C# BigInteger.Mod方法代码示例

		/**
		* Computes the Window NAF (non-adjacent Form) of an integer.
		* @param width The width <code>w</code> of the Window NAF. The width is
		* defined as the minimal number <code>w</code>, such that for any
		* <code>w</code> consecutive digits in the resulting representation, at
		* most one is non-zero.
		* @param k The integer of which the Window NAF is computed.
		* @return The Window NAF of the given width, such that the following holds:
		* <code>k = &#8722;<sub>i=0</sub><sup>l-1</sup> k<sub>i</sub>2<sup>i</sup>
		* </code>, where the <code>k<sub>i</sub></code> denote the elements of the
		* returned <code>sbyte[]</code>.
		*/
		public sbyte[] WindowNaf(sbyte width, BigInteger k)
		{
			// The window NAF is at most 1 element longer than the binary
			// representation of the integer k. sbyte can be used instead of short or
			// int unless the window width is larger than 8. For larger width use
			// short or int. However, a width of more than 8 is not efficient for
			// m = log2(q) smaller than 2305 Bits. Note: Values for m larger than
			// 1000 Bits are currently not used in practice.
			sbyte[] wnaf = new sbyte[k.BitLength + 1];

			// 2^width as short and BigInteger
			short pow2wB = (short)(1 << width);
			BigInteger pow2wBI = BigInteger.ValueOf(pow2wB);

			int i = 0;

			// The actual length of the WNAF
			int length = 0;

			// while k >= 1
			while (k.SignValue > 0)
			{
				// if k is odd
				if (k.TestBit(0))
				{
					// k Mod 2^width
					BigInteger remainder = k.Mod(pow2wBI);

					// if remainder > 2^(width - 1) - 1
					if (remainder.TestBit(width - 1))
					{
						wnaf[i] = (sbyte)(remainder.IntValue - pow2wB);
					}
					else
					{
						wnaf[i] = (sbyte)remainder.IntValue;
					}
					// wnaf[i] is now in [-2^(width-1), 2^(width-1)-1]

					k = k.Subtract(BigInteger.ValueOf(wnaf[i]));
					length = i;
				}
				else
				{
					wnaf[i] = 0;
				}

				// k = k/2
				k = k.ShiftRight(1);
				i++;
			}

			length++;

			// Reduce the WNAF array to its actual length
			sbyte[] wnafShort = new sbyte[length];
			Array.Copy(wnaf, 0, wnafShort, 0, length);
			return wnafShort;
		}

		public static BigInteger ValidatePublicValue(BigInteger N, BigInteger val)
		{
		    val = val.Mod(N);

	        // Check that val % N != 0
	        if (val.Equals(BigInteger.Zero))
	            throw new CryptoException("Invalid public value: 0");

		    return val;
		}

        /// <summary>
        /// Converts a byte array produced by EncodeMod3Tight(int[]) back to an <c>int</c> array
        /// </summary>
        /// 
        /// <param name="Data">The byte array</param>
        /// <param name="N">The number of coefficients</param>
        /// 
        /// <returns>The decoded array</returns>
        public static int[] DecodeMod3Tight(byte[] Data, int N)
        {
            BigInteger sum = new BigInteger(1, Data);
            int[] coeffs = new int[N];

            for (int i = 0; i < N; i++)
            {
                coeffs[i] = sum.Mod(THREE).ToInt32() - 1;
                if (coeffs[i] > 1)
                    coeffs[i] -= 3;
                sum = sum.Divide(THREE);
            }

            return coeffs;
        }

        protected override ECPoint MultiplyPositive(ECPoint p, BigInteger k)
        {
            if (!curve.Equals(p.Curve))
                throw new InvalidOperationException();

            BigInteger n = p.Curve.Order;
            BigInteger[] ab = glvEndomorphism.DecomposeScalar(k.Mod(n));
            BigInteger a = ab[0], b = ab[1];

            ECPointMap pointMap = glvEndomorphism.PointMap;
            if (glvEndomorphism.HasEfficientPointMap)
            {
                return ECAlgorithms.ImplShamirsTrickWNaf(p, a, pointMap, b);
            }

            return ECAlgorithms.ImplShamirsTrickWNaf(p, a, pointMap.Map(p), b);
        }

		/**
		 * Generate a signature for the given message using the key we were
		 * initialised with. For conventional DSA the message should be a SHA-1
		 * hash of the message of interest.
		 *
		 * @param message the message that will be verified later.
		 */
		public BigInteger[] GenerateSignature(
			byte[] message)
		{
			DsaParameters parameters = key.Parameters;
			BigInteger q = parameters.Q;
			BigInteger m = calculateE(q, message);
			BigInteger k;

			do
			{
				k = new BigInteger(q.BitLength, random);
			}
			while (k.CompareTo(q) >= 0);

