Initial implementation of SM2 elliptic curve

- includes custom curve code
- add lots of OIDs from GM standard

4 files changed, 876 insertions, 0 deletions

diff --git a/crypto/src/math/ec/custom/gm/SM2P256V1Curve.cs b/crypto/src/math/ec/custom/gm/SM2P256V1Curve.cs
new file mode 100644
index 000000000..70b1190c9
--- /dev/null
+++ b/crypto/src/math/ec/custom/gm/SM2P256V1Curve.cs
@@ -0,0 +1,77 @@
+using System;
+
+using Org.BouncyCastle.Utilities.Encoders;
+
+namespace Org.BouncyCastle.Math.EC.Custom.GM
+{
+    internal class SM2P256V1Curve
+        : AbstractFpCurve
+    {
+        public static readonly BigInteger q = new BigInteger(1,
+            Hex.Decode("FFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000FFFFFFFFFFFFFFFF"));
+
+        private const int SM2P256V1_DEFAULT_COORDS = COORD_JACOBIAN;
+
+        protected readonly SM2P256V1Point m_infinity;
+
+        public SM2P256V1Curve()
+            : base(q)
+        {
+            this.m_infinity = new SM2P256V1Point(this, null, null);
+
+            this.m_a = FromBigInteger(new BigInteger(1,
+                Hex.Decode("FFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000FFFFFFFFFFFFFFFC")));
+            this.m_b = FromBigInteger(new BigInteger(1,
+                Hex.Decode("28E9FA9E9D9F5E344D5A9E4BCF6509A7F39789F515AB8F92DDBCBD414D940E93")));
+            this.m_order = new BigInteger(1, Hex.Decode("FFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFF7203DF6B21C6052B53BBF40939D54123"));
+            this.m_cofactor = BigInteger.One;
+            this.m_coord = SM2P256V1_DEFAULT_COORDS;
+        }
+
+        protected override ECCurve CloneCurve()
+        {
+            return new SM2P256V1Curve();
+        }
+
+        public override bool SupportsCoordinateSystem(int coord)
+        {
+            switch (coord)
+            {
+            case COORD_JACOBIAN:
+                return true;
+            default:
+                return false;
+            }
+        }
+
+        public virtual BigInteger Q
+        {
+            get { return q; }
+        }
+
+        public override ECPoint Infinity
+        {
+            get { return m_infinity; }
+        }
+
+        public override int FieldSize
+        {
+            get { return q.BitLength; }
+        }
+
+        public override ECFieldElement FromBigInteger(BigInteger x)
+        {
+            return new SM2P256V1FieldElement(x);
+        }
+
+        protected internal override ECPoint CreateRawPoint(ECFieldElement x, ECFieldElement y, bool withCompression)
+        {
+            return new SM2P256V1Point(this, x, y, withCompression);
+        }
+
+        protected internal override ECPoint CreateRawPoint(ECFieldElement x, ECFieldElement y, ECFieldElement[] zs, bool withCompression)
+        {
+            return new SM2P256V1Point(this, x, y, zs, withCompression);
+        }
+    }
+}
diff --git a/crypto/src/math/ec/custom/gm/SM2P256V1Field.cs b/crypto/src/math/ec/custom/gm/SM2P256V1Field.cs
new file mode 100644
index 000000000..b1d232347
--- /dev/null
+++ b/crypto/src/math/ec/custom/gm/SM2P256V1Field.cs
@@ -0,0 +1,307 @@
+using System;
+using System.Diagnostics;
+
+using Org.BouncyCastle.Math.Raw;
+
+namespace Org.BouncyCastle.Math.EC.Custom.GM
+{
+    internal class SM2P256V1Field
+    {
+        // 2^256 - 2^224 - 2^96 + 2^64 - 1
+        internal static readonly uint[] P = new uint[]{ 0xFFFFFFFF, 0xFFFFFFFF, 0x00000000, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF,
+            0xFFFFFFFF, 0xFFFFFFFE };
