Add custom curve for secp224k1

5 files changed, 697 insertions, 0 deletions

diff --git a/crypto/src/crypto/ec/CustomNamedCurves.cs b/crypto/src/crypto/ec/CustomNamedCurves.cs
index 3bc7b16cc..7d6b00339 100644
--- a/crypto/src/crypto/ec/CustomNamedCurves.cs
+++ b/crypto/src/crypto/ec/CustomNamedCurves.cs
@@ -72,6 +72,27 @@ namespace Org.BouncyCastle.Crypto.EC
         }
 
         /*
+         * secp224k1
+         */
+        internal class Secp224k1Holder
+            : X9ECParametersHolder
+        {
+            private Secp224k1Holder() { }
+
+            internal static readonly X9ECParametersHolder Instance = new Secp224k1Holder();
+
+            protected override X9ECParameters CreateParameters()
+            {
+                byte[] S = null;
+                ECCurve curve = ConfigureCurve(new SecP224K1Curve());
+                ECPoint G = curve.DecodePoint(Hex.Decode("04"
+                    + "A1455B334DF099DF30FC28A169A467E9E47075A90F7E650EB6B7A45C"
+                    + "7E089FED7FBA344282CAFBD6F7E319F7C0B0BD59E2CA4BDB556D61A5"));
+                return new X9ECParameters(curve, G, curve.Order, curve.Cofactor, S);
+            }
+        }
+
+        /*
          * secp224r1
          */
         internal class Secp224r1Holder
@@ -170,6 +191,7 @@ namespace Org.BouncyCastle.Crypto.EC
         {
             DefineCurve("secp192k1", SecObjectIdentifiers.SecP192k1, Secp192k1Holder.Instance);
             DefineCurve("secp192r1", SecObjectIdentifiers.SecP192r1, Secp192r1Holder.Instance);
+            DefineCurve("secp224k1", SecObjectIdentifiers.SecP224k1, Secp224k1Holder.Instance);
             DefineCurve("secp224r1", SecObjectIdentifiers.SecP224r1, Secp224r1Holder.Instance);
             DefineCurve("secp256k1", SecObjectIdentifiers.SecP256k1, Secp256k1Holder.Instance);
             DefineCurve("secp256r1", SecObjectIdentifiers.SecP256r1, Secp256r1Holder.Instance);
diff --git a/crypto/src/math/ec/custom/sec/SecP224K1Curve.cs b/crypto/src/math/ec/custom/sec/SecP224K1Curve.cs
new file mode 100644
index 000000000..5d82eaed8
--- /dev/null
+++ b/crypto/src/math/ec/custom/sec/SecP224K1Curve.cs
@@ -0,0 +1,93 @@
+using System;
+
+using Org.BouncyCastle.Math.Field;
+using Org.BouncyCastle.Utilities.Encoders;
+
+namespace Org.BouncyCastle.Math.EC.Custom.Sec
+{
+    internal class SecP224K1Curve
+        : ECCurve
+    {
+        public static readonly BigInteger q = new BigInteger(1,
+            Hex.Decode("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFE56D"));
+
+        private const int SECP224K1_DEFAULT_COORDS = COORD_JACOBIAN;
+
+        protected readonly SecP224K1Point m_infinity;
+
+        public SecP224K1Curve()
+            : base(FiniteFields.GetPrimeField(q))
+        {
+            this.m_infinity = new SecP224K1Point(this, null, null);
+
+            this.m_a = FromBigInteger(BigInteger.Zero);
+            this.m_b = FromBigInteger(BigInteger.ValueOf(5));
+            this.m_order = new BigInteger(1, Hex.Decode("010000000000000000000000000001DCE8D2EC6184CAF0A971769FB1F7"));
+            this.m_cofactor = BigInteger.One;
+            this.m_coord = SECP224K1_DEFAULT_COORDS;
+        }
+
+        protected override ECCurve CloneCurve()
+        {
+            return new SecP224K1Curve();
+        }
+
+        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 SecP224K1FieldElement(x);
+        }
+
+        protected internal override ECPoint CreateRawPoint(ECFieldElement x, ECFieldElement y, bool withCompression)
+        {
+            return new SecP224K1Point(this, x, y, withCompression);
+        }
+
+        protected override ECPoint DecompressPoint(int yTilde, BigInteger X1)
+        {
+            ECFieldElement x = FromBigInteger(X1);
+            ECFieldElement alpha = x.Square().Multiply(x).Add(B);
+            ECFieldElement beta = alpha.Sqrt();
+
+            //
+            // if we can't find a sqrt we haven't got a point on the
+            // curve - run!
