C# BigInteger.TestBit方法代码示例

		private static ECPoint ImplShamirsTrick(ECPoint P, BigInteger k,
			ECPoint Q, BigInteger l)
		{
			int m = System.Math.Max(k.BitLength, l.BitLength);
			ECPoint Z = P.Add(Q);
			ECPoint R = P.Curve.Infinity;

			for (int i = m - 1; i >= 0; --i)
			{
				R = R.Twice();

				if (k.TestBit(i))
				{
					if (l.TestBit(i))
					{
						R = R.Add(Z);
					}
					else
					{
						R = R.Add(P);
					}
				}
				else
				{
					if (l.TestBit(i))
					{
						R = R.Add(Q);
					}
				}
			}

			return R;
		}

		/**
		* 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 int[] GenerateCompactWindowNaf(int width, BigInteger k)
        {
            if (width == 2)
            {
                return GenerateCompactNaf(k);
            }

            if (width < 2 || width > 16)
                throw new ArgumentException("must be in the range [2, 16]", "width");
            if ((k.BitLength >> 16) != 0)
                throw new ArgumentException("must have bitlength < 2^16", "k");
            if (k.SignValue == 0)
                return EMPTY_INTS;

            int[] wnaf = new int[k.BitLength / width + 1];

            // 2^width and a mask and sign bit set accordingly
            int pow2 = 1 << width;
            int mask = pow2 - 1;
            int sign = pow2 >> 1;

            bool carry = false;
            int length = 0, pos = 0;

            while (pos <= k.BitLength)
            {
                if (k.TestBit(pos) == carry)
                {
                    ++pos;
                    continue;
                }

                k = k.ShiftRight(pos);

                int digit = k.IntValue & mask;
                if (carry)
                {
                    ++digit;
                }

                carry = (digit & sign) != 0;
                if (carry)
                {
                    digit -= pow2;
                }

                int zeroes = length > 0 ? pos - 1 : pos;
                wnaf[length++] = (digit << 16) | zeroes;
                pos = width;
            }

            // Reduce the WNAF array to its actual length
            if (wnaf.Length > length)
            {
                wnaf = Trim(wnaf, length);
            }

            return wnaf;
        }

 /**
  * Simple shift-and-add multiplication. Serves as reference implementation
  * to verify (possibly faster) implementations in
  * {@link org.bouncycastle.math.ec.ECPoint ECPoint}.
  * 
  * @param p The point to multiply.
  * @param k The factor by which to multiply.
  * @return The result of the point multiplication <code>k * p</code>.
  */
 protected override ECPoint MultiplyPositive(ECPoint p, BigInteger k)
 {
     ECPoint q = p.Curve.Infinity;
     int t = k.BitLength;
     if (t > 0)
     {
         if (k.TestBit(0))
         {
             q = p;
         }
         for (int i = 1; i < t; i++)
         {
             p = p.Twice();
             if (k.TestBit(i))
             {
                 q = q.Add(p);
             }
         }
     }
     return q;
 }

		/**
		* Simple shift-and-add multiplication. Serves as reference implementation
		* to verify (possibly faster) implementations in
		* {@link org.bouncycastle.math.ec.ECPoint ECPoint}.
		* 
		* @param p The point to multiply.
		* @param k The factor by which to multiply.
		* @return The result of the point multiplication <code>k * p</code>.
		*/
		public ECPoint Multiply(ECPoint p, BigInteger k, PreCompInfo preCompInfo)
		{
			ECPoint q = p.Curve.Infinity;
			int t = k.BitLength;
			for (int i = 0; i < t; i++)
			{
				if (k.TestBit(i))
				{
					q = q.Add(p);
				}
				p = p.Twice();
			}
			return q;
		}