+        internal static readonly uint[] PExt = new uint[]{ 00000001, 0x00000000, 0xFFFFFFFE, 0x00000001, 0x00000001,
+            0xFFFFFFFE, 0x00000000, 0x00000002, 0xFFFFFFFE, 0xFFFFFFFD, 0x00000003, 0xFFFFFFFE, 0xFFFFFFFF, 0xFFFFFFFF,
+            0x00000000, 0xFFFFFFFE };
+        internal const uint P7 = 0xFFFFFFFE;
+        internal const uint PExt15 = 0xFFFFFFFE;
+
+        public static void Add(uint[] x, uint[] y, uint[] z)
+        {
+            uint c = Nat256.Add(x, y, z);
+            if (c != 0 || (z[7] >= P7 && Nat256.Gte(z, P)))
+            {
+                AddPInvTo(z);
+            }
+        }
+
+        public static void AddExt(uint[] xx, uint[] yy, uint[] zz)
+        {
+            uint c = Nat.Add(16, xx, yy, zz);
+            if (c != 0 || (zz[15] >= PExt15 && Nat.Gte(16, zz, PExt)))
+            {
+                Nat.SubFrom(16, PExt, zz);
+            }
+        }
+
+        public static void AddOne(uint[] x, uint[] z)
+        {
+            uint c = Nat.Inc(8, x, z);
+            if (c != 0 || (z[7] >= P7 && Nat256.Gte(z, P)))
+            {
+                AddPInvTo(z);
+            }
+        }
+
+        public static uint[] FromBigInteger(BigInteger x)
+        {
+            uint[] z = Nat256.FromBigInteger(x);
+            if (z[7] >= P7 && Nat256.Gte(z, P))
+            {
+                Nat256.SubFrom(P, z);
+            }
+            return z;
+        }
+
+        public static void Half(uint[] x, uint[] z)
+        {
+            if ((x[0] & 1) == 0)
+            {
+                Nat.ShiftDownBit(8, x, 0, z);
+            }
+            else
+            {
+                uint c = Nat256.Add(x, P, z);
+                Nat.ShiftDownBit(8, z, c);
+            }
+        }
+
+        public static void Multiply(uint[] x, uint[] y, uint[] z)
+        {
+            uint[] tt = Nat256.CreateExt();
+            Nat256.Mul(x, y, tt);
+            Reduce(tt, z);
+        }
+
+        public static void MultiplyAddToExt(uint[] x, uint[] y, uint[] zz)
+        {
+            uint c = Nat256.MulAddTo(x, y, zz);
+            if (c != 0 || (zz[15] >= PExt15 && Nat.Gte(16, zz, PExt)))
+            {
+                Nat.SubFrom(16, PExt, zz);
+            }
+        }
+
+        public static void Negate(uint[] x, uint[] z)
+        {
+            if (Nat256.IsZero(x))
+            {
+                Nat256.Zero(z);
+            }
+            else
+            {
+                Nat256.Sub(P, x, z);
+            }
+        }
+
+        public static void Reduce(uint[] xx, uint[] z)
+        {
+            long xx08 = xx[8], xx09 = xx[9], xx10 = xx[10], xx11 = xx[11];
+            long xx12 = xx[12], xx13 = xx[13], xx14 = xx[14], xx15 = xx[15];
+
+            long t0 = xx08 + xx09;
+            long t1 = xx10 + xx11;
+            long t2 = xx12 + xx15;
+            long t3 = xx13 + xx14;
+            long t4 = t3 + (xx15 << 1);
+
+            long ts = t0 + t3;
+            long tt = t1 + t2 + ts;
+
+            long cc = 0;
+            cc += (long)xx[0] + tt + xx13 + xx14 + xx15;
+            z[0] = (uint)cc;
+            cc >>= 32;
+            cc += (long)xx[1] + tt - xx08 + xx14 + xx15;
+            z[1] = (uint)cc;
+            cc >>= 32;
+            cc += (long)xx[2] - ts;
+            z[2] = (uint)cc;
+            cc >>= 32;
+            cc += (long)xx[3] + tt - xx09 - xx10 + xx13;
+            z[3] = (uint)cc;
+            cc >>= 32;
+            cc += (long)xx[4] + tt - t1 - xx08 + xx14;