			BigInteger r = parameters.G.ModPow(k, parameters.P).Mod(q);

			k = k.ModInverse(q).Multiply(
				m.Add(((DsaPrivateKeyParameters)key).X.Multiply(r)));

			BigInteger s = k.Mod(q);

			return new BigInteger[]{ r, s };
		}

        public void TestMod()
        {
            // TODO Basic tests

            for (int rep = 0; rep < 100; ++rep)
            {
                int diff = Rnd.Next(25);
                var a = new BigInteger(100 - diff, 0, Rnd);
                var b = new BigInteger(100 + diff, 0, Rnd);
                var c = new BigInteger(10 + diff, 0, Rnd);

                BigInteger d = a.Multiply(b).Add(c);
                BigInteger e = d.Mod(a);
                Assert.AreEqual(c, e);

                BigInteger pow2 = One.ShiftLeft(Rnd.Next(128));
                Assert.AreEqual(b.And(pow2.Subtract(One)), b.Mod(pow2));
            }
        }

        /// <summary>
        /// Short trial-division test to find out whether a number is not prime.
        /// <para>This test is usually used before a Miller-Rabin primality test.</para>
        /// </summary>
        /// 
        /// <param name="Candidate">he number to test</param>
        /// 
        /// <returns>Returns <c>true</c> if the number has no factor of the tested primes, <c>false</c> if the number is definitely composite</returns>
        public static bool IsSmallPrime(BigInteger Candidate)
        {
            int[] smallPrime =
            {
                2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37,
                41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103,
                107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167,
                173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233,
                239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307,
                311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379,
                383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449,
                457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523,
                541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607,
                613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677,
                683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761,
                769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853,
                857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937,
                941, 947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, 1019,
                1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087,
                1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153,
                1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229,
                1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297,
                1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381,
                1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453,
                1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499
            };

            for (int i = 0; i < smallPrime.Length; i++)
            {
                if (Candidate.Mod(BigInteger.ValueOf(smallPrime[i])).Equals(ZERO))
                    return false;
            }

            return true;
        }

        /// <summary>
        /// Create a random BigInteger
        /// </summary>
        /// 
        /// <param name="UpperBound">The upper bound</param>
        /// <param name="SecRnd">An instance of the SecureRandom class</param>
        /// 
        /// <returns>A random BigInteger</returns>
        public static BigInteger Randomize(BigInteger UpperBound, SecureRandom SecRnd)
        {
            int blen = UpperBound.BitLength;
            BigInteger randomNum = BigInteger.ValueOf(0);

            if (SecRnd == null)
                SecRnd = _secRnd != null ? _secRnd : new SecureRandom();

            for (int i = 0; i < 20; i++)
            {
                randomNum = new BigInteger(blen, SecRnd);
                if (randomNum.CompareTo(UpperBound) < 0)
                    return randomNum;
            }

            return randomNum.Mod(UpperBound);
        }

 protected virtual BigInteger ModReduce(BigInteger x)
 {
     if (r == null)
     {
         x = x.Mod(q);
     }
     else
     {
         bool negative = x.SignValue < 0;
         if (negative)
         {
             x = x.Abs();
         }
         int qLen = q.BitLength;
         if (r.SignValue > 0)
         {
             BigInteger qMod = BigInteger.One.ShiftLeft(qLen);
             bool rIsOne = r.Equals(BigInteger.One);
             while (x.BitLength > (qLen + 1))
             {
                 BigInteger u = x.ShiftRight(qLen);
                 BigInteger v = x.Remainder(qMod);
                 if (!rIsOne)
                 {
                     u = u.Multiply(r);
                 }
                 x = u.Add(v);
             }
         }
         else
         {
             int d = ((qLen - 1) & 31) + 1;
             BigInteger mu = r.Negate();
             BigInteger u = mu.Multiply(x.ShiftRight(qLen - d));
             BigInteger quot = u.ShiftRight(qLen + d);
             BigInteger v = quot.Multiply(q);
             BigInteger bk1 = BigInteger.One.ShiftLeft(qLen + d);
             v = v.Remainder(bk1);
             x = x.Remainder(bk1);
             x = x.Subtract(v);
             if (x.SignValue < 0)
             {
                 x = x.Add(bk1);
             }
         }
         while (x.CompareTo(q) >= 0)
         {
             x = x.Subtract(q);
         }
         if (negative && x.SignValue != 0)
         {
             x = q.Subtract(x);
         }
     }
     return x;
 }

		public AsymmetricCipherKeyPair GenerateKeyPair()
        {
            BigInteger p, q, n, d, e, pSub1, qSub1, phi;

