/// <summary>
/// Gets BigNum <paramref name="b"/>.
/// Generates p and q, prime numbers.
/// While b is not inverse number to p-1 and q-1, p and q re-generates.
/// After finding good p and q, calculate a that is inverse of b mod ((p-1)(q-1)).
/// n is calculated as p * q.
/// Returns by reference the BigNum a, p, q, and n.
/// </summary>
/// <param name="b"></param>
/// <param name="a"></param>
/// <param name="q"></param>
/// <param name="p"></param>
/// <param name="nByRef"></param>
public static void GenRSA(BigNum b, BigNum a, BigNum q, BigNum p, BigNum nByRef)
{
bool isBInverseOfPMinus1AndQMinus1 = false;
BigNum n = new BigNum();
while (!isBInverseOfPMinus1AndQMinus1)
{
p.Set(GenPrime());
q.Set(GenPrime());
BigNum pMinus1 = new BigNum(p);
pMinus1.SubNum(GlobalVariables.one);
BigNum qMinus1 = new BigNum(q);
qMinus1.SubNum(GlobalVariables.one);
BigNum fiOfN = new BigNum(pMinus1);
fiOfN.MultNum(qMinus1);
BigNum gcd = new BigNum();
ExtendedGCD(b, fiOfN, new BigNum(), new BigNum(), gcd);
if (gcd.CompNumWithoutPrint(GlobalVariables.one))
{
isBInverseOfPMinus1AndQMinus1 = true;
a.Set(Inverse(b, fiOfN));
if (a.IsNegative)
{
a.AddNum(fiOfN);
}
n = new BigNum(p);
n.MultNum(q);
}
}
nByRef.Set(n);
}
/// <summary>
/// K.
/// Gets two BigNum type numbers a and m and returns by reference (d, x, y), also BigNum type numbers.
/// d represents GCD(m,a). (Greatest common divider).
/// Note: If d = 1, it means that x is the opposite number of m(mod a) and
/// y is the opposite number of a(mod m).
/// Proofe for Note: 1 = [m*x + a*y](mod m) ==> 1 = a*y.
/// </summary>
/// <param name="a"></param>
/// <param name="m"></param>
/// <param name="x"></param>
/// <param name="y"></param>
/// <param name="d"></param>
public static void ExtendedGCD(BigNum a, BigNum m, BigNum x, BigNum y, BigNum d)
{
BigNum r0 = new BigNum(m);
BigNum x0 = new BigNum(GlobalVariables.one);
BigNum y0 = new BigNum(GlobalVariables.zero);
BigNum r1 = new BigNum(a);
BigNum x1 = new BigNum(GlobalVariables.zero);
BigNum y1 = new BigNum(GlobalVariables.one);
BigNum r = new BigNum(GlobalVariables.one); // Just to be able to enter the while loop.
BigNum q = new BigNum();
DivNum(r0, r1, q, r);
while (!r.CompNumWithoutPrint(GlobalVariables.zero))
{
// x = x0 - qx1.
BigNum qx1 = new BigNum(q);
qx1.MultNum(x1);
x.Set(x0);
x.SubNum(qx1);
// y = y0 - qy1.
BigNum qy1 = new BigNum(q);
qy1.MultNum(y1);
y.Set(y0);
y.SubNum(qy1);
r0.Set(r1);
x0.Set(x1);
y0.Set(y1);
r1.Set(r);
x1.Set(x);
y1.Set(y);
DivNum(r0, r1, q, r);
}
d.Set(r1);
x.Set(x1);
y.Set(y1);
}
public static void G()
{
Console.WriteLine("(G) Using MultNum method.");
Console.WriteLine("Multiply 7 by 3. Equals 21 (10101 in base 2)");
BigNum bigNumG1 = new BigNum(7L);
BigNum bigNumG2 = new BigNum(3L);
bigNumG1.MultNum(bigNumG2);
Console.WriteLine(bigNumG1.WriteNum());
Console.WriteLine("Multiply 113 by 73. Equals 8249 (10000000111001 in base 2)");
BigNum bigNumG3 = new BigNum(113L);
BigNum bigNumG4 = new BigNum(73L);
bigNumG3.MultNum(bigNumG4);
Console.WriteLine(bigNumG3.WriteNum());
Console.WriteLine();
}