Port custom curve for secp256k1 from Java

6 files changed, 1474 insertions, 15 deletions

diff --git a/crypto/src/crypto/ec/CustomNamedCurves.cs b/crypto/src/crypto/ec/CustomNamedCurves.cs
index ab609fdb9..16badbe97 100644
--- a/crypto/src/crypto/ec/CustomNamedCurves.cs
+++ b/crypto/src/crypto/ec/CustomNamedCurves.cs
@@ -2,10 +2,14 @@
 using System.Collections;
 
 using Org.BouncyCastle.Asn1;
+using Org.BouncyCastle.Asn1.Sec;
 using Org.BouncyCastle.Asn1.X9;
+using Org.BouncyCastle.Math;
 using Org.BouncyCastle.Math.EC;
+using Org.BouncyCastle.Math.EC.Custom.Sec;
 using Org.BouncyCastle.Utilities;
 using Org.BouncyCastle.Utilities.Collections;
+using Org.BouncyCastle.Utilities.Encoders;
 
 namespace Org.BouncyCastle.Crypto.EC
 {
@@ -15,19 +19,45 @@ namespace Org.BouncyCastle.Crypto.EC
         {
         }
 
+        private static BigInteger FromHex(string hex)
+        {
+            return new BigInteger(1, Hex.Decode(hex));
+        }
+
         private static ECCurve ConfigureCurve(ECCurve curve)
         {
             return curve;
         }
 
+        /*
+         * secp256k1
+         */
+        internal class Secp256k1Holder
+            : X9ECParametersHolder
+        {
+            private Secp256k1Holder() {}
+
+            internal static readonly X9ECParametersHolder Instance = new Secp256k1Holder();
+
+            protected override X9ECParameters CreateParameters()
+            {
+                byte[] S = null;
+                ECCurve curve = ConfigureCurve(new SecP256K1Curve());
+                ECPoint G = curve.DecodePoint(Hex.Decode("04"
+                    + "79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798"
+                    + "483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8"));
+                //return new X9ECParameters(curve, G, curve.getOrder(), curve.getCofactor(), S);
+                BigInteger n = FromHex("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141");
+                BigInteger h = BigInteger.ValueOf(1);
+                return new X9ECParameters(curve, G, n, h, S);
+            }
+        }
+
         private static readonly IDictionary objIds = Platform.CreateHashtable();
         private static readonly IDictionary curves = Platform.CreateHashtable();
         private static readonly IDictionary names = Platform.CreateHashtable();
 
-        private static void DefineCurve(
-            string					name,
-            DerObjectIdentifier		oid,
-            X9ECParametersHolder	holder)
+        private static void DefineCurve(string name, DerObjectIdentifier oid, X9ECParametersHolder holder)
         {
             objIds.Add(name, oid);
             names.Add(oid, name);
@@ -36,26 +66,23 @@ namespace Org.BouncyCastle.Crypto.EC
 
         static CustomNamedCurves()
         {
+            DefineCurve("secp256k1", SecObjectIdentifiers.SecP256k1, Secp256k1Holder.Instance);
         }
 
-        public static X9ECParameters GetByName(
-            string name)
+        public static X9ECParameters GetByName(string name)
         {
-            DerObjectIdentifier oid = (DerObjectIdentifier)
-                objIds[Platform.ToLowerInvariant(name)];
+            DerObjectIdentifier oid = (DerObjectIdentifier)objIds[Platform.ToLowerInvariant(name)];
 
             return oid == null ? null : GetByOid(oid);
         }
 
-
         /**
          * return the X9ECParameters object for the named curve represented by
          * the passed in object identifier. Null if the curve isn't present.
          *
          * @param oid an object identifier representing a named curve, if present.
          */
-        public static X9ECParameters GetByOid(
-            DerObjectIdentifier oid)
+        public static X9ECParameters GetByOid(DerObjectIdentifier oid)
         {
             X9ECParametersHolder holder = (X9ECParametersHolder)curves[oid];
 