        /**
         * Joye's double-add algorithm.
         */
        protected override ECPoint MultiplyPositive(ECPoint p, BigInteger k)
        {
            ECPoint[] R = new ECPoint[]{ p.Curve.Infinity, p };

            int n = k.BitLength;
            for (int i = 0; i < n; ++i)
            {
                int b = k.TestBit(i) ? 1 : 0;
                int bp = 1 - b;
                R[bp] = R[bp].TwicePlus(R[b]);
            }

            return R[0];
        }

        /**
         * Montgomery ladder.
         */
        protected override ECPoint MultiplyPositive(ECPoint p, BigInteger k)
        {
            ECPoint[] R = new ECPoint[]{ p.Curve.Infinity, p };

            int n = k.BitLength;
            int i = n;
            while (--i >= 0)
            {
                int b = k.TestBit(i) ? 1 : 0;
                int bp = 1 - b;
                R[bp] = R[bp].Add(R[b]);
                R[b] = R[b].Twice();
            }
            return R[0];
        }

        protected override ECPoint MultiplyPositive(ECPoint p, BigInteger k)
        {
            ECCurve c = p.Curve;
            int size = FixedPointUtilities.GetCombSize(c);

            if (k.BitLength > size)
            {
                /*
                 * TODO The comb works best when the scalars are less than the (possibly unknown) order.
                 * Still, if we want to handle larger scalars, we could allow customization of the comb
                 * size, or alternatively we could deal with the 'extra' bits either by running the comb
                 * multiple times as necessary, or by using an alternative multiplier as prelude.
                 */
                throw new InvalidOperationException("fixed-point comb doesn't support scalars larger than the curve order");
            }

            int minWidth = GetWidthForCombSize(size);

            FixedPointPreCompInfo info = FixedPointUtilities.Precompute(p, minWidth);
            ECPoint[] lookupTable = info.PreComp;
            int width = info.Width;

            int d = (size + width - 1) / width;

            ECPoint R = c.Infinity;

            int top = d * width - 1;
            for (int i = 0; i < d; ++i)
            {
                int index = 0;

                for (int j = top - i; j >= 0; j -= d)
                {
                    index <<= 1;
                    if (k.TestBit(j))
                    {
                        index |= 1;
                    }
                }

                R = R.TwicePlus(lookupTable[index]);
            }

            return R;
        }

        /**
         * 'Zeroless' Signed Digit Left-to-Right.
         */
        protected override ECPoint MultiplyPositive(ECPoint p, BigInteger k)
        {
            ECPoint addP = p.Normalize(), subP = addP.Negate();

            ECPoint R0 = addP;

            int n = k.BitLength;
            int s = k.GetLowestSetBit();

            int i = n;
            while (--i > s)
            {
                R0 = R0.TwicePlus(k.TestBit(i) ? addP : subP);
            }

            R0 = R0.TimesPow2(s);

            return R0;
        }

		public DHParameters(
			BigInteger				p,
			BigInteger				g,
			BigInteger				q,
			int						m,
			int						l,
			BigInteger				j,
			DHValidationParameters	validation)
		{
			if (p == null)
				throw new ArgumentNullException("p");
			if (g == null)
				throw new ArgumentNullException("g");
			if (!p.TestBit(0))
				throw new ArgumentException("field must be an odd prime", "p");
			if (g.CompareTo(BigInteger.Two) < 0
				|| g.CompareTo(p.Subtract(BigInteger.Two)) > 0)
				throw new ArgumentException("generator must in the range [2, p - 2]", "g");
			if (q != null && q.BitLength >= p.BitLength)
				throw new ArgumentException("q too big to be a factor of (p-1)", "q");
			if (m >= p.BitLength)
				throw new ArgumentException("m value must be < bitlength of p", "m");
			if (l != 0)
			{ 
	            if (l >= p.BitLength)
                	throw new ArgumentException("when l value specified, it must be less than bitlength(p)", "l");
				if (l < m)
					throw new ArgumentException("when l value specified, it may not be less than m value", "l");
			}
			if (j != null && j.CompareTo(BigInteger.Two) < 0)
				throw new ArgumentException("subgroup factor must be >= 2", "j");

			// TODO If q, j both provided, validate p = jq + 1 ?

			this.p = p;
			this.g = g;
			this.q = q;
			this.m = m;
			this.l = l;
			this.j = j;
			this.validation = validation;
        }

        /**
         * 'Zeroless' Signed Digit Right-to-Left.
         */
        protected override ECPoint MultiplyPositive(ECPoint p, BigInteger k)
        {
            ECPoint R0 = p.Curve.Infinity, R1 = p;

            int n = k.BitLength;
            int s = k.GetLowestSetBit();

