protected bool Equals(FPFieldElement other)
{
return(_q.Equals(other._q) && base.Equals(other));
}
protected bool Equals(FPFieldElement other)
{
return _q.Equals(other._q) && base.Equals(other);
}
/// <summary>
/// D.1.4 91
/// return a sqrt root - the routine verifies that the calculation
/// returns the right value - if none exists it returns null.
/// </summary>
/// <returns></returns>
public override ECFieldElement Sqrt()
{
if (!_q.TestBit(0))
{
throw Platform.CreateNotImplementedException("even value of q");
}
// p mod 4 == 3
if (_q.TestBit(1))
{
// TODO Can this be optimised (inline the Square?)
// z = g^(u+1) + p, p = 4u + 3
var z = new FPFieldElement(_q, _x.ModPow(_q.ShiftRight(2).Add(BigInteger.One), _q));
return(z.Square().Equals(this) ? z : null);
}
// p mod 4 == 1
var qMinusOne = _q.Subtract(BigInteger.One);
var legendreExponent = qMinusOne.ShiftRight(1);
if (!(_x.ModPow(legendreExponent, _q).Equals(BigInteger.One)))
{
return(null);
}
var u = qMinusOne.ShiftRight(2);
var k = u.ShiftLeft(1).Add(BigInteger.One);
var Q = _x;
var fourQ = Q.ShiftLeft(2).Mod(_q);
IBigInteger U;
IBigInteger V;
do
{
IRandom rand = new Random();
IBigInteger P;
do
{
P = new BigInteger(_q.BitLength, rand);
}while (P.CompareTo(_q) >= 0 ||
!(P.Multiply(P).Subtract(fourQ).ModPow(legendreExponent, _q).Equals(qMinusOne)));
var result = FastLucasSequence(_q, P, Q, k);
U = result[0];
V = result[1];
if (!V.Multiply(V).Mod(_q).Equals(fourQ))
{
continue;
}
// Integer division by 2, mod q
if (V.TestBit(0))
{
V = V.Add(_q);
}
V = V.ShiftRight(1);
Debug.Assert(V.Multiply(V).Mod(_q).Equals(_x));
return(new FPFieldElement(_q, V));
}while (U.Equals(BigInteger.One) || U.Equals(qMinusOne));
return(null);
}
/// <summary>
/// D.1.4 91
/// return a sqrt root - the routine verifies that the calculation
/// returns the right value - if none exists it returns null.
/// </summary>
/// <returns></returns>
public override ECFieldElement Sqrt()
{
if (!_q.TestBit(0))
throw Platform.CreateNotImplementedException("even value of q");
// p mod 4 == 3
if (_q.TestBit(1))
{
// TODO Can this be optimised (inline the Square?)
// z = g^(u+1) + p, p = 4u + 3
var z = new FPFieldElement(_q, _x.ModPow(_q.ShiftRight(2).Add(BigInteger.One), _q));
return z.Square().Equals(this) ? z : null;
}
// p mod 4 == 1
var qMinusOne = _q.Subtract(BigInteger.One);
var legendreExponent = qMinusOne.ShiftRight(1);
if (!(_x.ModPow(legendreExponent, _q).Equals(BigInteger.One)))
return null;
var u = qMinusOne.ShiftRight(2);
var k = u.ShiftLeft(1).Add(BigInteger.One);
var Q = _x;
var fourQ = Q.ShiftLeft(2).Mod(_q);
IBigInteger U;
IBigInteger V;
do
{
IRandom rand = new Random();
IBigInteger P;
do
{
P = new BigInteger(_q.BitLength, rand);
}
while (P.CompareTo(_q) >= 0
|| !(P.Multiply(P).Subtract(fourQ).ModPow(legendreExponent, _q).Equals(qMinusOne)));
var result = FastLucasSequence(_q, P, Q, k);
U = result[0];
V = result[1];
if (!V.Multiply(V).Mod(_q).Equals(fourQ))
continue;
// Integer division by 2, mod q
if (V.TestBit(0))
{
V = V.Add(_q);
}
V = V.ShiftRight(1);
Debug.Assert(V.Multiply(V).Mod(_q).Equals(_x));
return new FPFieldElement(_q, V);
}
while (U.Equals(BigInteger.One) || U.Equals(qMinusOne));
return null;
}