+            z[4] = (uint)cc;
+            cc >>= 32;
+            cc += (long)xx[5] + t4 + xx10;
+            z[5] = (uint)cc;
+            cc >>= 32;
+            cc += (long)xx[6] + xx11 + xx14 + xx15;
+            z[6] = (uint)cc;
+            cc >>= 32;
+            cc += (long)xx[7] + tt + t4 + xx12;
+            z[7] = (uint)cc;
+            cc >>= 32;
+
+            Debug.Assert(cc >= 0);
+
+            Reduce32((uint)cc, z);
+        }
+
+        public static void Reduce32(uint x, uint[] z)
+        {
+            long cc = 0;
+
+            if (x != 0)
+            {
+                long xx08 = x;
+
+                cc += (long)z[0] + xx08;
+                z[0] = (uint)cc;
+                cc >>= 32;
+                if (cc != 0)
+                {
+                    cc += (long)z[1];
+                    z[1] = (uint)cc;
+                    cc >>= 32;
+                }
+                cc += (long)z[2] - xx08;
+                z[2] = (uint)cc;
+                cc >>= 32;
+                cc += (long)z[3] + xx08;
+                z[3] = (uint)cc;
+                cc >>= 32;
+                if (cc != 0)
+                {
+                    cc += (long)z[4];
+                    z[4] = (uint)cc;
+                    cc >>= 32;
+                    cc += (long)z[5];
+                    z[5] = (uint)cc;
+                    cc >>= 32;
+                    cc += (long)z[6];
+                    z[6] = (uint)cc;
+                    cc >>= 32;
+                }
+                cc += (long)z[7] + xx08;
+                z[7] = (uint)cc;
+                cc >>= 32;
+
+                Debug.Assert(cc == 0 || cc == 1);
+            }
+
+            if (cc != 0 || (z[7] >= P7 && Nat256.Gte(z, P)))
+            {
+                AddPInvTo(z);
+            }
+        }
+
+        public static void Square(uint[] x, uint[] z)
+        {
+            uint[] tt = Nat256.CreateExt();
+            Nat256.Square(x, tt);
+            Reduce(tt, z);
+        }
+
+        public static void SquareN(uint[] x, int n, uint[] z)
+        {
+            Debug.Assert(n > 0);
+
+            uint[] tt = Nat256.CreateExt();
+            Nat256.Square(x, tt);
+            Reduce(tt, z);
+
+            while (--n > 0)
+            {
+                Nat256.Square(z, tt);
+                Reduce(tt, z);
+            }
+        }
+
+        public static void Subtract(uint[] x, uint[] y, uint[] z)
+        {
+            int c = Nat256.Sub(x, y, z);
+            if (c != 0)
+            {
+                SubPInvFrom(z);
+            }
+        }
+
+        public static void SubtractExt(uint[] xx, uint[] yy, uint[] zz)
+        {
+            int c = Nat.Sub(16, xx, yy, zz);
+            if (c != 0)
+            {
+                Nat.AddTo(16, PExt, zz);
+            }
+        }
+
+        public static void Twice(uint[] x, uint[] z)
+        {
+            uint c = Nat.ShiftUpBit(8, x, 0, z);
+            if (c != 0 || (z[7] >= P7 && Nat256.Gte(z, P)))
+            {
+                AddPInvTo(z);
+            }
+        }
+
+        private static void AddPInvTo(uint[] z)
+        {
+            long c = (long)z[0] + 1;
+            z[0] = (uint)c;
+            c >>= 32;
+            if (c != 0)
+            {
+                c += (long)z[1];
+                z[1] = (uint)c;
+                c >>= 32;
+            }
+            c += (long)z[2] - 1;
+            z[2] = (uint)c;
+            c >>= 32;
+            c += (long)z[3] + 1;
+            z[3] = (uint)c;
