//функция вычисления квадратоного корня по модулю простого числа q
public BInteger ModSqrt(BInteger a, BInteger q)
{
BInteger b = new BInteger();
do
{
b.genRandomBits(255, new Random());
} while (Legendre(b, q) == 1);
BInteger s = 0;
BInteger t = q - 1;
while ((t & 1) != 1)
{
s++;
t = t >> 1;
}
BInteger InvA = a.modInverse(q);
BInteger c = b.modPow(t, q);
BInteger r = a.modPow(((t + 1) / 2), q);
BInteger d = new BInteger();
for (int i = 1; i < s; i++)
{
BInteger temp = 2;
temp = temp.modPow((s - i - 1), q);
d = (r.modPow(2, q) * InvA).modPow(temp, q);
if (d == (q - 1))
r = (r * c) % q;
c = c.modPow(2, q);
}
return r;
}
//Вычисляем символ Лежандра
public BInteger Legendre(BInteger a, BInteger q)
{
return a.modPow((q - 1) / 2, q);
}
public static void RSATest2(int rounds)
{
Random rand = new Random();
byte[] val = new byte[64];
byte[] pseudoPrime1 = {
0x85, 0x84, 0x64, 0xFD, 0x70, 0x6A,
0x9F, 0xF0, 0x94, 0x0C, 0x3E, 0x2C,
0x74, 0x34, 0x05, 0xC9, 0x55, 0xB3,
0x85, 0x32, 0x98, 0x71, 0xF9, 0x41,
0x21, 0x5F, 0x02, 0x9E, 0xEA, 0x56,
0x8D, 0x8C, 0x44, 0xCC, 0xEE, 0xEE,
0x3D, 0x2C, 0x9D, 0x2C, 0x12, 0x41,
0x1E, 0xF1, 0xC5, 0x32, 0xC3, 0xAA,
0x31, 0x4A, 0x52, 0xD8, 0xE8, 0xAF,
0x42, 0xF4, 0x72, 0xA1, 0x2A, 0x0D,
0x97, 0xB1, 0x31, 0xB3,
};
byte[] pseudoPrime2 = {
0x99, 0x98, 0xCA, 0xB8, 0x5E, 0xD7,
0xE5, 0xDC, 0x28, 0x5C, 0x6F, 0x0E,
0x15, 0x09, 0x59, 0x6E, 0x84, 0xF3,
0x81, 0xCD, 0xDE, 0x42, 0xDC, 0x93,
0xC2, 0x7A, 0x62, 0xAC, 0x6C, 0xAF,
0xDE, 0x74, 0xE3, 0xCB, 0x60, 0x20,
0x38, 0x9C, 0x21, 0xC3, 0xDC, 0xC8,
0xA2, 0x4D, 0xC6, 0x2A, 0x35, 0x7F,
0xF3, 0xA9, 0xE8, 0x1D, 0x7B, 0x2C,
0x78, 0xFA, 0xB8, 0x02, 0x55, 0x80,
0x9B, 0xC2, 0xA5, 0xCB,
};
BInteger bi_p = new BInteger(pseudoPrime1);
BInteger bi_q = new BInteger(pseudoPrime2);
BInteger bi_pq = (bi_p - 1) * (bi_q - 1);
BInteger bi_n = bi_p * bi_q;
for (int count = 0; count < rounds; count++)
{
// generate private and public key
BInteger bi_e = bi_pq.genCoPrime(512, rand);
BInteger bi_d = bi_e.modInverse(bi_pq);
Console.WriteLine("\ne =\n" + bi_e.ToString(10));
Console.WriteLine("\nd =\n" + bi_d.ToString(10));
Console.WriteLine("\nn =\n" + bi_n.ToString(10) + "\n");
// generate data of random length
int t1 = 0;
while (t1 == 0)
t1 = (int)(rand.NextDouble() * 65);
bool done = false;
while (!done)
{
for (int i = 0; i < 64; i++)
{
if (i < t1)
val[i] = (byte)(rand.NextDouble() * 256);
else
val[i] = 0;
if (val[i] != 0)
done = true;
}
}
while (val[0] == 0)
val[0] = (byte)(rand.NextDouble() * 256);
Console.Write("Round = " + count);
// encrypt and decrypt data
BInteger bi_data = new BInteger(val, t1);
BInteger bi_encrypted = bi_data.modPow(bi_e, bi_n);
BInteger bi_decrypted = bi_encrypted.modPow(bi_d, bi_n);
// compare
if (bi_decrypted != bi_data)
{
Console.WriteLine("\nError at round " + count);
Console.WriteLine(bi_data + "\n");
return;
}
Console.WriteLine(" <PASSED>.");
}
}
public static void RSATest(int rounds)
{
Random rand = new Random(1);
byte[] val = new byte[64];
// private and public key
BInteger bi_e = new BInteger("a932b948feed4fb2b692609bd22164fc9edb59fae7880cc1eaff7b3c9626b7e5b241c27a974833b2622ebe09beb451917663d47232488f23a117fc97720f1e7", 16);
