C# BigInteger.ShiftLeft方法代码示例

        /*
         * Finds a pair of prime BigInteger's {p, q: p = 2q + 1}
         * 
         * (see: Handbook of Applied Cryptography 4.86)
         */
        internal static BigInteger[] GenerateSafePrimes(int size, int certainty, SecureRandom random)
        {
            BigInteger p, q;
            int qLength = size - 1;
            int minWeight = size >> 2;

            if (size <= 32)
            {
                for (;;)
                {
                    q = new BigInteger(qLength, 2, random);

                    p = q.ShiftLeft(1).Add(BigInteger.One);

                    if (!p.IsProbablePrime(certainty))
                        continue;

                    if (certainty > 2 && !q.IsProbablePrime(certainty - 2))
                        continue;

                    break;
                }
            }
            else
            {
                // Note: Modified from Java version for speed
                for (;;)
                {
                    q = new BigInteger(qLength, 0, random);

                retry:
                    for (int i = 0; i < primeLists.Length; ++i)
                    {
                        int test = q.Remainder(BigPrimeProducts[i]).IntValue;

                        if (i == 0)
                        {
                            int rem3 = test % 3;
                            if (rem3 != 2)
                            {
                                int diff = 2 * rem3 + 2;
                                q = q.Add(BigInteger.ValueOf(diff));
                                test = (test + diff) % primeProducts[i];
                            }
                        }

                        int[] primeList = primeLists[i];
                        for (int j = 0; j < primeList.Length; ++j)
                        {
                            int prime = primeList[j];
                            int qRem = test % prime;
                            if (qRem == 0 || qRem == (prime >> 1))
                            {
                                q = q.Add(Six);
                                goto retry;
                            }
                        }
                    }

                    if (q.BitLength != qLength)
                        continue;

                    if (!q.RabinMillerTest(2, random))
                        continue;

                    p = q.ShiftLeft(1).Add(BigInteger.One);

                    if (!p.RabinMillerTest(certainty, random))
                        continue;

                    if (certainty > 2 && !q.RabinMillerTest(certainty - 2, random))
                        continue;

                    /*
                     * Require a minimum weight of the NAF representation, since low-weight primes may be
                     * weak against a version of the number-field-sieve for the discrete-logarithm-problem.
                     * 
                     * See "The number field sieve for integers of low weight", Oliver Schirokauer.
                     */
                    if (WNafUtilities.GetNafWeight(p) < minWeight)
                        continue;

                    break;
                }
            }

            return new BigInteger[] { p, q };
        }

        public BigInteger Multiply(
            BigInteger val)
        {
            if (val == this)
                return Square();

            if ((sign & val.sign) == 0)
                return Zero;

            if (val.QuickPow2Check()) // val is power of two
            {
                BigInteger result = this.ShiftLeft(val.Abs().BitLength - 1);
                return val.sign > 0 ? result : result.Negate();
            }

            if (this.QuickPow2Check()) // this is power of two
            {
                BigInteger result = val.ShiftLeft(this.Abs().BitLength - 1);
                return this.sign > 0 ? result : result.Negate();
            }

            int resLength = magnitude.Length + val.magnitude.Length;
            int[] res = new int[resLength];

            Multiply(res, this.magnitude, val.magnitude);

            int resSign = sign ^ val.sign ^ 1;
            return new BigInteger(resSign, res, true);
        }

        /**
         * generate suitable parameters for DSA, in line with
         * <i>FIPS 186-3 A.1 Generation of the FFC Primes p and q</i>.
         */
        protected virtual DsaParameters GenerateParameters_FIPS186_3()
        {
// A.1.1.2 Generation of the Probable Primes p and q Using an Approved Hash Function
            IDigest d = digest;
            int outlen = d.GetDigestSize() * 8;

// 1. Check that the (L, N) pair is in the list of acceptable (L, N pairs) (see Section 4.2). If
//    the pair is not in the list, then return INVALID.
            // Note: checked at initialisation
            
// 2. If (seedlen < N), then return INVALID.
            // FIXME This should be configurable (must be >= N)
            int seedlen = N;
            byte[] seed = new byte[seedlen / 8];

// 3. n = ceiling(L ⁄ outlen) – 1.
            int n = (L - 1) / outlen;