@@ -68,8 +95,7 @@ namespace Org.BouncyCastle.Crypto.EC
          *
          * @return the object identifier associated with name, if present.
          */
-        public static DerObjectIdentifier GetOid(
-            string name)
+        public static DerObjectIdentifier GetOid(string name)
         {
             return (DerObjectIdentifier)objIds[Platform.ToLowerInvariant(name)];
         }
@@ -77,8 +103,7 @@ namespace Org.BouncyCastle.Crypto.EC
         /**
          * return the named curve name represented by the given object identifier.
          */
-        public static string GetName(
-            DerObjectIdentifier oid)
+        public static string GetName(DerObjectIdentifier oid)
         {
             return (string)names[oid];
         }
diff --git a/crypto/src/math/ec/custom/sec/Nat256.cs b/crypto/src/math/ec/custom/sec/Nat256.cs
new file mode 100644
index 000000000..a55e7bc0d
--- /dev/null
+++ b/crypto/src/math/ec/custom/sec/Nat256.cs
@@ -0,0 +1,767 @@
+using System;
+using System.Diagnostics;
+
+using Org.BouncyCastle.Crypto.Utilities;
+
+namespace Org.BouncyCastle.Math.EC.Custom.Sec
+{
+    internal abstract class Nat256
+    {
+        private const ulong M = 0xFFFFFFFFUL;
+
+        public static uint Add(uint[] x, uint[] y, uint[] z)
+        {
+            ulong c = 0;
+            c += (ulong)x[0] + y[0];
+            z[0] = (uint)c;
+            c >>= 32;
+            c += (ulong)x[1] + y[1];
+            z[1] = (uint)c;
+            c >>= 32;
+            c += (ulong)x[2] + y[2];
+            z[2] = (uint)c;
+            c >>= 32;
+            c += (ulong)x[3] + y[3];
+            z[3] = (uint)c;
+            c >>= 32;
+            c += (ulong)x[4] + y[4];
+            z[4] = (uint)c;
+            c >>= 32;
+            c += (ulong)x[5] + y[5];
+            z[5] = (uint)c;
+            c >>= 32;
+            c += (ulong)x[6] + y[6];
+            z[6] = (uint)c;
+            c >>= 32;
+            c += (ulong)x[7] + y[7];
+            z[7] = (uint)c;
+            c >>= 32;
+            return (uint)c;
+        }
+
+        public static uint AddBothTo(uint[] x, uint[] y, uint[] z)
+        {
+            ulong c = 0;
+            c += (ulong)x[0] + y[0] + z[0];
+            z[0] = (uint)c;
+            c >>= 32;
+            c += (ulong)x[1] + y[1] + z[1];
+            z[1] = (uint)c;
+            c >>= 32;
+            c += (ulong)x[2] + y[2] + z[2];
+            z[2] = (uint)c;
+            c >>= 32;
+            c += (ulong)x[3] + y[3] + z[3];
+            z[3] = (uint)c;
+            c >>= 32;
+            c += (ulong)x[4] + y[4] + z[4];
+            z[4] = (uint)c;
+            c >>= 32;
+            c += (ulong)x[5] + y[5] + z[5];
+            z[5] = (uint)c;
+            c >>= 32;
+            c += (ulong)x[6] + y[6] + z[6];
+            z[6] = (uint)c;
+            c >>= 32;
+            c += (ulong)x[7] + y[7] + z[7];
+            z[7] = (uint)c;
+            c >>= 32;
+            return (uint)c;
+        }
+
+        // TODO Re-write to allow full range for x?
+        public static uint AddDWord(ulong x, uint[] z, int zOff)
+        {
+            Debug.Assert(zOff < 6);
+            ulong c = x;
+            c += (ulong)z[zOff + 0];
+            z[zOff + 0] = (uint)c;
+            c >>= 32;
+            c += (ulong)z[zOff + 1];
+            z[zOff + 1] = (uint)c;
+            c >>= 32;
+            return c == 0 ? 0 : Inc(z, zOff + 2);
+        }
+
+        public static uint AddExt(uint[] xx, uint[] yy, uint[] zz)
+        {
+            ulong c = 0;
+            for (int i = 0; i < 16; ++i)
+            {
+                c += (ulong)xx[i] + yy[i];
+                zz[i] = (uint)c;
+                c >>= 32;
+            }
+            return (uint)c;
+        }
+
+        public static uint AddToExt(uint[] x, int xOff, uint[] zz, int zzOff)
+        {
+            Debug.Assert(zzOff <= 8);
+            ulong c = 0;
+            c += (ulong)x[xOff + 0] + zz[zzOff + 0];
+            zz[zzOff + 0] = (uint)c;
+            c >>= 32;
+            c += (ulong)x[xOff + 1] + zz[zzOff + 1];
+            zz[zzOff + 1] = (uint)c;
+            c >>= 32;
+            c += (ulong)x[xOff + 2] + zz[zzOff + 2];
+            zz[zzOff + 2] = (uint)c;
+            c >>= 32;
+            c += (ulong)x[xOff + 3] + zz[zzOff + 3];
+            zz[zzOff + 3] = (uint)c;
+            c >>= 32;
+            c += (ulong)x[xOff + 4] + zz[zzOff + 4];
+            zz[zzOff + 4] = (uint)c;
+            c >>= 32;
+            c += (ulong)x[xOff + 5] + zz[zzOff + 5];
+            zz[zzOff + 5] = (uint)c;
+            c >>= 32;
+            c += (ulong)x[xOff + 6] + zz[zzOff + 6];
+            zz[zzOff + 6] = (uint)c;
+            c >>= 32;
+            c += (ulong)x[xOff + 7] + zz[zzOff + 7];
+            zz[zzOff + 7] = (uint)c;
+            c >>= 32;
+            return (uint)c;
+        }
+
+        public static uint AddWordExt(uint x, uint[] zz, int zzOff)
+        {
+            Debug.Assert(zzOff < 15);
+            ulong c = (ulong)x + zz[zzOff + 0];
+            zz[zzOff + 0] = (uint)c;
+            c >>= 32;
+            return c == 0 ? 0 : IncExt(zz, zzOff + 1);
+        }
+
+        public static uint[] Create()
+        {
+            return new uint[8];