+            c >>= 32;
+            if (c != 0)
+            {
+                c += (long)z[4];
+                z[4] = (uint)c;
+                c >>= 32;
+                c += (long)z[5];
+                z[5] = (uint)c;
+                c >>= 32;
+                c += (long)z[6];
+                z[6] = (uint)c;
+                c >>= 32;
+            }
+            c += (long)z[7] + 1;
+            z[7] = (uint)c;
+            //c >>= 32;
+        }
+
+        private static void SubPInvFrom(uint[] z)
+        {
+            long c = (long)z[0] - 1;
+            z[0] = (uint)c;
+            c >>= 32;
+            if (c != 0)
+            {
+                c += (long)z[1];
+                z[1] = (uint)c;
+                c >>= 32;
+            }
+            c += (long)z[2] + 1;
+            z[2] = (uint)c;
+            c >>= 32;
+            c += (long)z[3] - 1;
+            z[3] = (uint)c;
+            c >>= 32;
+            if (c != 0)
+            {
+                c += (long)z[4];
+                z[4] = (uint)c;
+                c >>= 32;
+                c += (long)z[5];
+                z[5] = (uint)c;
+                c >>= 32;
+                c += (long)z[6];
+                z[6] = (uint)c;
+                c >>= 32;
+            }
+            c += (long)z[7] - 1;
+            z[7] = (uint)c;
+            //c >>= 32;
+        }
+    }
+}
diff --git a/crypto/src/math/ec/custom/gm/SM2P256V1FieldElement.cs b/crypto/src/math/ec/custom/gm/SM2P256V1FieldElement.cs
new file mode 100644
index 000000000..669c73bd2
--- /dev/null
+++ b/crypto/src/math/ec/custom/gm/SM2P256V1FieldElement.cs
@@ -0,0 +1,213 @@
+using System;
+
+using Org.BouncyCastle.Math.Raw;
+using Org.BouncyCastle.Utilities;
+
+namespace Org.BouncyCastle.Math.EC.Custom.GM
+{
+    internal class SM2P256V1FieldElement
+        : ECFieldElement
+    {
+        public static readonly BigInteger Q = SM2P256V1Curve.q;
+
+        protected internal readonly uint[] x;
+
+        public SM2P256V1FieldElement(BigInteger x)
+        {
+            if (x == null || x.SignValue < 0 || x.CompareTo(Q) >= 0)
+                throw new ArgumentException("value invalid for SM2P256V1FieldElement", "x");
+
+            this.x = SM2P256V1Field.FromBigInteger(x);
+        }
+
+        public SM2P256V1FieldElement()
+        {
+            this.x = Nat256.Create();
+        }
+
+        protected internal SM2P256V1FieldElement(uint[] x)
+        {
+            this.x = x;
+        }
+
+        public override bool IsZero
+        {
+            get { return Nat256.IsZero(x); }
+        }
+
+        public override bool IsOne
+        {
+            get { return Nat256.IsOne(x); }
+        }
+
+        public override bool TestBitZero()
+        {
+            return Nat256.GetBit(x, 0) == 1;
+        }
+
+        public override BigInteger ToBigInteger()
+        {
+            return Nat256.ToBigInteger(x);
+        }
+
+        public override string FieldName
+        {
+            get { return "SM2P256V1Field"; }
+        }
+
+        public override int FieldSize
+        {
+            get { return Q.BitLength; }
+        }
+
+        public override ECFieldElement Add(ECFieldElement b)
+        {
+            uint[] z = Nat256.Create();
+            SM2P256V1Field.Add(x, ((SM2P256V1FieldElement)b).x, z);
+            return new SM2P256V1FieldElement(z);
+        }
+
+        public override ECFieldElement AddOne()
+        {
+            uint[] z = Nat256.Create();
+            SM2P256V1Field.AddOne(x, z);
