public override ECFieldElement Sqrt()
{
uint[] y = x;
if (Nat256.IsZero(y) || Nat256.IsOne(y))
{
return(this);
}
uint[] array = Nat256.Create();
Curve25519Field.Square(y, array);
Curve25519Field.Multiply(array, y, array);
uint[] array2 = array;
Curve25519Field.Square(array, array2);
Curve25519Field.Multiply(array2, y, array2);
uint[] array3 = Nat256.Create();
Curve25519Field.Square(array2, array3);
Curve25519Field.Multiply(array3, y, array3);
uint[] array4 = Nat256.Create();
Curve25519Field.SquareN(array3, 3, array4);
Curve25519Field.Multiply(array4, array2, array4);
uint[] array5 = array2;
Curve25519Field.SquareN(array4, 4, array5);
Curve25519Field.Multiply(array5, array3, array5);
uint[] array6 = array4;
Curve25519Field.SquareN(array5, 4, array6);
Curve25519Field.Multiply(array6, array3, array6);
uint[] array7 = array3;
Curve25519Field.SquareN(array6, 15, array7);
Curve25519Field.Multiply(array7, array6, array7);
uint[] array8 = array6;
Curve25519Field.SquareN(array7, 30, array8);
Curve25519Field.Multiply(array8, array7, array8);
uint[] array9 = array7;
Curve25519Field.SquareN(array8, 60, array9);
Curve25519Field.Multiply(array9, array8, array9);
uint[] z = array8;
Curve25519Field.SquareN(array9, 11, z);
Curve25519Field.Multiply(z, array5, z);
uint[] array10 = array5;
Curve25519Field.SquareN(z, 120, array10);
Curve25519Field.Multiply(array10, array9, array10);
uint[] z2 = array10;
Curve25519Field.Square(z2, z2);
uint[] array11 = array9;
Curve25519Field.Square(z2, array11);
if (Nat256.Eq(y, array11))
{
return(new Curve25519FieldElement(z2));
}
Curve25519Field.Multiply(z2, PRECOMP_POW2, z2);
Curve25519Field.Square(z2, array11);
if (Nat256.Eq(y, array11))
{
return(new Curve25519FieldElement(z2));
}
return(null);
}
public override ECFieldElement Sqrt()
{
uint[] x = this.x;
if (Nat256.IsZero(x) || Nat256.IsOne(x))
{
return(this);
}
uint[] z = Nat256.Create();
Curve25519Field.Square(x, z);
Curve25519Field.Multiply(z, x, z);
uint[] numArray3 = z;
Curve25519Field.Square(z, numArray3);
Curve25519Field.Multiply(numArray3, x, numArray3);
uint[] numArray4 = Nat256.Create();
Curve25519Field.Square(numArray3, numArray4);
Curve25519Field.Multiply(numArray4, x, numArray4);
uint[] numArray5 = Nat256.Create();
Curve25519Field.SquareN(numArray4, 3, numArray5);
Curve25519Field.Multiply(numArray5, numArray3, numArray5);
uint[] numArray6 = numArray3;
Curve25519Field.SquareN(numArray5, 4, numArray6);
Curve25519Field.Multiply(numArray6, numArray4, numArray6);
uint[] numArray7 = numArray5;
Curve25519Field.SquareN(numArray6, 4, numArray7);
Curve25519Field.Multiply(numArray7, numArray4, numArray7);
uint[] numArray8 = numArray4;
Curve25519Field.SquareN(numArray7, 15, numArray8);
Curve25519Field.Multiply(numArray8, numArray7, numArray8);
uint[] numArray9 = numArray7;
Curve25519Field.SquareN(numArray8, 30, numArray9);
Curve25519Field.Multiply(numArray9, numArray8, numArray9);
uint[] numArray10 = numArray8;
Curve25519Field.SquareN(numArray9, 60, numArray10);
Curve25519Field.Multiply(numArray10, numArray9, numArray10);
uint[] numArray11 = numArray9;
Curve25519Field.SquareN(numArray10, 11, numArray11);
Curve25519Field.Multiply(numArray11, numArray6, numArray11);
uint[] numArray12 = numArray6;
Curve25519Field.SquareN(numArray11, 120, numArray12);
Curve25519Field.Multiply(numArray12, numArray10, numArray12);
uint[] numArray13 = numArray12;
Curve25519Field.Square(numArray13, numArray13);
uint[] numArray14 = numArray10;
Curve25519Field.Square(numArray13, numArray14);
if (Nat256.Eq(x, numArray14))
{
return(new Curve25519FieldElement(numArray13));
}
Curve25519Field.Multiply(numArray13, PRECOMP_POW2, numArray13);
Curve25519Field.Square(numArray13, numArray14);
if (Nat256.Eq(x, numArray14))
{
return(new Curve25519FieldElement(numArray13));
}
return(null);
}
/**
* return a sqrt root - the routine verifies that the calculation returns the right value - if
* none exists it returns null.
