C# ECPoint.Twice方法代码示例

        public override ECPoint TwicePlus(ECPoint b)
        {
            if (this.IsInfinity)
                return b;
            if (b.IsInfinity)
                return Twice();

            ECCurve curve = this.Curve;

            ECFieldElement X1 = this.RawXCoord;
            if (X1.IsZero)
            {
                // A point with X == 0 is it's own additive inverse
                return b;
            }

            int coord = curve.CoordinateSystem;

            switch (coord)
            {
                case ECCurve.COORD_LAMBDA_PROJECTIVE:
                {
                    // NOTE: twicePlus() only optimized for lambda-affine argument
                    ECFieldElement X2 = b.RawXCoord, Z2 = b.RawZCoords[0];
                    if (X2.IsZero || !Z2.IsOne)
                    {
                        return Twice().Add(b);
                    }

                    ECFieldElement L1 = this.RawYCoord, Z1 = this.RawZCoords[0];
                    ECFieldElement L2 = b.RawYCoord;

                    ECFieldElement X1Sq = X1.Square();
                    ECFieldElement L1Sq = L1.Square();
                    ECFieldElement Z1Sq = Z1.Square();
                    ECFieldElement L1Z1 = L1.Multiply(Z1);

                    ECFieldElement T = curve.A.Multiply(Z1Sq).Add(L1Sq).Add(L1Z1);
                    ECFieldElement L2plus1 = L2.AddOne();
                    ECFieldElement A = curve.A.Add(L2plus1).Multiply(Z1Sq).Add(L1Sq).MultiplyPlusProduct(T, X1Sq, Z1Sq);
                    ECFieldElement X2Z1Sq = X2.Multiply(Z1Sq);
                    ECFieldElement B = X2Z1Sq.Add(T).Square();

                    if (B.IsZero)
                    {
                        if (A.IsZero)
                        {
                            return b.Twice();
                        }

                        return curve.Infinity;
                    }

                    if (A.IsZero)
                    {
                        return new F2mPoint(curve, A, curve.B.Sqrt(), IsCompressed);
                    }

                    ECFieldElement X3 = A.Square().Multiply(X2Z1Sq);
                    ECFieldElement Z3 = A.Multiply(B).Multiply(Z1Sq);
                    ECFieldElement L3 = A.Add(B).Square().MultiplyPlusProduct(T, L2plus1, Z3);

                    return new F2mPoint(curve, X3, L3, new ECFieldElement[] { Z3 }, IsCompressed);
                }
                default:
                {
                    return Twice().Add(b);
                }
            }
        }

 /**
  * Tests <code>ECPoint.add()</code> and <code>ECPoint.subtract()</code>
  * for the given point and the given point at infinity.
  *
  * @param p
  *            The point on which the tests are performed.
  * @param infinity
  *            The point at infinity on the same curve as <code>p</code>.
  */
 private void ImplTestAddSubtract(ECPoint p, ECPoint infinity)
 {
     AssertPointsEqual("Twice and Add inconsistent", p.Twice(), p.Add(p));
     AssertPointsEqual("Twice p - p is not p", p, p.Twice().Subtract(p));
     AssertPointsEqual("TwicePlus(p, -p) is not p", p, p.TwicePlus(p.Negate()));
     AssertPointsEqual("p - p is not infinity", infinity, p.Subtract(p));
     AssertPointsEqual("p plus infinity is not p", p, p.Add(infinity));
     AssertPointsEqual("infinity plus p is not p", p, infinity.Add(p));
     AssertPointsEqual("infinity plus infinity is not infinity ", infinity, infinity.Add(infinity));
     AssertPointsEqual("Twice infinity is not infinity ", infinity, infinity.Twice());
 }

		/**
		 * Tests <code>ECPoint.add()</code> and <code>ECPoint.subtract()</code>
		 * for the given point and the given point at infinity.
		 *
		 * @param p
		 *            The point on which the tests are performed.
		 * @param infinity
		 *            The point at infinity on the same curve as <code>p</code>.
		 */
		private void implTestAddSubtract(ECPoint p, ECPoint infinity)
		{
			Assert.AreEqual(p.Twice(), p.Add(p), "Twice and Add inconsistent");
			Assert.AreEqual(p, p.Twice().Subtract(p), "Twice p - p is not p");
			Assert.AreEqual(infinity, p.Subtract(p), "p - p is not infinity");
			Assert.AreEqual(p, p.Add(infinity), "p plus infinity is not p");
			Assert.AreEqual(p, infinity.Add(p), "infinity plus p is not p");
			Assert.AreEqual(infinity, infinity.Add(infinity), "infinity plus infinity is not infinity ");
		}

 /**
  * 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 multiplier.
  * @return The result of the point multiplication <code>kP</code>.
  */
 private ECPoint Multiply(ECPoint p, BigInteger k)
 {
     ECPoint q = p.Curve.Infinity;
     int t = k.BitLength;
     for (int i = 0; i < t; i++)
     {
         if (i != 0)
         {
             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, and for very small scalars.
  * 
  * @param p
  *            The point to multiply.
  * @param k
  *            The multiplier.
  * @return The result of the point multiplication <code>kP</code>.
  */
 public static ECPoint ReferenceMultiply(ECPoint p, BigInteger k)
 {
     BigInteger x = k.Abs();
     ECPoint q = p.Curve.Infinity;
     int t = x.BitLength;
     if (t > 0)
     {
         if (x.TestBit(0))
         {
             q = p;
         }
         for (int i = 1; i < t; i++)
         {
             p = p.Twice();
             if (x.TestBit(i))
             {
                 q = q.Add(p);
             }
         }
     }
     return k.SignValue < 0 ? q.Negate() : q;
 }