+            return new SM2P256V1FieldElement(z);
+        }
+
+        public override ECFieldElement Subtract(ECFieldElement b)
+        {
+            uint[] z = Nat256.Create();
+            SM2P256V1Field.Subtract(x, ((SM2P256V1FieldElement)b).x, z);
+            return new SM2P256V1FieldElement(z);
+        }
+
+        public override ECFieldElement Multiply(ECFieldElement b)
+        {
+            uint[] z = Nat256.Create();
+            SM2P256V1Field.Multiply(x, ((SM2P256V1FieldElement)b).x, z);
+            return new SM2P256V1FieldElement(z);
+        }
+
+        public override ECFieldElement Divide(ECFieldElement b)
+        {
+            //return Multiply(b.Invert());
+            uint[] z = Nat256.Create();
+            Mod.Invert(SM2P256V1Field.P, ((SM2P256V1FieldElement)b).x, z);
+            SM2P256V1Field.Multiply(z, x, z);
+            return new SM2P256V1FieldElement(z);
+        }
+
+        public override ECFieldElement Negate()
+        {
+            uint[] z = Nat256.Create();
+            SM2P256V1Field.Negate(x, z);
+            return new SM2P256V1FieldElement(z);
+        }
+
+        public override ECFieldElement Square()
+        {
+            uint[] z = Nat256.Create();
+            SM2P256V1Field.Square(x, z);
+            return new SM2P256V1FieldElement(z);
+        }
+
+        public override ECFieldElement Invert()
+        {
+            //return new SM2P256V1FieldElement(ToBigInteger().ModInverse(Q));
+            uint[] z = Nat256.Create();
+            Mod.Invert(SM2P256V1Field.P, x, z);
+            return new SM2P256V1FieldElement(z);
+        }
+
+        /**
+         * return a sqrt root - the routine verifies that the calculation returns the right value - if
+         * none exists it returns null.
+         */
+        public override ECFieldElement Sqrt()
+        {
+            /*
+             * Raise this element to the exponent 2^254 - 2^222 - 2^94 + 2^62
+             *
+             * Breaking up the exponent's binary representation into "repunits", we get:
+             * { 31 1s } { 1 0s } { 128 1s } { 31 0s } { 1 1s } { 62 0s}
+             *
+             * We use an addition chain for the beginning: [1], 2, 3, 6, 12, [24], 30, [31] 
+             */
+
+            uint[] x1 = this.x;
+            if (Nat256.IsZero(x1) || Nat256.IsOne(x1))
+            {
+                return this;
+            }
+
+            uint[] x2 = Nat256.Create();
+            SM2P256V1Field.Square(x1, x2);
+            SM2P256V1Field.Multiply(x2, x1, x2);
+            uint[] x3 = x2;
+            SM2P256V1Field.Square(x2, x3);
+            SM2P256V1Field.Multiply(x3, x1, x3);
+            uint[] x6 = Nat256.Create();
+            SM2P256V1Field.SquareN(x3, 3, x6);
+            SM2P256V1Field.Multiply(x6, x3, x6);
+            uint[] x12 = x3;
+            SM2P256V1Field.SquareN(x6, 6, x12);
+            SM2P256V1Field.Multiply(x12, x6, x12);
+            uint[] x24 = Nat256.Create();
+            SM2P256V1Field.SquareN(x12, 12, x24);
+            SM2P256V1Field.Multiply(x24, x12, x24);
+            uint[] x30 = x12;
+            SM2P256V1Field.SquareN(x24, 6, x30);
+            SM2P256V1Field.Multiply(x30, x6, x30);
+            uint[] x31 = x6;
+            SM2P256V1Field.Square(x30, x31);
+            SM2P256V1Field.Multiply(x31, x1, x31);
+
+            uint[] t1 = x31;
+            SM2P256V1Field.Square(x31, t1);
+
+            uint[] x32 = x12;
+            SM2P256V1Field.Multiply(t1, x1, x32);
+