+            //
+            if (beta == null)
+                throw new ArithmeticException("Invalid point compression");
+
+            if (beta.TestBitZero() != (yTilde == 1))
+            {
+                // Use the other root
+                beta = beta.Negate();
+            }
+
+            return new SecP224K1Point(this, x, beta, true);
+        }
+    }
+}
diff --git a/crypto/src/math/ec/custom/sec/SecP224K1Field.cs b/crypto/src/math/ec/custom/sec/SecP224K1Field.cs
new file mode 100644
index 000000000..edc938d22
--- /dev/null
+++ b/crypto/src/math/ec/custom/sec/SecP224K1Field.cs
@@ -0,0 +1,150 @@
+using System;
+using System.Diagnostics;
+
+namespace Org.BouncyCastle.Math.EC.Custom.Sec
+{
+    internal class SecP224K1Field
+    {
+        // 2^224 - 2^32 - 2^12 - 2^11 - 2^9 - 2^7 - 2^4 - 2 - 1
+        internal static readonly uint[] P = new uint[]{ 0xFFFFE56D, 0xFFFFFFFE, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF,
+            0xFFFFFFFF };
+        private const uint P6 = 0xFFFFFFFF;
+        private static readonly uint[] PExt = new uint[]{ 0x02C23069, 0x00003526, 0x00000001, 0x00000000, 0x00000000,
+            0x00000000, 0x00000000, 0xFFFFCADA, 0xFFFFFFFD, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF };
+        private const uint PExt13 = 0xFFFFFFFF;
+        private const ulong PInv = 0x0000000100001A93L; 
+        private const uint PInv33 = 0x1A93;
+
+        public static void Add(uint[] x, uint[] y, uint[] z)
+        {
+            uint c = Nat224.Add(x, y, z);
+            if (c != 0 || (z[6] == P6 && Nat224.Gte(z, P)))
+            {
+                Nat224.AddDWord(PInv, z, 0);
+            }
+        }
+
+        public static void AddExt(uint[] xx, uint[] yy, uint[] zz)
+        {
+            uint c = Nat224.AddExt(xx, yy, zz);
+            if (c != 0 || (zz[13] == PExt13 && Nat224.GteExt(zz, PExt)))
+            {
+                Nat224.SubExt(zz, PExt, zz);
+            }
+        }
+
+        public static void AddOne(uint[] x, uint[] z)
+        {
+            Array.Copy(x, 0, z, 0, 8);
+            uint c = Nat224.Inc(z, 0);
+            if (c != 0 || (z[6] == P6 && Nat224.Gte(z, P)))
+            {
+                Nat224.AddDWord(PInv, z, 0);
+            }
+        }
+
+        public static uint[] FromBigInteger(BigInteger x)
+        {
+            uint[] z = Nat224.FromBigInteger(x);
+            if (z[6] == P6 && Nat224.Gte(z, P))
+            {
+                Nat224.AddDWord(PInv, z, 0);
+            }
+            return z;
+        }
+
+        public static void Half(uint[] x, uint[] z)
+        {
+            if ((x[0] & 1) == 0)
+            {
+                Nat224.ShiftDownBit(x, 0, z);
+            }
+            else
+            {
+                uint c = Nat224.Add(x, P, z);
+                Nat224.ShiftDownBit(z, c, z);
+            }
+        }
+
+        public static void Multiply(uint[] x, uint[] y, uint[] z)
+        {
+            uint[] tt = Nat224.CreateExt();
+            Nat224.Mul(x, y, tt);
+            Reduce(tt, z);
+        }
+
+        public static void Negate(uint[] x, uint[] z)
+        {
+            if (Nat224.IsZero(x))
+            {
+                Nat224.Zero(z);
+            }
+            else
+            {
+                Nat224.Sub(P, x, z);
+            }
+        }
+
+        public static void Reduce(uint[] xx, uint[] z)
+        {
+            ulong c = Nat224.Mul33Add(PInv33, xx, 7, xx, 0, z, 0);
+            c = Nat224.Mul33DWordAdd(PInv33, c, z, 0);
+
+            Debug.Assert(c == 0 || c == 1);
+
+            if (c != 0 || (z[6] == P6 && Nat224.Gte(z, P)))
+            {
+                Nat224.AddDWord(PInv, z, 0);
+            }
+        }
+
+        public static void Square(uint[] x, uint[] z)
+        {
+            uint[] tt = Nat224.CreateExt();
+            Nat224.Square(x, tt);
+            Reduce(tt, z);
+        }
+
+        public static void SquareN(uint[] x, int n, uint[] z)
+        {
+            Debug.Assert(n > 0);
+
+            uint[] tt = Nat224.CreateExt();
+            Nat224.Square(x, tt);
