C# BigInteger.GCD方法代码示例

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

//.........这里部分代码省略.........
                }

                //Console.WriteLine(D);
                D = (Math.Abs(D) + 2) * sign;
                sign = -sign;
            }
            dCount++;
        }

        long Q = (1 - D) >> 2;

        /*
        Console.WriteLine("D = " + D);
        Console.WriteLine("Q = " + Q);
        Console.WriteLine("(n,D) = " + thisVal.gcd(D));
        Console.WriteLine("(n,Q) = " + thisVal.gcd(Q));
        Console.WriteLine("J(D|n) = " + BigInteger.Jacobi(D, thisVal));
        */

        BigInteger p_add1 = thisVal + 1;
        int s = 0;

        for (int index = 0; index < p_add1.dataLength; index++)
        {
            uint mask = 0x01;

            for (int i = 0; i < 32; i++)
            {
                if ((p_add1.data[index] & mask) != 0)
                {
                    index = p_add1.dataLength;      // to break the outer loop
                    break;
                }
                mask <<= 1;
                s++;
            }
        }

        BigInteger t = p_add1 >> s;

        // calculate constant = b^(2k) / m
        // for Barrett Reduction
        BigInteger constant = new BigInteger();

        int nLen = thisVal.dataLength << 1;
        constant.data[nLen] = 0x00000001;
        constant.dataLength = nLen + 1;

        constant = constant / thisVal;

        BigInteger[] lucas = LucasSequenceHelper(1, Q, t, thisVal, constant, 0);
        bool isPrime = false;

        if ((lucas[0].dataLength == 1 && lucas[0].data[0] == 0) ||
           (lucas[1].dataLength == 1 && lucas[1].data[0] == 0))
        {
            // u(t) = 0 or V(t) = 0
            isPrime = true;
        }

        for (int i = 1; i < s; i++)
        {
            if (!isPrime)
            {
                // doubling of index
                lucas[1] = thisVal.BarrettReduction(lucas[1] * lucas[1], thisVal, constant);
                lucas[1] = (lucas[1] - (lucas[2] << 1)) % thisVal;

                //lucas[1] = ((lucas[1] * lucas[1]) - (lucas[2] << 1)) % thisVal;

                if ((lucas[1].dataLength == 1 && lucas[1].data[0] == 0))
                    isPrime = true;
            }

            lucas[2] = thisVal.BarrettReduction(lucas[2] * lucas[2], thisVal, constant);     //Q^k
        }


        if (isPrime)     // additional checks for composite numbers
        {
            // If n is prime and gcd(n, Q) == 1, then
            // Q^((n+1)/2) = Q * Q^((n-1)/2) is congruent to (Q * J(Q, n)) mod n

            BigInteger g = thisVal.GCD(Q);
            if (g.dataLength == 1 && g.data[0] == 1)         // gcd(this, Q) == 1
            {
                if ((lucas[2].data[maxLength - 1] & 0x80000000) != 0)
                    lucas[2] += thisVal;

                BigInteger temp = (Q * BigInteger.Jacobi(Q, thisVal)) % thisVal;
                if ((temp.data[maxLength - 1] & 0x80000000) != 0)
                    temp += thisVal;

                if (lucas[2] != temp)
                    isPrime = false;
            }
        }

        return isPrime;
    }

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

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