+            SM2P256V1Field.SquareN(t1, 32, t1);
+            SM2P256V1Field.Multiply(t1, x32, t1);
+
+            uint[] t2 = x24;
+            SM2P256V1Field.SquareN(t1, 32, t2);
+            SM2P256V1Field.Multiply(t2, x1, t2);
+            SM2P256V1Field.SquareN(t2, 32, t2);
+            SM2P256V1Field.Multiply(t2, t1, t2);
+            SM2P256V1Field.SquareN(t2, 32, t2);
+            SM2P256V1Field.Multiply(t2, x32, t2);
+            SM2P256V1Field.SquareN(t2, 32, t2);
+            SM2P256V1Field.Multiply(t2, x1, t2);
+            SM2P256V1Field.SquareN(t2, 62, t1);
+            SM2P256V1Field.Square(t1, t2);
+
+            return Nat256.Eq(x1, t2) ? new SM2P256V1FieldElement(t1) : null;
+        }
+
+        public override bool Equals(object obj)
+        {
+            return Equals(obj as SM2P256V1FieldElement);
+        }
+
+        public override bool Equals(ECFieldElement other)
+        {
+            return Equals(other as SM2P256V1FieldElement);
+        }
+
+        public virtual bool Equals(SM2P256V1FieldElement other)
+        {
+            if (this == other)
+                return true;
+            if (null == other)
+                return false;
+            return Nat256.Eq(x, other.x);
+        }
+
+        public override int GetHashCode()
+        {
+            return Q.GetHashCode() ^ Arrays.GetHashCode(x, 0, 8);
+        }
+    }
+}
diff --git a/crypto/src/math/ec/custom/gm/SM2P256V1Point.cs b/crypto/src/math/ec/custom/gm/SM2P256V1Point.cs
new file mode 100644
index 000000000..916c90633
--- /dev/null
+++ b/crypto/src/math/ec/custom/gm/SM2P256V1Point.cs
@@ -0,0 +1,279 @@
+using System;
+
+using Org.BouncyCastle.Math.Raw;
+
+namespace Org.BouncyCastle.Math.EC.Custom.GM
+{
+    internal class SM2P256V1Point
+        : AbstractFpPoint
+    {
+        /**
+         * Create a point which encodes with point compression.
+         * 
+         * @param curve
+         *            the curve to use
+         * @param x
+         *            affine x co-ordinate
+         * @param y
+         *            affine y co-ordinate
+         * 
+         * @deprecated Use ECCurve.createPoint to construct points
+         */
+        public SM2P256V1Point(ECCurve curve, ECFieldElement x, ECFieldElement y)
+            : this(curve, x, y, false)
+        {
+        }
+
+        /**
+         * Create a point that encodes with or without point compresion.
+         * 
+         * @param curve
+         *            the curve to use
+         * @param x
+         *            affine x co-ordinate
+         * @param y
+         *            affine y co-ordinate
+         * @param withCompression
+         *            if true encode with point compression
+         * 
+         * @deprecated per-point compression property will be removed, refer
+         *             {@link #getEncoded(bool)}
+         */
+        public SM2P256V1Point(ECCurve curve, ECFieldElement x, ECFieldElement y, bool withCompression)
+            : base(curve, x, y, withCompression)
+        {
+            if ((x == null) != (y == null))
+                throw new ArgumentException("Exactly one of the field elements is null");
+        }
+
+        internal SM2P256V1Point(ECCurve curve, ECFieldElement x, ECFieldElement y, ECFieldElement[] zs, bool withCompression)
+            : base(curve, x, y, zs, withCompression)
+        {
+        }
+
+        protected override ECPoint Detach()
+        {
+            return new SM2P256V1Point(null, AffineXCoord, AffineYCoord);
+        }
+