// 4. b = L – 1 – (n ∗ outlen).
            int b = (L - 1) % outlen;

            byte[] output = new byte[d.GetDigestSize()];
            for (;;)
            {
// 5. Get an arbitrary sequence of seedlen bits as the domain_parameter_seed.
                random.NextBytes(seed);

// 6. U = Hash (domain_parameter_seed) mod 2^(N–1).
                Hash(d, seed, output);
                BigInteger U = new BigInteger(1, output).Mod(BigInteger.One.ShiftLeft(N - 1));

// 7. q = 2^(N–1) + U + 1 – ( U mod 2).
                BigInteger q = BigInteger.One.ShiftLeft(N - 1).Add(U).Add(BigInteger.One).Subtract(
                    U.Mod(BigInteger.Two));

// 8. Test whether or not q is prime as specified in Appendix C.3.
                // TODO Review C.3 for primality checking
                if (!q.IsProbablePrime(certainty))
                {
// 9. If q is not a prime, then go to step 5.
                    continue;
                }

// 10. offset = 1.
                // Note: 'offset' value managed incrementally
                byte[] offset = Arrays.Clone(seed);

// 11. For counter = 0 to (4L – 1) do
                int counterLimit = 4 * L;
                for (int counter = 0; counter < counterLimit; ++counter)
                {
// 11.1 For j = 0 to n do
//      Vj = Hash ((domain_parameter_seed + offset + j) mod 2^seedlen).
// 11.2 W = V0 + (V1 ∗ 2^outlen) + ... + (V^(n–1) ∗ 2^((n–1) ∗ outlen)) + ((Vn mod 2^b) ∗ 2^(n ∗ outlen)).
                    // TODO Assemble w as a byte array
                    BigInteger W = BigInteger.Zero;
                    for (int j = 0, exp = 0; j <= n; ++j, exp += outlen)
                    {
                        Inc(offset);
                        Hash(d, offset, output);

                        BigInteger Vj = new BigInteger(1, output);
                        if (j == n)
                        {
                            Vj = Vj.Mod(BigInteger.One.ShiftLeft(b));
                        }

                        W = W.Add(Vj.ShiftLeft(exp));
                    }

// 11.3 X = W + 2^(L–1). Comment: 0 ≤ W < 2L–1; hence, 2L–1 ≤ X < 2L.
                    BigInteger X = W.Add(BigInteger.One.ShiftLeft(L - 1));

// 11.4 c = X mod 2q.
                    BigInteger c = X.Mod(q.ShiftLeft(1));

// 11.5 p = X - (c - 1). Comment: p ≡ 1 (mod 2q).
                    BigInteger p = X.Subtract(c.Subtract(BigInteger.One));

                    // 11.6 If (p < 2^(L - 1)), then go to step 11.9
                    if (p.BitLength != L)
                        continue;

// 11.7 Test whether or not p is prime as specified in Appendix C.3.
                    // TODO Review C.3 for primality checking
                    if (p.IsProbablePrime(certainty))
                    {
// 11.8 If p is determined to be prime, then return VALID and the values of p, q and
//      (optionally) the values of domain_parameter_seed and counter.
                        // TODO Make configurable (8-bit unsigned)?

                        if (usageIndex >= 0)
                        {
                            BigInteger g = CalculateGenerator_FIPS186_3_Verifiable(d, p, q, seed, usageIndex);
                            if (g != null)
                                return new DsaParameters(p, q, g, new DsaValidationParameters(seed, counter, usageIndex));
//.........这里部分代码省略.........

        private static BigInteger ModPowMonty(BigInteger b, BigInteger e, BigInteger m, bool convert)
        {
            int n = m.magnitude.Length;
            int powR = 32 * n;
            bool smallMontyModulus = m.BitLength + 2 <= powR;
            uint mDash = (uint)m.GetMQuote();

            // tmp = this * R mod m
            if (convert)
            {
                b = b.ShiftLeft(powR).Remainder(m);
            }

            int[] yAccum = new int[n + 1];

            int[] zVal = b.magnitude;
            Debug.Assert(zVal.Length <= n);
            if (zVal.Length < n)
            {
                int[] tmp = new int[n];
                zVal.CopyTo(tmp, n - zVal.Length);
                zVal = tmp;
            }

            // Sliding window from MSW to LSW

            int extraBits = 0;