            //
            // p and q values should have a length of half the strength in bits
            //
			int strength = param.Strength;
            int pbitlength = (strength + 1) / 2;
            int qbitlength = (strength - pbitlength);
			int mindiffbits = strength / 3;

			e = param.PublicExponent;

			// TODO Consider generating safe primes for p, q (see DHParametersHelper.generateSafePrimes)
			// (then p-1 and q-1 will not consist of only small factors - see "Pollard's algorithm")

			//
            // Generate p, prime and (p-1) relatively prime to e
            //
            for (;;)
            {
				p = new BigInteger(pbitlength, 1, param.Random);

				if (p.Mod(e).Equals(BigInteger.One))
					continue;

				if (!p.IsProbablePrime(param.Certainty))
					continue;

				if (e.Gcd(p.Subtract(BigInteger.One)).Equals(BigInteger.One)) 
					break;
			}

            //
            // Generate a modulus of the required length
            //
            for (;;)
            {
                // Generate q, prime and (q-1) relatively prime to e,
                // and not equal to p
                //
                for (;;)
                {
					q = new BigInteger(qbitlength, 1, param.Random);

					if (q.Subtract(p).Abs().BitLength < mindiffbits)
						continue;

					if (q.Mod(e).Equals(BigInteger.One))
						continue;

					if (!q.IsProbablePrime(param.Certainty))
						continue;

					if (e.Gcd(q.Subtract(BigInteger.One)).Equals(BigInteger.One)) 
						break;
				}

                //
                // calculate the modulus
                //
                n = p.Multiply(q);

                if (n.BitLength == param.Strength)
					break;

                //
                // if we Get here our primes aren't big enough, make the largest
                // of the two p and try again
                //
                p = p.Max(q);
            }

			if (p.CompareTo(q) < 0)
			{
				phi = p;
				p = q;
				q = phi;
			}

            pSub1 = p.Subtract(BigInteger.One);
            qSub1 = q.Subtract(BigInteger.One);
            phi = pSub1.Multiply(qSub1);

            //
            // calculate the private exponent
            //
            d = e.ModInverse(phi);

            //
            // calculate the CRT factors
            //
            BigInteger dP, dQ, qInv;

            dP = d.Remainder(pSub1);
            dQ = d.Remainder(qSub1);
            qInv = q.ModInverse(p);

            return new AsymmetricCipherKeyPair(
//.........这里部分代码省略.........

        private void TestDiv(BigInteger i1, BigInteger i2)
        {
            BigInteger q = i1.Divide(i2);
            BigInteger r = i1.Remainder(i2);
            BigInteger remainder;
            BigInteger quotient = i1.DivideAndRemainder(i2, out remainder);

            Assert.IsTrue(q.Equals(quotient), "Divide and DivideAndRemainder do not agree");
            Assert.IsTrue(r.Equals(remainder), "Remainder and DivideAndRemainder do not agree");
            Assert.IsTrue(q.Sign != 0 || q.Equals(zero), "signum and equals(zero) do not agree on quotient");
            Assert.IsTrue(r.Sign != 0 || r.Equals(zero), "signum and equals(zero) do not agree on remainder");
            Assert.IsTrue(q.Sign == 0 || q.Sign == i1.Sign * i2.Sign, "wrong sign on quotient");
            Assert.IsTrue(r.Sign == 0 || r.Sign == i1.Sign, "wrong sign on remainder");
            Assert.IsTrue(r.Abs().CompareTo(i2.Abs()) < 0, "remainder out of range");
            Assert.IsTrue(q.Abs().Add(one).Multiply(i2.Abs()).CompareTo(i1.Abs()) > 0, "quotient too small");
            Assert.IsTrue(q.Abs().Multiply(i2.Abs()).CompareTo(i1.Abs()) <= 0, "quotient too large");
            BigInteger p = q.Multiply(i2);
            BigInteger a = p.Add(r);
            Assert.IsTrue(a.Equals(i1), "(a/b)*b+(a%b) != a");
            try {
                BigInteger mod = i1.Mod(i2);
                Assert.IsTrue(mod.Sign >= 0, "mod is negative");
                Assert.IsTrue(mod.Abs().CompareTo(i2.Abs()) < 0, "mod out of range");
                Assert.IsTrue(r.Sign < 0 || r.Equals(mod), "positive remainder == mod");
                Assert.IsTrue(r.Sign >= 0 || r.Equals(mod.Subtract(i2)), "negative remainder == mod - divisor");
            } catch (ArithmeticException e) {
                Assert.IsTrue(i2.Sign <= 0, "mod fails on negative divisor only");
            }
        }