+        public override ECPoint Add(ECPoint b)
+        {
+            if (this.IsInfinity)
+                return b;
+            if (b.IsInfinity)
+                return this;
+            if (this == b)
+                return Twice();
+
+            ECCurve curve = this.Curve;
+
+            SM2P256V1FieldElement X1 = (SM2P256V1FieldElement)this.RawXCoord, Y1 = (SM2P256V1FieldElement)this.RawYCoord;
+            SM2P256V1FieldElement X2 = (SM2P256V1FieldElement)b.RawXCoord, Y2 = (SM2P256V1FieldElement)b.RawYCoord;
+
+            SM2P256V1FieldElement Z1 = (SM2P256V1FieldElement)this.RawZCoords[0];
+            SM2P256V1FieldElement Z2 = (SM2P256V1FieldElement)b.RawZCoords[0];
+
+            uint c;
+            uint[] tt1 = Nat256.CreateExt();
+            uint[] t2 = Nat256.Create();
+            uint[] t3 = Nat256.Create();
+            uint[] t4 = Nat256.Create();
+
+            bool Z1IsOne = Z1.IsOne;
+            uint[] U2, S2;
+            if (Z1IsOne)
+            {
+                U2 = X2.x;
+                S2 = Y2.x;
+            }
+            else
+            {
+                S2 = t3;
+                SM2P256V1Field.Square(Z1.x, S2);
+
+                U2 = t2;
+                SM2P256V1Field.Multiply(S2, X2.x, U2);
+
+                SM2P256V1Field.Multiply(S2, Z1.x, S2);
+                SM2P256V1Field.Multiply(S2, Y2.x, S2);
+            }
+
+            bool Z2IsOne = Z2.IsOne;
+            uint[] U1, S1;
+            if (Z2IsOne)
+            {
+                U1 = X1.x;
+                S1 = Y1.x;
+            }
+            else
+            {
+                S1 = t4;
+                SM2P256V1Field.Square(Z2.x, S1);
+
+                U1 = tt1;
+                SM2P256V1Field.Multiply(S1, X1.x, U1);
+
+                SM2P256V1Field.Multiply(S1, Z2.x, S1);
+                SM2P256V1Field.Multiply(S1, Y1.x, S1);
+            }
+
+            uint[] H = Nat256.Create();
+            SM2P256V1Field.Subtract(U1, U2, H);
+
+            uint[] R = t2;
+            SM2P256V1Field.Subtract(S1, S2, R);
+
+            // Check if b == this or b == -this
+            if (Nat256.IsZero(H))
+            {
+                if (Nat256.IsZero(R))
+                {
+                    // this == b, i.e. this must be doubled
+                    return this.Twice();
+                }
+
+                // this == -b, i.e. the result is the point at infinity
+                return curve.Infinity;
+            }
+
+            uint[] HSquared = t3;
+            SM2P256V1Field.Square(H, HSquared);
+
+            uint[] G = Nat256.Create();
+            SM2P256V1Field.Multiply(HSquared, H, G);
+
+            uint[] V = t3;
+            SM2P256V1Field.Multiply(HSquared, U1, V);
+
+            SM2P256V1Field.Negate(G, G);
+            Nat256.Mul(S1, G, tt1);
+
+            c = Nat256.AddBothTo(V, V, G);
+            SM2P256V1Field.Reduce32(c, G);
+
+            SM2P256V1FieldElement X3 = new SM2P256V1FieldElement(t4);
+            SM2P256V1Field.Square(R, X3.x);
+            SM2P256V1Field.Subtract(X3.x, G, X3.x);
+
+            SM2P256V1FieldElement Y3 = new SM2P256V1FieldElement(G);
+            SM2P256V1Field.Subtract(V, X3.x, Y3.x);
+            SM2P256V1Field.MultiplyAddToExt(Y3.x, R, tt1);
+            SM2P256V1Field.Reduce(tt1, Y3.x);
+
+            SM2P256V1FieldElement Z3 = new SM2P256V1FieldElement(H);
+            if (!Z1IsOne)
+            {
+                SM2P256V1Field.Multiply(Z3.x, Z1.x, Z3.x);
+            }
+            if (!Z2IsOne)