BInteger bi_d = new BInteger("4adf2f7a89da93248509347d2ae506d683dd3a16357e859a980c4f77a4e2f7a01fae289f13a851df6e9db5adaa60bfd2b162bbbe31f7c8f828261a6839311929d2cef4f864dde65e556ce43c89bbbf9f1ac5511315847ce9cc8dc92470a747b8792d6a83b0092d2e5ebaf852c85cacf34278efa99160f2f8aa7ee7214de07b7", 16);
BInteger bi_n = new BInteger("e8e77781f36a7b3188d711c2190b560f205a52391b3479cdb99fa010745cbeba5f2adc08e1de6bf38398a0487c4a73610d94ec36f17f3f46ad75e17bc1adfec99839589f45f95ccc94cb2a5c500b477eb3323d8cfab0c8458c96f0147a45d27e45a4d11d54d77684f65d48f15fafcc1ba208e71e921b9bd9017c16a5231af7f", 16);
Console.WriteLine("e =\n" + bi_e.ToString(10));
Console.WriteLine("\nd =\n" + bi_d.ToString(10));
Console.WriteLine("\nn =\n" + bi_n.ToString(10) + "\n");
for (int count = 0; count < rounds; count++)
{
// generate data of random length
int t1 = 0;
while (t1 == 0)
t1 = (int)(rand.NextDouble() * 65);
bool done = false;
while (!done)
{
for (int i = 0; i < 64; i++)
{
if (i < t1)
val[i] = (byte)(rand.NextDouble() * 256);
else
val[i] = 0;
if (val[i] != 0)
done = true;
}
}
while (val[0] == 0)
val[0] = (byte)(rand.NextDouble() * 256);
Console.Write("Round = " + count);
// encrypt and decrypt data
BInteger bi_data = new BInteger(val, t1);
BInteger bi_encrypted = bi_data.modPow(bi_e, bi_n);
BInteger bi_decrypted = bi_encrypted.modPow(bi_d, bi_n);
// compare
if (bi_decrypted != bi_data)
{
Console.WriteLine("\nError at round " + count);
Console.WriteLine(bi_data + "\n");
return;
}
Console.WriteLine(" <PASSED>.");
}
}
public bool SolovayStrassenTest(int confidence)
{
BInteger thisVal;
if ((this.data[maxLength - 1] & 0x80000000) != 0) // negative
thisVal = -this;
else
thisVal = this;
if (thisVal.dataLength == 1)
{
// test small numbers
if (thisVal.data[0] == 0 || thisVal.data[0] == 1)
return false;
else if (thisVal.data[0] == 2 || thisVal.data[0] == 3)
return true;
}
if ((thisVal.data[0] & 0x1) == 0) // even numbers
return false;
int bits = thisVal.bitCount();
BInteger a = new BInteger();
BInteger p_sub1 = thisVal - 1;
BInteger p_sub1_shift = p_sub1 >> 1;
Random rand = new Random();
for (int round = 0; round < confidence; round++)
{
bool done = false;
while (!done) // generate a < n
{
int testBits = 0;
// make sure "a" has at least 2 bits
while (testBits < 2)
testBits = (int)(rand.NextDouble() * bits);
a.genRandomBits(testBits, rand);
int byteLen = a.dataLength;
// make sure "a" is not 0
if (byteLen > 1 || (byteLen == 1 && a.data[0] != 1))
done = true;
}
// check whether a factor exists (fix for version 1.03)
BInteger gcdTest = a.gcd(thisVal);
if (gcdTest.dataLength == 1 && gcdTest.data[0] != 1)
return false;
// calculate a^((p-1)/2) mod p
BInteger expResult = a.modPow(p_sub1_shift, thisVal);
if (expResult == p_sub1)
expResult = -1;
// calculate Jacobi symbol
BInteger jacob = Jacobi(a, thisVal);
//Console.WriteLine("a = " + a.ToString(10) + " b = " + thisVal.ToString(10));
//Console.WriteLine("expResult = " + expResult.ToString(10) + " Jacob = " + jacob.ToString(10));
// if they are different then it is not prime
if (expResult != jacob)
return false;
}
return true;
}
