] = c;
}
public virtual bool Equals(SecP521R1FieldElement other)
{
if (this == other)
{
return(true);
}
if (other == null)
{
return(false);
}
return(Nat.Eq(17, x, other.x));
}
public static void Reduce23(uint[] z)
{
uint num = z[16];
uint num2 = Nat.AddWordTo(16, num >> 9, z) + (num & 511u);
if (num2 > 511u || (num2 == 511u && Nat.Eq(16, z, SecP521R1Field.P)))
{
num2 += Nat.Inc(16, z);
num2 &= 511u;
}
z[16] = num2;
}
public virtual bool Equals(SecP384R1FieldElement other)
{
if (this == other)
{
return(true);
}
if (null == other)
{
return(false);
}
return(Nat.Eq(12, x, other.x));
}
public static void Reduce23(uint[] z)
{
uint num = z[16];
uint num2 = Nat.AddWordTo(16, num >> 9, z) + (num & 0x1FF);
if (num2 > 511 || (num2 == 511 && Nat.Eq(16, z, P)))
{
num2 += Nat.Inc(16, z);
num2 &= 0x1FF;
}
z[16] = num2;
}
public static void Reduce23(uint[] z)
{
uint num = z[0x10];
uint num2 = Nat.AddWordTo(0x10, num >> 9, z) + (num & 0x1ff);
if ((num2 > 0x1ff) || ((num2 == 0x1ff) && Nat.Eq(0x10, z, P)))
{
num2 += Nat.Inc(0x10, z);
num2 &= 0x1ff;
}
z[0x10] = num2;
}
public override ECFieldElement Sqrt()
{
uint[] array = x;
if (Nat.IsZero(17, array) || Nat.IsOne(17, array))
{
return(this);
}
uint[] z = Nat.Create(17);
uint[] array2 = Nat.Create(17);
SecP521R1Field.SquareN(array, 519, z);
SecP521R1Field.Square(z, array2);
return((!Nat.Eq(17, array, array2)) ? null : new SecP521R1FieldElement(z));
}
public override ECFieldElement Sqrt()
{
uint[] x = this.x;
if (Nat.IsZero(0x11, x) || Nat.IsOne(0x11, x))
{
return(this);
}
uint[] z = Nat.Create(0x11);
uint[] numArray3 = Nat.Create(0x11);
SecP521R1Field.SquareN(x, 0x207, z);
SecP521R1Field.Square(z, numArray3);
return(!Nat.Eq(0x11, x, numArray3) ? null : new SecP521R1FieldElement(z));
}
public static void Reduce(uint[] xx, uint[] z)
{
uint num = xx[32];
uint num2 = Nat.ShiftDownBits(16, xx, 16, 9, num, z, 0) >> 23;
num2 += num >> 9;
num2 += Nat.AddTo(16, xx, z);
if (num2 > 511 || (num2 == 511 && Nat.Eq(16, z, P)))
{
num2 += Nat.Inc(16, z);
num2 &= 0x1FF;
}
z[16] = num2;
}
public static void Reduce(uint[] xx, uint[] z)
{
uint c = xx[0x20];
uint num2 = Nat.ShiftDownBits(0x10, xx, 0x10, 9, c, z, 0) >> 0x17;
num2 += c >> 9;
num2 += Nat.AddTo(0x10, xx, z);
if ((num2 > 0x1ff) || ((num2 == 0x1ff) && Nat.Eq(0x10, z, P)))
{
num2 += Nat.Inc(0x10, z);
num2 &= 0x1ff;
}
z[0x10] = num2;
}
public static void Reduce(uint[] xx, uint[] z)
{
Debug.Assert(xx[32] >> 18 == 0);
uint xx32 = xx[32];
uint c = Nat.ShiftDownBits(16, xx, 16, 9, xx32, z, 0) >> 23;
c += xx32 >> 9;
c += Nat.AddTo(16, xx, z);
if (c > P16 || (c == P16 && Nat.Eq(16, z, P)))
{
c += Nat.Inc(16, z);
c &= P16;
}
z[16] = c;
}
public override ECFieldElement Sqrt()
{
uint[] y = this.x;
if (Nat.IsZero(12, y) || Nat.IsOne(12, y))
{
return(this);
}
uint[] array = Nat.Create(12);
uint[] array2 = Nat.Create(12);
uint[] array3 = Nat.Create(12);
uint[] array4 = Nat.Create(12);
SecP384R1Field.Square(y, array);
SecP384R1Field.Multiply(array, y, array);
SecP384R1Field.SquareN(array, 2, array2);
SecP384R1Field.Multiply(array2, array, array2);
SecP384R1Field.Square(array2, array2);
SecP384R1Field.Multiply(array2, y, array2);
SecP384R1Field.SquareN(array2, 5, array3);
SecP384R1Field.Multiply(array3, array2, array3);
SecP384R1Field.SquareN(array3, 5, array4);