+            {
+                SM2P256V1Field.Multiply(Z3.x, Z2.x, Z3.x);
+            }
+
+            ECFieldElement[] zs = new ECFieldElement[]{ Z3 };
+
+            return new SM2P256V1Point(curve, X3, Y3, zs, IsCompressed);
+        }
+
+        public override ECPoint Twice()
+        {
+            if (this.IsInfinity)
+                return this;
+
+            ECCurve curve = this.Curve;
+
+            SM2P256V1FieldElement Y1 = (SM2P256V1FieldElement)this.RawYCoord;
+            if (Y1.IsZero)
+                return curve.Infinity;
+
+            SM2P256V1FieldElement X1 = (SM2P256V1FieldElement)this.RawXCoord, Z1 = (SM2P256V1FieldElement)this.RawZCoords[0];
+
+            uint c;
+            uint[] t1 = Nat256.Create();
+            uint[] t2 = Nat256.Create();
+
+            uint[] Y1Squared = Nat256.Create();
+            SM2P256V1Field.Square(Y1.x, Y1Squared);
+
+            uint[] T = Nat256.Create();
+            SM2P256V1Field.Square(Y1Squared, T);
+
+            bool Z1IsOne = Z1.IsOne;
+
+            uint[] Z1Squared = Z1.x;
+            if (!Z1IsOne)
+            {
+                Z1Squared = t2;
+                SM2P256V1Field.Square(Z1.x, Z1Squared);
+            }
+
+            SM2P256V1Field.Subtract(X1.x, Z1Squared, t1);
+
+            uint[] M = t2;
+            SM2P256V1Field.Add(X1.x, Z1Squared, M);
+            SM2P256V1Field.Multiply(M, t1, M);
+            c = Nat256.AddBothTo(M, M, M);
+            SM2P256V1Field.Reduce32(c, M);
+
+            uint[] S = Y1Squared;
+            SM2P256V1Field.Multiply(Y1Squared, X1.x, S);
+            c = Nat.ShiftUpBits(8, S, 2, 0);
+            SM2P256V1Field.Reduce32(c, S);
+
+            c = Nat.ShiftUpBits(8, T, 3, 0, t1);
+            SM2P256V1Field.Reduce32(c, t1);
+
+            SM2P256V1FieldElement X3 = new SM2P256V1FieldElement(T);
+            SM2P256V1Field.Square(M, X3.x);
+            SM2P256V1Field.Subtract(X3.x, S, X3.x);
+            SM2P256V1Field.Subtract(X3.x, S, X3.x);
+
+            SM2P256V1FieldElement Y3 = new SM2P256V1FieldElement(S);
+            SM2P256V1Field.Subtract(S, X3.x, Y3.x);
+            SM2P256V1Field.Multiply(Y3.x, M, Y3.x);
+            SM2P256V1Field.Subtract(Y3.x, t1, Y3.x);
+
+            SM2P256V1FieldElement Z3 = new SM2P256V1FieldElement(M);
+            SM2P256V1Field.Twice(Y1.x, Z3.x);
+            if (!Z1IsOne)
+            {
+                SM2P256V1Field.Multiply(Z3.x, Z1.x, Z3.x);
+            }
+
+            return new SM2P256V1Point(curve, X3, Y3, new ECFieldElement[]{ Z3 }, IsCompressed);
+        }
+
+        public override ECPoint TwicePlus(ECPoint b)
+        {
+            if (this == b)
+                return ThreeTimes();
+            if (this.IsInfinity)
+                return b;
+            if (b.IsInfinity)
+                return Twice();
+
+            ECFieldElement Y1 = this.RawYCoord;
+            if (Y1.IsZero)
+                return b;
+
+            return Twice().Add(b);
+        }
+
+        public override ECPoint ThreeTimes()
+        {
+            if (this.IsInfinity || this.RawYCoord.IsZero)
+                return this;
+
+            // NOTE: Be careful about recursions between TwicePlus and ThreeTimes
+            return Twice().Add(this);
+        }
+
+        public override ECPoint Negate()
+        {
+            if (IsInfinity)
+                return this;
+
+            return new SM2P256V1Point(Curve, RawXCoord, RawYCoord.Negate(), RawZCoords, IsCompressed);
+        }
+    }
+}