            R1 = R1.TimesPow2(s);

            int i = s;
            while (++i < n)
            {
                R0 = R0.Add(k.TestBit(i) ? R1 : R1.Negate());
                R1 = R1.Twice();
            }

            R0 = R0.Add(R1);

            return R0;
        }

        public static int[] GenerateCompactNaf(BigInteger k)
        {
            if ((k.BitLength >> 16) != 0)
                throw new ArgumentException("must have bitlength < 2^16", "k");
            if (k.SignValue == 0)
                return EMPTY_INTS;

            BigInteger _3k = k.ShiftLeft(1).Add(k);

            int bits = _3k.BitLength;
            int[] naf = new int[bits >> 1];

            BigInteger diff = _3k.Xor(k);

            int highBit = bits - 1, length = 0, zeroes = 0;
            for (int i = 1; i < highBit; ++i)
            {
                if (!diff.TestBit(i))
                {
                    ++zeroes;
                    continue;
                }

                int digit = k.TestBit(i) ? -1 : 1;
                naf[length++] = (digit << 16) | zeroes;
                zeroes = 1;
                ++i;
            }

            naf[length++] = (1 << 16) | zeroes;

            if (naf.Length > length)
            {
                naf = Trim(naf, length);
            }

            return naf;
        }

 protected virtual BigInteger ModHalf(BigInteger x)
 {
     if (x.TestBit(0))
     {
         x = q.Add(x);
     }
     return x.ShiftRight(1);
 }

        private BigInteger[] LucasSequence(
            BigInteger	P,
            BigInteger	Q,
            BigInteger	k)
        {
            // TODO Research and apply "common-multiplicand multiplication here"

            int n = k.BitLength;
            int s = k.GetLowestSetBit();

            Debug.Assert(k.TestBit(s));

            BigInteger Uh = BigInteger.One;
            BigInteger Vl = BigInteger.Two;
            BigInteger Vh = P;
            BigInteger Ql = BigInteger.One;
            BigInteger Qh = BigInteger.One;

            for (int j = n - 1; j >= s + 1; --j)
            {
                Ql = ModMult(Ql, Qh);

                if (k.TestBit(j))
                {
                    Qh = ModMult(Ql, Q);
                    Uh = ModMult(Uh, Vh);
                    Vl = ModReduce(Vh.Multiply(Vl).Subtract(P.Multiply(Ql)));
                    Vh = ModReduce(Vh.Multiply(Vh).Subtract(Qh.ShiftLeft(1)));
                }
                else
                {
                    Qh = Ql;
                    Uh = ModReduce(Uh.Multiply(Vl).Subtract(Ql));
                    Vh = ModReduce(Vh.Multiply(Vl).Subtract(P.Multiply(Ql)));
                    Vl = ModReduce(Vl.Multiply(Vl).Subtract(Ql.ShiftLeft(1)));
                }
            }

            Ql = ModMult(Ql, Qh);
            Qh = ModMult(Ql, Q);
            Uh = ModReduce(Uh.Multiply(Vl).Subtract(Ql));
            Vl = ModReduce(Vh.Multiply(Vl).Subtract(P.Multiply(Ql)));
            Ql = ModMult(Ql, Qh);

            for (int j = 1; j <= s; ++j)
            {
                Uh = ModMult(Uh, Vl);
                Vl = ModReduce(Vl.Multiply(Vl).Subtract(Ql.ShiftLeft(1)));
                Ql = ModMult(Ql, Ql);
            }

            return new BigInteger[] { Uh, Vl };
        }

        public void TestShiftRight()
        {
            for (int i = 0; i < 10; ++i)
            {
                int shift = Rnd.Next(128);
                BigInteger a = new BigInteger(256 + i, Rnd).SetBit(256 + i);
                BigInteger b = a.ShiftRight(shift);

                Assert.AreEqual(a.BitLength - shift, b.BitLength);

                for (int j = 0; j < b.BitLength; ++j)
                {
                    Assert.AreEqual(a.TestBit(j + shift), b.TestBit(j));
                }
            }
        }