SecP384R1Field.Multiply(array4, array2, array4);
SecP384R1Field.SquareN(array4, 15, array2);
SecP384R1Field.Multiply(array2, array4, array2);
SecP384R1Field.SquareN(array2, 2, array3);
SecP384R1Field.Multiply(array, array3, array);
SecP384R1Field.SquareN(array3, 28, array3);
SecP384R1Field.Multiply(array2, array3, array2);
SecP384R1Field.SquareN(array2, 60, array3);
SecP384R1Field.Multiply(array3, array2, array3);
uint[] z = array2;
SecP384R1Field.SquareN(array3, 120, z);
SecP384R1Field.Multiply(z, array3, z);
SecP384R1Field.SquareN(z, 15, z);
SecP384R1Field.Multiply(z, array4, z);
SecP384R1Field.SquareN(z, 33, z);
SecP384R1Field.Multiply(z, array, z);
SecP384R1Field.SquareN(z, 64, z);
SecP384R1Field.Multiply(z, y, z);
SecP384R1Field.SquareN(z, 30, array);
SecP384R1Field.Square(array, array2);
if (!Nat.Eq(12, y, array2))
{
return(null);
}
return(new SecP384R1FieldElement(array));
}
/**
* return a sqrt root - the routine verifies that the calculation returns the right value - if
* none exists it returns null.
*/
public override ECFieldElement Sqrt()
{
// Raise this element to the exponent 2^519
uint[] x1 = this.x;
if (Nat.IsZero(17, x1) || Nat.IsOne(17, x1))
{
return(this);
}
uint[] t1 = Nat.Create(17);
uint[] t2 = Nat.Create(17);
SecP521R1Field.SquareN(x1, 519, t1);
SecP521R1Field.Square(t1, t2);
return(Nat.Eq(17, x1, t2) ? new SecP521R1FieldElement(t1) : null);
}
public override ECFieldElement Sqrt()
{
uint[] x = this.x;
if (Nat.IsZero(12, x) || Nat.IsOne(12, x))
{
return(this);
}
uint[] z = Nat.Create(12);
uint[] numArray3 = Nat.Create(12);
uint[] numArray4 = Nat.Create(12);
uint[] numArray5 = Nat.Create(12);
SecP384R1Field.Square(x, z);
SecP384R1Field.Multiply(z, x, z);
SecP384R1Field.SquareN(z, 2, numArray3);
SecP384R1Field.Multiply(numArray3, z, numArray3);
SecP384R1Field.Square(numArray3, numArray3);
SecP384R1Field.Multiply(numArray3, x, numArray3);
SecP384R1Field.SquareN(numArray3, 5, numArray4);
SecP384R1Field.Multiply(numArray4, numArray3, numArray4);
SecP384R1Field.SquareN(numArray4, 5, numArray5);
SecP384R1Field.Multiply(numArray5, numArray3, numArray5);
SecP384R1Field.SquareN(numArray5, 15, numArray3);
SecP384R1Field.Multiply(numArray3, numArray5, numArray3);
SecP384R1Field.SquareN(numArray3, 2, numArray4);
SecP384R1Field.Multiply(z, numArray4, z);
SecP384R1Field.SquareN(numArray4, 0x1c, numArray4);
SecP384R1Field.Multiply(numArray3, numArray4, numArray3);
SecP384R1Field.SquareN(numArray3, 60, numArray4);
SecP384R1Field.Multiply(numArray4, numArray3, numArray4);
uint[] numArray6 = numArray3;
SecP384R1Field.SquareN(numArray4, 120, numArray6);
SecP384R1Field.Multiply(numArray6, numArray4, numArray6);
SecP384R1Field.SquareN(numArray6, 15, numArray6);
SecP384R1Field.Multiply(numArray6, numArray5, numArray6);
SecP384R1Field.SquareN(numArray6, 0x21, numArray6);
SecP384R1Field.Multiply(numArray6, z, numArray6);
SecP384R1Field.SquareN(numArray6, 0x40, numArray6);
SecP384R1Field.Multiply(numArray6, x, numArray6);
SecP384R1Field.SquareN(numArray6, 30, z);
SecP384R1Field.Square(z, numArray3);
return(!Nat.Eq(12, x, numArray3) ? null : new SecP384R1FieldElement(z));
}
public virtual bool Equals(SecP384R1FieldElement other)
{
return(this == other || (other != null && Nat.Eq(12, this.x, other.x)));
}