		private DsaParameters GenerateParameters_FIPS186_2()
		{
            byte[] seed = new byte[20];
            byte[] part1 = new byte[20];
            byte[] part2 = new byte[20];
            byte[] u = new byte[20];
            Sha1Digest sha1 = new Sha1Digest();
			int n = (L - 1) / 160;
			byte[] w = new byte[L / 8];

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

				Hash(sha1, seed, part1);
				Array.Copy(seed, 0, part2, 0, seed.Length);
				Inc(part2);
				Hash(sha1, 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(sha1, offset, part1);
						Array.Copy(part1, 0, w, w.Length - (k + 1) * part1.Length, part1.Length);
					}

					Inc(offset);
					Hash(sha1, 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));
					}
				}
			}
		}

		/**
		 * generate suitable parameters for DSA, in line with
		 * <i>FIPS 186-3 A.1 Generation of the FFC Primes p and q</i>.
		 */
		private DsaParameters GenerateParameters_FIPS186_3()
		{
// A.1.1.2 Generation of the Probable Primes p and q Using an Approved Hash Function
			// FIXME This should be configurable (digest size in bits must be >= N)
			IDigest d = new Sha256Digest();
			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)?
//	                    int index = 1;
//	                    BigInteger g = CalculateGenerator_FIPS186_3_Verifiable(d, p, q, seed, index);
//	                    if (g != null)
//	                    {
//	                        // TODO Should 'index' be a part of the validation parameters?
//.........这里部分代码省略.........

 public override Number Calculate(BigInteger bigint1, BigInteger bigint2)
 {
     if (bigint1 == null || bigint2 == null)
     {
         return 0;
     }
     var comp = bigint2.CompareTo(BigInteger.Zero);
     if (comp == 0)
     {
         return 0;
     }
     if (comp < 0)
     {
         return bigint1.Negate().Mod(bigint2).Negate();
     }
     return bigint1.Mod(bigint2);
 }

		/**
		* @exception InvalidCipherTextException if the decrypted block is not a valid ISO 9796 bit string
		*/
		private byte[] DecodeBlock(
			byte[]	input,
			int		inOff,
			int		inLen)
		{
			byte[]  block = engine.ProcessBlock(input, inOff, inLen);
			int     r = 1;
			int     t = (bitSize + 13) / 16;

			BigInteger iS = new BigInteger(1, block);
			BigInteger iR;
			if (iS.Mod(Sixteen).Equals(Six))
			{
				iR = iS;
			}
			else
			{
				iR = modulus.Subtract(iS);

				if (!iR.Mod(Sixteen).Equals(Six))
					throw new InvalidCipherTextException("resulting integer iS or (modulus - iS) is not congruent to 6 mod 16");
			}

			block = iR.ToByteArrayUnsigned();

			if ((block[block.Length - 1] & 0x0f) != 0x6)
				throw new InvalidCipherTextException("invalid forcing byte in block");

			block[block.Length - 1] =
				(byte)(((ushort)(block[block.Length - 1] & 0xff) >> 4)
				| ((inverse[(block[block.Length - 2] & 0xff) >> 4]) << 4));

			block[0] = (byte)((shadows[(uint) (block[1] & 0xff) >> 4] << 4)
				| shadows[block[1] & 0x0f]);

			bool boundaryFound = false;
			int boundary = 0;

			for (int i = block.Length - 1; i >= block.Length - 2 * t; i -= 2)
			{
				int val = ((shadows[(uint) (block[i] & 0xff) >> 4] << 4)
					| shadows[block[i] & 0x0f]);

				if (((block[i - 1] ^ val) & 0xff) != 0)
				{
					if (!boundaryFound)
					{
						boundaryFound = true;
						r = (block[i - 1] ^ val) & 0xff;
						boundary = i - 1;
					}
					else
					{
						throw new InvalidCipherTextException("invalid tsums in block");
					}
				}
			}

			block[boundary] = 0;

			byte[] nblock = new byte[(block.Length - boundary) / 2];

			for (int i = 0; i < nblock.Length; i++)
			{
				nblock[i] = block[2 * i + boundary + 1];
			}

			padBits = r - 1;

			return nblock;
		}