*/
public override ECFieldElement Sqrt()
{
/*
* Q == 8m + 5, so we use Pocklington's method for this case.
*
* First, raise this element to the exponent 2^252 - 2^1 (i.e. m + 1)
*
* Breaking up the exponent's binary representation into "repunits", we get:
* { 251 1s } { 1 0s }
*
* Therefore we need an addition chain containing 251 (the lengths of the repunits)
* We use: 1, 2, 3, 4, 7, 11, 15, 30, 60, 120, 131, [251]
*/
uint[] x1 = this.x;
if (Nat256.IsZero(x1) || Nat256.IsOne(x1))
{
return(this);
}
uint[] x2 = Nat256.Create();
Curve25519Field.Square(x1, x2);
Curve25519Field.Multiply(x2, x1, x2);
uint[] x3 = x2;
Curve25519Field.Square(x2, x3);
Curve25519Field.Multiply(x3, x1, x3);
uint[] x4 = Nat256.Create();
Curve25519Field.Square(x3, x4);
Curve25519Field.Multiply(x4, x1, x4);
uint[] x7 = Nat256.Create();
Curve25519Field.SquareN(x4, 3, x7);
Curve25519Field.Multiply(x7, x3, x7);
uint[] x11 = x3;
Curve25519Field.SquareN(x7, 4, x11);
Curve25519Field.Multiply(x11, x4, x11);
uint[] x15 = x7;
Curve25519Field.SquareN(x11, 4, x15);
Curve25519Field.Multiply(x15, x4, x15);
uint[] x30 = x4;
Curve25519Field.SquareN(x15, 15, x30);
Curve25519Field.Multiply(x30, x15, x30);
uint[] x60 = x15;
Curve25519Field.SquareN(x30, 30, x60);
Curve25519Field.Multiply(x60, x30, x60);
uint[] x120 = x30;
Curve25519Field.SquareN(x60, 60, x120);
Curve25519Field.Multiply(x120, x60, x120);
uint[] x131 = x60;
Curve25519Field.SquareN(x120, 11, x131);
Curve25519Field.Multiply(x131, x11, x131);
uint[] x251 = x11;
Curve25519Field.SquareN(x131, 120, x251);
Curve25519Field.Multiply(x251, x120, x251);
uint[] t1 = x251;
Curve25519Field.Square(t1, t1);
uint[] t2 = x120;
Curve25519Field.Square(t1, t2);
if (Nat256.Eq(x1, t2))
{
return(new Curve25519FieldElement(t1));
}
/*
* If the first guess is incorrect, we multiply by a precomputed power of 2 to get the second guess,
* which is ((4x)^(m + 1))/2 mod Q
*/
Curve25519Field.Multiply(t1, PRECOMP_POW2, t1);
Curve25519Field.Square(t1, t2);
if (Nat256.Eq(x1, t2))
{
return(new Curve25519FieldElement(t1));
}
return(null);
}
