public RSA(int max, int powMin, int powMax)
{
SignInitialize(max, powMin, powMax);
max = (int)Math.Pow(2, max);
powMin = (int)Math.Pow(2, powMin);
powMax = (int)Math.Pow(2, powMax);
do
{
p = BigInt.PrimeGenerate(powMin, powMax);
q = BigInt.PrimeGenerate(powMin, powMax);
mod = BigInt.multiply(p, q);
}while ((BigInt.less(mod, new BigInt(max.ToString()))) || (BigInt.equal(p, q)));
Console.WriteLine("P: " + p.toString());
Console.WriteLine("Q: " + q.toString());
Console.WriteLine("mod: " + mod.toString());
A = Karmichael(p, q);
Console.WriteLine("A: " + A.toString());
do
{
do
{
e = BigInt.PrimeGenerate(0, Int32.Parse(A.toString()));
}while ((BigInt.mod(A, e)).isZero());
BigInt temp;
BigInt.ExtendedGCD(A, e, out temp, out d);
}while (BigInt.less(d, new BigInt("0")));
Console.WriteLine("E: " + e.toString());
Console.WriteLine("D: " + d.toString());
}
public void SignInitialize(int max, int powMin, int powMax)
{
Console.WriteLine("------------------------------------------------");
max = (int)Math.Pow(2, max);
powMin = (int)Math.Pow(2, powMin);
powMax = (int)Math.Pow(2, powMax);
do
{
pSign = BigInt.PrimeGenerate(powMin, powMax);
Console.WriteLine("P Sign: " + pSign.toString());
qSign = BigInt.PrimeGenerate(powMin, powMax);
modSign = BigInt.multiply(pSign, qSign);
}while ((BigInt.less(modSign, new BigInt(max.ToString()))) || (BigInt.equal(pSign, qSign)));
Console.WriteLine("P Sign: " + pSign.toString());
Console.WriteLine("Q Sign: " + qSign.toString());
Console.WriteLine("mod Sign: " + modSign.toString());
ASign = Karmichael(pSign, qSign);
Console.WriteLine("A Sign: " + ASign.toString());
do
{
do
{
eSign = BigInt.PrimeGenerate(0, Int32.Parse(ASign.toString()));
}while ((BigInt.mod(ASign, eSign)).isZero());
BigInt temp;
BigInt.ExtendedGCD(ASign, eSign, out temp, out dSign);
}while (BigInt.less(dSign, new BigInt("0")));
Console.WriteLine("E Sign: " + eSign.toString());
Console.WriteLine("D Sign: " + dSign.toString());
Console.WriteLine("------------------------------------------------");
}
public static BigInt powByModFast(BigInt x, BigInt y, BigInt N)
{
if (y.isZero())
{
return(new BigInt("1"));
}
string binary = Convert.ToString(Int32.Parse(y.toString()), 2);
binary = new string(binary.ToCharArray().Reverse().ToArray());
List <BigInt> temp = new List <BigInt>();
BigInt last = x;
temp.Add(last);
for (int i = 1; i < binary.Length; i++)
{
last = mod((multiply(last, last)), N);
temp.Add(last);
}
BigInt res = new BigInt("1");
for (int i = 0; i < binary.Length; i++)
{
if (binary[i] == '1')
{
res = multiply(res, temp[i]);
}
}
res = mod(res, N);
return(res);
}
public static string MillerRabin(BigInt x)
{
BigInt xMinusOne = subtract(x, new BigInt("1"));
BigInt two = new BigInt("2");
int i = 0;
BigInt m = xMinusOne;
while (true)
{
if (BigInt.subtract(m, BigInt.multiply(two, BigInt.divide(m, two))).toString() != "0")
{
break;
}
m = divide(m, two);
i++;
}
Random r = new Random();
BigInt a;
if (xMinusOne.toString().Length >= 10)
{
a = new BigInt((r.Next(2, 1000000000)).ToString());
}
else
{
a = new BigInt((r.Next(2, Int32.Parse(subtract(xMinusOne, new BigInt("1")).toString()))).ToString());
}
BigInt b = powByModFast(a, m, x);
BigInt one = new BigInt("1");
BigInt counter = new BigInt("0");
BigInt iBigInt = new BigInt(i.ToString());
if (equal(b, one))
{
return("probably prime");
}
while (less(counter, iBigInt))
{
if (equal(b, xMinusOne))
{
return("probably prime");
}
b = powByModFast(b, two, x);
counter = add(counter, one);
}
return("composite");
}
public static string ToEight(this BigInt x)
{
BigInt num = new BigInt(x.toString());
BigInt zero = new BigInt("0");
BigInt two = new BigInt("8");
string res = "";
BigInt temp;
while (num.toString() != "0")
{
temp = BigInt.mod(num, two);
num = BigInt.subtract(num, temp);
num = BigInt.divide(num, two);
res += temp.toString();
}
return(new string(res.ToCharArray().Reverse().ToArray()));
}
public static string ToBiase64(this BigInt x)
{
BigInt num = new BigInt(x.toString());
BigInt zero = new BigInt("0");
BigInt two = new BigInt("64");
string res = "";
BigInt temp;
while (num.toString() != "0")
{
temp = BigInt.mod(num, two);
num = BigInt.subtract(num, temp);
num = BigInt.divide(num, two);
res += base64Table[Int32.Parse(temp.toString())];
}
return(new string(res.ToCharArray().Reverse().ToArray()));
}
public static bool Vn(BigInt n, BigInt D)
{
BigInt P = new BigInt("1");
BigInt Q = divide(subtract(P, D), new BigInt("4"));
Console.WriteLine("Q:" + Q.toString());
BigInt U = new BigInt("1");
BigInt V = new BigInt("1");
BigInt k = new BigInt("1");
BigInt one = new BigInt("1");
BigInt two = new BigInt("2");
BigInt nPlusOne = add(one, n);
string bin = nPlusOne.ToBinary();
Console.WriteLine("n+1 bin: " + bin);
BigInt U_temp = new BigInt(U.toString());
BigInt V_temp = new BigInt(V.toString());
int i = 0;
while (i < bin.Length)
{
//if ((bin[i] == '1') && (i == 0))
//{
// U = U2k(U_temp, V_temp);
// V = V2k(V_temp, Q, k);
//}
if ((bin[i] == '1') && (i != 0))
{
U = U2k(U_temp, V_temp);
V = V2k(V_temp, Q, k);
U_temp = new BigInt(U.toString());
V_temp = new BigInt(V.toString());
//Console.WriteLine("V:" + V.toString());
//Console.WriteLine("U" + U.toString());
k = multiply(two, k);
U = U2kPlusOne(U_temp, V_temp, P);
V = V2kPlusOne(U_temp, V_temp, P, D);
k = add(k, one);
}
;
if ((bin[i] == '0'))
{
U = U2k(U_temp, V_temp);
V = V2k(V_temp, Q, k);
k = multiply(two, k);
}
;
//Console.WriteLine("V:" + V.toString());
//Console.WriteLine("U" + U.toString());
i++;
U_temp = new BigInt(U.toString());
V_temp = new BigInt(V.toString());
}
Console.WriteLine("k: " + k.toString());
Console.WriteLine("Vn+1 mod n: " + mod(V, n).toString());
BigInt compare = multiply(two, Q);
while (less(compare, new BigInt("0")))
{
compare = add(compare, n);
}
Console.WriteLine("Result:");
return(equal(mod(V, n), compare));
}