C# BigInteger.genRandomBits方法代码示例

        //***********************************************************************
        // Tests the correct implementation of sqrt() method.
        //***********************************************************************

        public static void SqrtTest(int rounds) {
            Random rand = new Random();
            for (int count = 0; count < rounds; count++) {
                // generate data of random length
                int t1 = 0;
                while (t1 == 0)
                    t1 = (int)(rand.NextDouble() * 1024);

                Console.Write("Round = " + count);

                BigInteger a = new BigInteger();
                a.genRandomBits(t1, rand);

                BigInteger b = a.sqrt();
                BigInteger c = (b + 1) * (b + 1);

                // check that b is the largest integer such that b*b <= a
                if (c <= a) {
                    Console.WriteLine("\nError at round " + count);
                    Console.WriteLine(a + "\n");
                    return;
                }
                Console.WriteLine(" <PASSED>.");
            }
        }

        //***********************************************************************
        // Generates a random number with the specified number of bits such
        // that gcd(number, this) = 1
        //***********************************************************************

        public BigInteger genCoPrime(int bits, Random rand) {
            bool done = false;
            BigInteger result = new BigInteger();

            while (!done) {
                result.genRandomBits(bits, rand);
                //Console.WriteLine(result.ToString(16));

                // gcd test
                BigInteger g = result.gcd(this);
                if (g.dataLength == 1 && g.data[0] == 1)
                    done = true;
            }

            return result;
        }

        //***********************************************************************
        // Generates a positive BigInteger that is probably prime.
        //***********************************************************************

        public static BigInteger genPseudoPrime(int bits, int confidence, Random rand) {
            BigInteger result = new BigInteger();
            bool done = false;

            while (!done) {
                result.genRandomBits(bits, rand);
                result.data[0] |= 0x01;		// make it odd

                // prime test
                done = result.isProbablePrime(confidence);
            }
            return result;
        }

        //***********************************************************************
        // 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 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;
//.........这里部分代码省略.........

        //***********************************************************************
        // 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;
        }