modPow() public method

public modPow ( BigInteger exp, BigInteger n ) : BigInteger
exp BigInteger
n BigInteger
return BigInteger
        //***********************************************************************
        // 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)
        {
            Random rand = new Random();
            byte[] val = new byte[64];

            byte[] pseudoPrime1 = {
                        (byte)0x85, (byte)0x84, (byte)0x64, (byte)0xFD, (byte)0x70, (byte)0x6A,
                        (byte)0x9F, (byte)0xF0, (byte)0x94, (byte)0x0C, (byte)0x3E, (byte)0x2C,
                        (byte)0x74, (byte)0x34, (byte)0x05, (byte)0xC9, (byte)0x55, (byte)0xB3,
                        (byte)0x85, (byte)0x32, (byte)0x98, (byte)0x71, (byte)0xF9, (byte)0x41,
                        (byte)0x21, (byte)0x5F, (byte)0x02, (byte)0x9E, (byte)0xEA, (byte)0x56,
                        (byte)0x8D, (byte)0x8C, (byte)0x44, (byte)0xCC, (byte)0xEE, (byte)0xEE,
                        (byte)0x3D, (byte)0x2C, (byte)0x9D, (byte)0x2C, (byte)0x12, (byte)0x41,
                        (byte)0x1E, (byte)0xF1, (byte)0xC5, (byte)0x32, (byte)0xC3, (byte)0xAA,
                        (byte)0x31, (byte)0x4A, (byte)0x52, (byte)0xD8, (byte)0xE8, (byte)0xAF,
                        (byte)0x42, (byte)0xF4, (byte)0x72, (byte)0xA1, (byte)0x2A, (byte)0x0D,
                        (byte)0x97, (byte)0xB1, (byte)0x31, (byte)0xB3,
                };

            byte[] pseudoPrime2 = {
                        (byte)0x99, (byte)0x98, (byte)0xCA, (byte)0xB8, (byte)0x5E, (byte)0xD7,
                        (byte)0xE5, (byte)0xDC, (byte)0x28, (byte)0x5C, (byte)0x6F, (byte)0x0E,
                        (byte)0x15, (byte)0x09, (byte)0x59, (byte)0x6E, (byte)0x84, (byte)0xF3,
                        (byte)0x81, (byte)0xCD, (byte)0xDE, (byte)0x42, (byte)0xDC, (byte)0x93,
                        (byte)0xC2, (byte)0x7A, (byte)0x62, (byte)0xAC, (byte)0x6C, (byte)0xAF,
                        (byte)0xDE, (byte)0x74, (byte)0xE3, (byte)0xCB, (byte)0x60, (byte)0x20,
                        (byte)0x38, (byte)0x9C, (byte)0x21, (byte)0xC3, (byte)0xDC, (byte)0xC8,
                        (byte)0xA2, (byte)0x4D, (byte)0xC6, (byte)0x2A, (byte)0x35, (byte)0x7F,
                        (byte)0xF3, (byte)0xA9, (byte)0xE8, (byte)0x1D, (byte)0x7B, (byte)0x2C,
                        (byte)0x78, (byte)0xFA, (byte)0xB8, (byte)0x02, (byte)0x55, (byte)0x80,
                        (byte)0x9B, (byte)0xC2, (byte)0xA5, (byte)0xCB,
                };


            BigInteger bi_p = new BigInteger(pseudoPrime1);
            BigInteger 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
                BigInteger 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)
        {
            Random rand = new Random(1);
            byte[] val = new byte[64];

            // private and public key
            BigInteger bi_e = new BigInteger("a932b948feed4fb2b692609bd22164fc9edb59fae7880cc1eaff7b3c9626b7e5b241c27a974833b2622ebe09beb451917663d47232488f23a117fc97720f1e7", 16);
            BigInteger bi_d = new BigInteger("4adf2f7a89da93248509347d2ae506d683dd3a16357e859a980c4f77a4e2f7a01fae289f13a851df6e9db5adaa60bfd2b162bbbe31f7c8f828261a6839311929d2cef4f864dde65e556ce43c89bbbf9f1ac5511315847ce9cc8dc92470a747b8792d6a83b0092d2e5ebaf852c85cacf34278efa99160f2f8aa7ee7214de07b7", 16);
            BigInteger 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
                BigInteger 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 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();
            BigInteger a = new BigInteger();
            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)
                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 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();
            BigInteger a = new BigInteger();
            BigInteger p_sub1 = thisVal - 1;
            BigInteger 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)
                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 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();
            BigInteger a = new BigInteger();
            BigInteger p_sub1 = thisVal - (new BigInteger(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)
                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;
        }