public static ulong Decrypt(ulong[] data)
{
if (data.Length != 2) throw new ArgumentException("data should have a length of 2");
BigInteger c1 = new BigInteger(data[0]), c2 = new BigInteger(data[1]);
BigInteger res = (c1.ModPow(Prefs.PrivateKey, M).modInverse(M)*c2)%M;
return (ulong) res.LongValue();
}
public static Guid DecryptGuid(ulong[] data)
{
if (data.Length != 5) throw new ArgumentException("data should have a length of 5");
var c1 = new BigInteger(data[0]);
var res = new byte[16];
for (int i = 1; i < 5; i++)
{
var c2 = new BigInteger(data[i]);
BigInteger part = (c1.ModPow(Prefs.PrivateKey, M).modInverse(M) * c2) % M;
byte[] partBytes = BitConverter.GetBytes((uint) part.LongValue());
partBytes.CopyTo(res, (i - 1)*4);
}
return new Guid(res);
}
//***********************************************************************
// Tests the correct implementation of the modulo exponential and
// inverse modulo functions using RSA encryption and decryption. The two
// pseudoprimes p and q are fixed, but the two RSA keys are generated
// for each round of testing.
//***********************************************************************
public static void RSATest2(int rounds)
{
var rand = new Random();
var 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,
};
var bi_p = new BigInteger(pseudoPrime1);
var bi_q = new BigInteger(pseudoPrime2);
BigInteger bi_pq = (bi_p - 1)*(bi_q - 1);
BigInteger bi_n = bi_p*bi_q;
for (int count = 0; count < rounds; count++)
{
// generate private and public key
BigInteger bi_e = bi_pq.genCoPrime(512, rand);
BigInteger 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
var bi_data = new BigInteger(val, t1);
BigInteger bi_encrypted = bi_data.ModPow(bi_e, bi_n);
BigInteger 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>.");
}
}
//***********************************************************************
// Tests the correct implementation of the modulo exponential function
// using RSA encryption and decryption (using pre-computed encryption and
// decryption keys).
//***********************************************************************
public static void RSATest(int rounds)
{
var rand = new Random(1);
var val = new byte[64];
// private and public key
var bi_e =
new BigInteger(
"a932b948feed4fb2b692609bd22164fc9edb59fae7880cc1eaff7b3c9626b7e5b241c27a974833b2622ebe09beb451917663d47232488f23a117fc97720f1e7",
16);
var bi_d =
new BigInteger(
"4adf2f7a89da93248509347d2ae506d683dd3a16357e859a980c4f77a4e2f7a01fae289f13a851df6e9db5adaa60bfd2b162bbbe31f7c8f828261a6839311929d2cef4f864dde65e556ce43c89bbbf9f1ac5511315847ce9cc8dc92470a747b8792d6a83b0092d2e5ebaf852c85cacf34278efa99160f2f8aa7ee7214de07b7",
16);
var bi_n =
new BigInteger(
"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
var bi_data = new BigInteger(val, t1);
BigInteger bi_encrypted = bi_data.ModPow(bi_e, bi_n);
BigInteger 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>.");
}
}
//***********************************************************************
// Probabilistic prime test based on Solovay-Strassen (Euler Criterion)
//
// p is probably prime if for any a < p (a is not multiple of p),
// a^((p-1)/2) mod p = J(a, p)
//
// where J is the Jacobi symbol.
//
// Otherwise, p is composite.
//
// Returns
// -------
// True if "this" is a Euler pseudoprime to randomly chosen
// bases. The number of chosen bases is given by the "confidence"
// parameter.
//
// False if "this" is definitely NOT prime.
//
//***********************************************************************
public bool SolovayStrassenTest(int confidence)
{
BigInteger 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();
var a = new BigInteger();
BigInteger p_sub1 = thisVal - 1;
BigInteger p_sub1_shift = p_sub1 >> 1;
var 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)
BigInteger gcdTest = a.gcd(thisVal);
if (gcdTest.dataLength == 1 && gcdTest.data[0] != 1)
return false;
// calculate a^((p-1)/2) mod p
BigInteger expResult = a.ModPow(p_sub1_shift, thisVal);
if (expResult == p_sub1)
expResult = -1;
// calculate Jacobi symbol
BigInteger 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;
}
//***********************************************************************
// Probabilistic prime test based on Rabin-Miller's
//
// for any p > 0 with p - 1 = 2^s * t
//
// p is probably prime (strong pseudoprime) if for any a < p,
// 1) a^t mod p = 1 or
// 2) a^((2^j)*t) mod p = p-1 for some 0 <= j <= s-1
//
// Otherwise, p is composite.
//
// Returns
// -------
// True if "this" is a strong pseudoprime to randomly chosen
// bases. The number of chosen bases is given by the "confidence"
// parameter.
//
// False if "this" is definitely NOT prime.
//
//***********************************************************************
public bool RabinMillerTest(int confidence)
{
BigInteger 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
BigInteger p_sub1 = thisVal - (new BigInteger(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++;
}
}
BigInteger t = p_sub1 >> s;
int bits = thisVal.bitCount();
var a = new BigInteger();
var 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)
BigInteger gcdTest = a.gcd(thisVal);
if (gcdTest.dataLength == 1 && gcdTest.data[0] != 1)
return false;
BigInteger b = a.ModPow(t, thisVal);
/*
Console.WriteLine("a = " + a.ToString(10));
Console.WriteLine("b = " + b.ToString(10));
Console.WriteLine("t = " + t.ToString(10));
Console.WriteLine("s = " + s);
*/
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;
}
//***********************************************************************
// Probabilistic prime test based on Fermat's little theorem
//
// for any a < p (p does not divide a) if
// a^(p-1) mod p != 1 then p is not prime.
//
// Otherwise, p is probably prime (pseudoprime to the chosen base).
//
// Returns
// -------
// True if "this" is a pseudoprime to randomly chosen
// bases. The number of chosen bases is given by the "confidence"
// parameter.
//
// False if "this" is definitely NOT prime.
//
// Note - this method is fast but fails for Carmichael numbers except
// when the randomly chosen base is a factor of the number.
//
//***********************************************************************
public bool FermatLittleTest(int confidence)
{
BigInteger 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();
var a = new BigInteger();
BigInteger p_sub1 = thisVal - (new BigInteger(1));
var 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)
BigInteger gcdTest = a.gcd(thisVal);
if (gcdTest.dataLength == 1 && gcdTest.data[0] != 1)
return false;
// calculate a^(p-1) mod p
BigInteger 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;
}