+            Reduce(tt, z);
+
+            while (--n > 0)
+            {
+                Nat224.Square(z, tt);
+                Reduce(tt, z);
+            }
+        }
+
+        public static void Subtract(uint[] x, uint[] y, uint[] z)
+        {
+            int c = Nat224.Sub(x, y, z);
+            if (c != 0)
+            {
+                Nat224.SubDWord(PInv, z);
+            }
+        }
+
+        public static void SubtractExt(uint[] xx, uint[] yy, uint[] zz)
+        {
+            int c = Nat224.SubExt(xx, yy, zz);
+            if (c != 0)
+            {
+                Nat224.AddExt(zz, PExt, zz);
+            }
+        }
+
+        public static void Twice(uint[] x, uint[] z)
+        {
+            uint c = Nat224.ShiftUpBit(x, 0, z);
+            if (c != 0 || (z[6] == P6 && Nat224.Gte(z, P)))
+            {
+                Nat224.AddDWord(PInv, z, 0);
+            }
+        }
+    }
+}
diff --git a/crypto/src/math/ec/custom/sec/SecP224K1FieldElement.cs b/crypto/src/math/ec/custom/sec/SecP224K1FieldElement.cs
new file mode 100644
index 000000000..cd9426769
--- /dev/null
+++ b/crypto/src/math/ec/custom/sec/SecP224K1FieldElement.cs
@@ -0,0 +1,156 @@
+using System;
+using System.Diagnostics;
+
+using Org.BouncyCastle.Utilities;
+
+namespace Org.BouncyCastle.Math.EC.Custom.Sec
+{
+    internal class SecP224K1FieldElement
+        : ECFieldElement
+    {
+        public static readonly BigInteger Q = SecP224K1Curve.q;
+
+        protected internal readonly uint[] x;
+
+        public SecP224K1FieldElement(BigInteger x)
+        {
+            if (x == null || x.SignValue < 0 || x.CompareTo(Q) >= 0)
+                throw new ArgumentException("value invalid for SecP224K1FieldElement", "x");
+
+            this.x = SecP224K1Field.FromBigInteger(x);
+        }
+
+        public SecP224K1FieldElement()
+        {
+            this.x = Nat224.Create();
+        }
+
+        protected internal SecP224K1FieldElement(uint[] x)
+        {
+            this.x = x;
+        }
+
+        public override bool IsZero
+        {
+            get { return Nat224.IsZero(x); }
+        }
+
+        public override bool IsOne
+        {
+            get { return Nat224.IsOne(x); }
+        }
+
+        public override bool TestBitZero()
+        {
+            return Nat224.GetBit(x, 0) == 1;
+        }
+
+        public override BigInteger ToBigInteger()
+        {
+            return Nat224.ToBigInteger(x);
+        }
+
+        public override string FieldName
+        {
+            get { return "SecP224K1Field"; }
+        }
+
+        public override int FieldSize
+        {
+            get { return Q.BitLength; }
+        }
+
+        public override ECFieldElement Add(ECFieldElement b)
+        {
+            uint[] z = Nat224.Create();
+            SecP224K1Field.Add(x, ((SecP224K1FieldElement)b).x, z);
+            return new SecP224K1FieldElement(z);
+        }
+
+        public override ECFieldElement AddOne()
+        {
+            uint[] z = Nat224.Create();
+            SecP224K1Field.AddOne(x, z);
+            return new SecP224K1FieldElement(z);
+        }
+
+        public override ECFieldElement Subtract(ECFieldElement b)
+        {
+            uint[] z = Nat224.Create();
+            SecP224K1Field.Subtract(x, ((SecP224K1FieldElement)b).x, z);
+            return new SecP224K1FieldElement(z);
+        }
+
+        public override ECFieldElement Multiply(ECFieldElement b)
+        {
+            uint[] z = Nat224.Create();
+            SecP224K1Field.Multiply(x, ((SecP224K1FieldElement)b).x, z);
+            return new SecP224K1FieldElement(z);
+        }
+
+        public override ECFieldElement Divide(ECFieldElement b)
+        {
+            //return Multiply(b.Invert());
+            uint[] z = Nat224.Create();
+            Mod.Invert(SecP224K1Field.P, ((SecP224K1FieldElement)b).x, z);
+            SecP224K1Field.Multiply(z, x, z);
+            return new SecP224K1FieldElement(z);
+        }
+
+        public override ECFieldElement Negate()
+        {
+            uint[] z = Nat224.Create();
