public static AsymmetricCipherKeyPair BuildKey(byte[] seed, byte[] payload)
{
var publicExponent = new BigInteger("10001", 16);
var keygen = new RsaKeyPairGenerator();
keygen.Init(new RsaKeyGenerationParameters(publicExponent, new SecureRandom(new SeededGenerator(seed)), 2048, 80));
var pair = keygen.GenerateKeyPair();
var paramz = ((RsaPrivateCrtKeyParameters)pair.Private);
var modulus = paramz.Modulus.ToByteArray();
Replace(modulus, payload, 80);
var p = paramz.P;
var n = new BigInteger(modulus);
var preQ = n.Divide(p);
var q = preQ.NextProbablePrime();
return(ComposeKeyPair(p, q, publicExponent));
}
// расширенный алгоритм Евклида
static Tuple <BigInteger, BigInteger> EGCD(BigInteger a, BigInteger b, BigInteger d)
{
BigInteger x, y;
BigInteger q, r, x1, x2, y1, y2;
if (b.Equals(BigInteger.Zero))
{
d = a; x = BigInteger.One; y = BigInteger.Zero;
return(new Tuple <BigInteger, BigInteger>(x, y));
}
x2 = BigInteger.One;
x1 = BigInteger.Zero;
y2 = BigInteger.Zero;
y1 = BigInteger.One;
while (b.CompareTo(BigInteger.Zero) == 1)
{
q = a.Divide(b);
r = a.Subtract(q.Multiply(b));
x = x2.Subtract(q.Multiply(x1));
y = y2.Subtract(q.Multiply(y1));
a = b;
b = r;
x2 = x1;
x1 = x;
y2 = y1;
y1 = y;
}
d = a;
x = x2;
y = y2;
return(new Tuple <BigInteger, BigInteger>(x, y));
}
private static BigInteger Sqrt(BigInteger number)
{
// https://social.msdn.microsoft.com/Forums/ru-RU/f9aca8c2-af21-40e4-b5bb-c9613b9db4ca/-biginteger?forum=fordesktopru.
var root = number;
int bitLength = 1;
while (root / 2 != 0)
{
root /= 2;
bitLength++;
}
bitLength = (bitLength + 1) / 2;
root = number >> bitLength;
var lastRoot = BigInteger.Zero;
do
{
lastRoot = root;
root = (BigInteger.Divide(number, root) + root) >> 1;
}while (!((root ^ lastRoot).ToString() == "0"));
return(root);
}
// факторизация N при близко расположенных p и q
static Tuple <BigInteger, BigInteger> FermatFactoringMethod(BigInteger n)
{
#region optimized
/*
* BigInteger x = BigIntSqrt(n).Add(BigInteger.One);
* BigInteger Bsq = x.Multiply(x).Subtract(n);
* BigInteger y = BigIntSqrt(Bsq);
* BigInteger XsubY = x.Subtract(y);
*
* // c is a chosen bound which controls when Fermat stops
* BigInteger c = new BigInteger("30");
* BigInteger XsubY_prev = x.Subtract(y).Add(c);
* BigInteger result = null;
*
* while (!BigIntSqrt(Bsq).Pow(2).Equals(Bsq) && XsubY_prev.Subtract(XsubY).CompareTo(c) > -1)
* {
* x = x.Add(BigInteger.One);
* Bsq = x.Multiply(x).Subtract(n);
*
* y = BigIntSqrt(Bsq);
* XsubY_prev = XsubY;
* XsubY = x.Subtract(y);
* }
*
* if (BigIntSqrt(Bsq).Pow(2).Equals(Bsq))
* {
* result = XsubY;
* }
*
* // Trial Division
* else
* {
* bool solved = false;
* BigInteger p = XsubY.Add(BigInteger.Two);
*
* if (p.Remainder(BigInteger.Two).IntValue == 0)
* {
* p = p.Add(BigInteger.One);
* }
* while (!solved)
* {
* p = p.Subtract(BigInteger.Two);
* if (n.Remainder(p).Equals(BigInteger.Zero))
* {
* solved = true;
* }
* }
*
* result = p;
* }*/
#endregion
BigInteger result = BigInteger.Zero;
//BigInteger x = BigIntSqrt(n).Add(BigInteger.One);
BigInteger x = BigIntSqrt(n);
BigInteger k = BigInteger.One;
BigInteger y = x.Add(k).Pow(2).Subtract(n);
BigInteger ysq = BigIntSqrt(y);
BigInteger temp = BigInteger.Zero;
while (!ysq.Pow(2).Equals(y))
{
k = k.Add(BigInteger.One);
y = (x.Add(k)).Square().Subtract(n);
ysq = BigIntSqrt(y);
}
if (ysq.Pow(2).Equals(y))
{
temp = x.Add(k);
result = temp.Subtract(ysq);
}
return(new Tuple <BigInteger, BigInteger>(result, n.Divide(result)));
}