            // Filter the common case of small RSA exponents with few bits set
            if (e.magnitude.Length > 1 || e.BitCount > 2)
            {
                int expLength = e.BitLength;
                while (expLength > ExpWindowThresholds[extraBits])
                {
                    ++extraBits;
                }
            }

            int numPowers = 1 << extraBits;
            int[][] oddPowers = new int[numPowers][];
            oddPowers[0] = zVal;

            int[] zSquared = Arrays.Clone(zVal);
            SquareMonty(yAccum, zSquared, m.magnitude, mDash, smallMontyModulus);

            for (int i = 1; i < numPowers; ++i)
            {
                oddPowers[i] = Arrays.Clone(oddPowers[i - 1]);
                MultiplyMonty(yAccum, oddPowers[i], zSquared, m.magnitude, mDash, smallMontyModulus);
            }

            int[] windowList = GetWindowList(e.magnitude, extraBits);
            Debug.Assert(windowList.Length > 1);

            int window = windowList[0];
            int mult = window & 0xFF, lastZeroes = window >> 8;

            int[] yVal;
            if (mult == 1)
            {
                yVal = zSquared;
                --lastZeroes;
            }
            else
            {
                yVal = Arrays.Clone(oddPowers[mult >> 1]);
            }

            int windowPos = 1;
            while ((window = windowList[windowPos++]) != -1)
            {
                mult = window & 0xFF;

                int bits = lastZeroes + BitLengthTable[mult];
                for (int j = 0; j < bits; ++j)
                {
                    SquareMonty(yAccum, yVal, m.magnitude, mDash, smallMontyModulus);
                }

                MultiplyMonty(yAccum, yVal, oddPowers[mult >> 1], m.magnitude, mDash, smallMontyModulus);

                lastZeroes = window >> 8;
            }

            for (int i = 0; i < lastZeroes; ++i)
            {
                SquareMonty(yAccum, yVal, m.magnitude, mDash, smallMontyModulus);
            }

            if (convert)
            {
                // Return y * R^(-1) mod m
                MontgomeryReduce(yVal, m.magnitude, mDash);
            }
            else if (smallMontyModulus && CompareTo(0, yVal, 0, m.magnitude) >= 0)
            {
                Subtract(0, yVal, 0, m.magnitude);
            }

            return new BigInteger(1, yVal, true);
//.........这里部分代码省略.........

        protected virtual DsaParameters GenerateParameters_FIPS186_2()
        {
            byte[] seed = new byte[20];
            byte[] part1 = new byte[20];
            byte[] part2 = new byte[20];
            byte[] u = new byte[20];
            int n = (L - 1) / 160;
            byte[] w = new byte[L / 8];

            if (!(digest is Sha1Digest))
                throw new InvalidOperationException("can only use SHA-1 for generating FIPS 186-2 parameters");

            for (;;)
            {
                random.NextBytes(seed);

                Hash(digest, seed, part1);
                Array.Copy(seed, 0, part2, 0, seed.Length);
                Inc(part2);
                Hash(digest, part2, part2);

                for (int i = 0; i != u.Length; i++)
                {
                    u[i] = (byte)(part1[i] ^ part2[i]);
                }

                u[0] |= (byte)0x80;
                u[19] |= (byte)0x01;

                BigInteger q = new BigInteger(1, u);

                if (!q.IsProbablePrime(certainty))
                    continue;

                byte[] offset = Arrays.Clone(seed);
                Inc(offset);

                for (int counter = 0; counter < 4096; ++counter)
                {
                    for (int k = 0; k < n; k++)
                    {
                        Inc(offset);
                        Hash(digest, offset, part1);
                        Array.Copy(part1, 0, w, w.Length - (k + 1) * part1.Length, part1.Length);
                    }

                    Inc(offset);
                    Hash(digest, offset, part1);
                    Array.Copy(part1, part1.Length - ((w.Length - (n) * part1.Length)), w, 0, w.Length - n * part1.Length);

                    w[0] |= (byte)0x80;

                    BigInteger x = new BigInteger(1, w);

                    BigInteger c = x.Mod(q.ShiftLeft(1));

                    BigInteger p = x.Subtract(c.Subtract(BigInteger.One));

                    if (p.BitLength != L)
                        continue;

                    if (p.IsProbablePrime(certainty))
                    {
                        BigInteger g = CalculateGenerator_FIPS186_2(p, q, random);

                        return new DsaParameters(p, q, g, new DsaValidationParameters(seed, counter));
                    }
                }
            }
        }