+            SecP224K1Field.Negate(x, z);
+            return new SecP224K1FieldElement(z);
+        }
+
+        public override ECFieldElement Square()
+        {
+            uint[] z = Nat224.Create();
+            SecP224K1Field.Square(x, z);
+            return new SecP224K1FieldElement(z);
+        }
+
+        public override ECFieldElement Invert()
+        {
+            //return new SecP224K1FieldElement(ToBigInteger().ModInverse(Q));
+            uint[] z = Nat224.Create();
+            Mod.Invert(SecP224K1Field.P, x, z);
+            return new SecP224K1FieldElement(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()
+        {
+            ECFieldElement root = new FpFieldElement(Q, ToBigInteger()).Sqrt();
+            return root == null ? null : new SecP224K1FieldElement(root.ToBigInteger());
+        }
+
+        public override bool Equals(object obj)
+        {
+            return Equals(obj as SecP224K1FieldElement);
+        }
+
+        public override bool Equals(ECFieldElement other)
+        {
+            return Equals(other as SecP224K1FieldElement);
+        }
+
+        public virtual bool Equals(SecP224K1FieldElement other)
+        {
+            if (this == other)
+                return true;
+            if (null == other)
+                return false;
+            return Arrays.AreEqual(x, other.x);
+        }
+
+        public override int GetHashCode()
+        {
+            return Q.GetHashCode() ^ Arrays.GetHashCode(x);
+        }
+    }
+}
diff --git a/crypto/src/math/ec/custom/sec/SecP224K1Point.cs b/crypto/src/math/ec/custom/sec/SecP224K1Point.cs
new file mode 100644
index 000000000..f85c64981
--- /dev/null
+++ b/crypto/src/math/ec/custom/sec/SecP224K1Point.cs
@@ -0,0 +1,276 @@
+using System;
+
+namespace Org.BouncyCastle.Math.EC.Custom.Sec
+{
+    internal class SecP224K1Point
+        : ECPointBase
+    {
+        /**
+         * 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 SecP224K1Point(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 SecP224K1Point(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 SecP224K1Point(ECCurve curve, ECFieldElement x, ECFieldElement y, ECFieldElement[] zs,
+            bool withCompression)
+            : base(curve, x, y, zs, withCompression)
+        {
+        }
+
+        protected override ECPoint Detach()
+        {
+            return new SecP224K1Point(null, AffineXCoord, AffineYCoord);
+        }
+
+        protected internal override bool CompressionYTilde
+        {
+            get { return this.AffineYCoord.TestBitZero(); }
+        }
+
+        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;
+
+            SecP224K1FieldElement X1 = (SecP224K1FieldElement)this.RawXCoord, Y1 = (SecP224K1FieldElement)this.RawYCoord;
+            SecP224K1FieldElement X2 = (SecP224K1FieldElement)b.RawXCoord, Y2 = (SecP224K1FieldElement)b.RawYCoord;
+
+            SecP224K1FieldElement Z1 = (SecP224K1FieldElement)this.RawZCoords[0];
+            SecP224K1FieldElement Z2 = (SecP224K1FieldElement)b.RawZCoords[0];
+
+            uint[] tt1 = Nat224.CreateExt();
+            uint[] tt2 = Nat224.CreateExt();
+            uint[] t3 = Nat224.Create();
+            uint[] t4 = Nat224.Create();
+
+            bool Z1IsOne = Z1.IsOne;
+            uint[] U2, S2;
+            if (Z1IsOne)
+            {
+                U2 = X2.x;
+                S2 = Y2.x;
+            }
+            else
+            {
+                S2 = t3;
+                SecP224K1Field.Square(Z1.x, S2);
+
+                U2 = tt2;
+                SecP224K1Field.Multiply(S2, X2.x, U2);
+
+                SecP224K1Field.Multiply(S2, Z1.x, S2);
+                SecP224K1Field.Multiply(S2, Y2.x, S2);
+            }
+
+            bool Z2IsOne = Z2.IsOne;
+            uint[] U1, S1;
+            if (Z2IsOne)
+            {
+                U1 = X1.x;
+                S1 = Y1.x;
+            }
+            else
+            {
+                S1 = t4;
+                SecP224K1Field.Square(Z2.x, S1);
+
+                U1 = tt1;
+                SecP224K1Field.Multiply(S1, X1.x, U1);