public bool RabinMillerTest(int confidence)
{
BInteger thisVal;
if ((this.data[maxLength - 1] & 0x80000000) != 0) // negative
thisVal = -this;
else
thisVal = this;
if (thisVal.dataLength == 1)
{
// test small numbers
if (thisVal.data[0] == 0 || thisVal.data[0] == 1)
return false;
else if (thisVal.data[0] == 2 || thisVal.data[0] == 3)
return true;
}
if ((thisVal.data[0] & 0x1) == 0) // even numbers
return false;
// calculate values of s and t
BInteger p_sub1 = thisVal - (new BInteger(1));
int s = 0;
for (int index = 0; index < p_sub1.dataLength; index++)
{
uint mask = 0x01;
for (int i = 0; i < 32; i++)
{
if ((p_sub1.data[index] & mask) != 0)
{
index = p_sub1.dataLength; // to break the outer loop
break;
}
mask <<= 1;
s++;
}
}
BInteger t = p_sub1 >> s;
int bits = thisVal.bitCount();
BInteger a = new BInteger();
Random rand = new Random();
for (int round = 0; round < confidence; round++)
{
bool done = false;
while (!done) // generate a < n
{
int testBits = 0;
// make sure "a" has at least 2 bits
while (testBits < 2)
testBits = (int)(rand.NextDouble() * bits);
a.genRandomBits(testBits, rand);
int byteLen = a.dataLength;
// make sure "a" is not 0
if (byteLen > 1 || (byteLen == 1 && a.data[0] != 1))
done = true;
}
// check whether a factor exists (fix for version 1.03)
BInteger gcdTest = a.gcd(thisVal);
if (gcdTest.dataLength == 1 && gcdTest.data[0] != 1)
return false;
BInteger b = a.modPow(t, thisVal);
bool result = false;
if (b.dataLength == 1 && b.data[0] == 1) // a^t mod p = 1
result = true;
for (int j = 0; result == false && j < s; j++)
{
if (b == p_sub1) // a^((2^j)*t) mod p = p-1 for some 0 <= j <= s-1
{
result = true;
break;
}
b = (b * b) % thisVal;
}
if (result == false)
return false;
}
return true;
}
public bool FermatLittleTest(int confidence)
{
BInteger thisVal;
if ((this.data[maxLength - 1] & 0x80000000) != 0) // negative
thisVal = -this;
else
thisVal = this;
if (thisVal.dataLength == 1)
{
// test small numbers
if (thisVal.data[0] == 0 || thisVal.data[0] == 1)
return false;
else if (thisVal.data[0] == 2 || thisVal.data[0] == 3)
return true;
}
if ((thisVal.data[0] & 0x1) == 0) // even numbers
return false;
int bits = thisVal.bitCount();
BInteger a = new BInteger();
BInteger p_sub1 = thisVal - (new BInteger(1));
Random rand = new Random();
for (int round = 0; round < confidence; round++)
{
bool done = false;
while (!done) // generate a < n
{
int testBits = 0;
// make sure "a" has at least 2 bits
while (testBits < 2)
testBits = (int)(rand.NextDouble() * bits);
a.genRandomBits(testBits, rand);
int byteLen = a.dataLength;
// make sure "a" is not 0
if (byteLen > 1 || (byteLen == 1 && a.data[0] != 1))
done = true;
}
// check whether a factor exists (fix for version 1.03)
BInteger gcdTest = a.gcd(thisVal);
if (gcdTest.dataLength == 1 && gcdTest.data[0] != 1)
return false;
// calculate a^(p-1) mod p
BInteger expResult = a.modPow(p_sub1, thisVal);
int resultLen = expResult.dataLength;
// is NOT prime is a^(p-1) mod p != 1
if (resultLen > 1 || (resultLen == 1 && expResult.data[0] != 1))
{
//Console.WriteLine("a = " + a.ToString());
return false;
}
}
return true;
}