+
+                SecP224K1Field.Multiply(S1, Z2.x, S1);
+                SecP224K1Field.Multiply(S1, Y1.x, S1);
+            }
+
+            uint[] H = Nat224.Create();
+            SecP224K1Field.Subtract(U1, U2, H);
+
+            uint[] R = tt2;
+            SecP224K1Field.Subtract(S1, S2, R);
+
+            // Check if b == this or b == -this
+            if (Nat224.IsZero(H))
+            {
+                if (Nat224.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;
+            SecP224K1Field.Square(H, HSquared);
+
+            uint[] G = Nat224.Create();
+            SecP224K1Field.Multiply(HSquared, H, G);
+
+            uint[] V = t3;
+            SecP224K1Field.Multiply(HSquared, U1, V);
+
+            Nat224.Mul(S1, G, tt1);
+
+            SecP224K1FieldElement X3 = new SecP224K1FieldElement(t4);
+            SecP224K1Field.Square(R, X3.x);
+            SecP224K1Field.Add(X3.x, G, X3.x);
+            SecP224K1Field.Subtract(X3.x, V, X3.x);
+            SecP224K1Field.Subtract(X3.x, V, X3.x);
+
+            SecP224K1FieldElement Y3 = new SecP224K1FieldElement(G);
+            SecP224K1Field.Subtract(V, X3.x, Y3.x);
+            Nat224.Mul(Y3.x, R, tt2);
+            SecP224K1Field.SubtractExt(tt2, tt1, tt2);
+            SecP224K1Field.Reduce(tt2, Y3.x);
+
+            SecP224K1FieldElement Z3 = new SecP224K1FieldElement(H);
+            if (!Z1IsOne)
+            {
+                SecP224K1Field.Multiply(Z3.x, Z1.x, Z3.x);
+            }
+            if (!Z2IsOne)
+            {
+                SecP224K1Field.Multiply(Z3.x, Z2.x, Z3.x);
+            }
+
+            ECFieldElement[] zs = new ECFieldElement[] { Z3 };
+
+            return new SecP224K1Point(curve, X3, Y3, zs, IsCompressed);
+        }
+
+        public override ECPoint Twice()
+        {
+            if (this.IsInfinity)
+                return this;
+
+            ECCurve curve = this.Curve;
+
+            SecP224K1FieldElement Y1 = (SecP224K1FieldElement)this.RawYCoord;
+            if (Y1.IsZero)
+                return curve.Infinity;
+
+            SecP224K1FieldElement X1 = (SecP224K1FieldElement)this.RawXCoord, Z1 = (SecP224K1FieldElement)this.RawZCoords[0];
+
+            uint[] Y1Squared = Nat224.Create();
+            SecP224K1Field.Square(Y1.x, Y1Squared);
+
+            uint[] T = Nat224.Create();
+            SecP224K1Field.Square(Y1Squared, T);
+
+            uint[] t1 = Nat224.Create();
+            SecP224K1Field.Square(X1.x, t1);
+
+            uint[] M = Nat224.Create();
+            SecP224K1Field.Twice(t1, M);
+            SecP224K1Field.Add(M, t1, M);
+
+            uint[] S = Y1Squared;
+            SecP224K1Field.Multiply(Y1Squared, X1.x, S);
+            SecP224K1Field.Twice(S, S);
+            SecP224K1Field.Twice(S, S);
+
+            SecP224K1Field.Twice(T, t1);
+            SecP224K1Field.Twice(t1, t1);
+            SecP224K1Field.Twice(t1, t1);
+
+            SecP224K1FieldElement X3 = new SecP224K1FieldElement(T);
+            SecP224K1Field.Square(M, X3.x);
+            SecP224K1Field.Subtract(X3.x, S, X3.x);
+            SecP224K1Field.Subtract(X3.x, S, X3.x);
+
+            SecP224K1FieldElement Y3 = new SecP224K1FieldElement(S);
+            SecP224K1Field.Subtract(S, X3.x, Y3.x);
+            SecP224K1Field.Multiply(Y3.x, M, Y3.x);
+            SecP224K1Field.Subtract(Y3.x, t1, Y3.x);
+
+            SecP224K1FieldElement Z3 = new SecP224K1FieldElement(M);
+            SecP224K1Field.Twice(Y1.x, Z3.x);
+            if (!Z1.IsOne)
+            {
+                SecP224K1Field.Multiply(Z3.x, Z1.x, Z3.x);
+            }
+
+            return new SecP224K1Point(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 Subtract(ECPoint b)
+        {
+            if (b.IsInfinity)
+                return this;
+
+            return Add(b.Negate());
+        }
+
+        public override ECPoint Negate()
+        {
+            if (IsInfinity)
+                return this;
+
+            return new SecP224K1Point(Curve, RawXCoord, RawYCoord.Negate(), RawZCoords, IsCompressed);
+        }
+    }
+}