+        }
+
+        public static uint[] CreateExt()
+        {
+            return new uint[16];
+        }
+
+        public static int Dec(uint[] z, int zOff)
+        {
+            Debug.Assert(zOff < 8);
+            int i = zOff;
+            do
+            {
+                if (--z[i] != uint.MaxValue)
+                {
+                    return 0;
+                }
+            }
+            while (++i < 8);
+            return -1;
+        }
+
+        public static uint[] FromBigInteger(BigInteger x)
+        {
+            if (x.SignValue < 0 || x.BitLength > 256)
+                throw new ArgumentException();
+
+            uint[] z = Create();
+            int i = 0;
+            while (x.SignValue != 0)
+            {
+                z[i++] = (uint)x.IntValue;
+                x = x.ShiftRight(32);
+            }
+            return z;
+        }
+
+        public static uint GetBit(uint[] x, int bit)
+        {
+            if (bit == 0)
+            {
+                return x[0] & 1;
+            }
+            if ((bit & 255) != bit)
+            {
+                return 0;
+            }
+            int w = bit >> 5;
+            int b = bit & 31;
+            return (x[w] >> b) & 1;
+        }
+
+        public static bool Gte(uint[] x, uint[] y)
+        {
+            for (int i = 7; i >= 0; --i)
+            {
+                uint x_i = x[i], y_i = y[i];
+                if (x_i < y_i)
+                    return false;
+                if (x_i > y_i)
+                    return true;
+            }
+            return false;
+        }
+
+        public static bool GteExt(uint[] xx, uint[] yy)
+        {
+            for (int i = 15; i >= 0; --i)
+            {
+                uint xx_i = xx[i], yy_i = yy[i];
+                if (xx_i < yy_i)
+                    return false;
+                if (xx_i > yy_i)
+                    return true;
+            }
+            return false;
+        }
+
+        public static uint Inc(uint[] z, int zOff)
+        {
+            Debug.Assert(zOff < 8);
+            for (int i = zOff; i < 8; ++i)
+            {
+                if (++z[i] != 0)
+                {
+                    return 0;
+                }
+            }
+            return 1;
+        }
+
+        public static uint IncExt(uint[] zz, int zzOff)
+        {
+            Debug.Assert(zzOff < 16);
+            for (int i = zzOff; i < 16; ++i)
+            {
+                if (++zz[i] != 0)
+                {
+                    return 0;
+                }
+            }
+            return 1;
+        }
+
+        public static bool IsOne(uint[] x)
+        {
+            if (x[0] != 1)
+            {
+                return false;
+            }
+            for (int i = 1; i < 8; ++i)
+            {
+                if (x[i] != 0)
+                {
+                    return false;
+                }
+            }
+            return true;
+        }
+
+        public static bool IsZero(uint[] x)
+        {
+            for (int i = 0; i < 8; ++i)
+            {
+                if (x[i] != 0)
+                {
+                    return false;
+                }
+            }
+            return true;
+        }
+
+        public static bool IsZeroExt(uint[] xx)
+        {
+            for (int i = 0; i < 16; ++i)
+            {
+                if (xx[i] != 0)
+                {
+                    return false;
+                }
+            }
+            return true;
+        }
+
+        public static void Mul(uint[] x, uint[] y, uint[] zz)
+        {
+            ulong y_0 = y[0];
+            ulong y_1 = y[1];
+            ulong y_2 = y[2];
+            ulong y_3 = y[3];
+            ulong y_4 = y[4];
+            ulong y_5 = y[5];
+            ulong y_6 = y[6];
+            ulong y_7 = y[7];
+
+            {
+                ulong c = 0, x_0 = x[0];
+                c += x_0 * y_0;
+                zz[0] = (uint)c;
+                c >>= 32;
+                c += x_0 * y_1;
+                zz[1] = (uint)c;
+                c >>= 32;
+                c += x_0 * y_2;
+                zz[2] = (uint)c;
+                c >>= 32;
+                c += x_0 * y_3;
+                zz[3] = (uint)c;
+                c >>= 32;
+                c += x_0 * y_4;
+                zz[4] = (uint)c;
+                c >>= 32;
+                c += x_0 * y_5;
+                zz[5] = (uint)c;
+                c >>= 32;
+                c += x_0 * y_6;
+                zz[6] = (uint)c;
+                c >>= 32;
+                c += x_0 * y_7;
+                zz[7] = (uint)c;
+                c >>= 32;
+                zz[8] = (uint)c;
+            }
+
+            for (int i = 1; i < 8; ++i)
+            {
+                ulong c = 0, x_i = x[i];
+                c += x_i * y_0 + zz[i + 0];
+                zz[i + 0] = (uint)c;
+                c >>= 32;
+                c += x_i * y_1 + zz[i + 1];
+                zz[i + 1] = (uint)c;
+                c >>= 32;
+                c += x_i * y_2 + zz[i + 2];
+                zz[i + 2] = (uint)c;
+                c >>= 32;
+                c += x_i * y_3 + zz[i + 3];
+                zz[i + 3] = (uint)c;
+                c >>= 32;
+                c += x_i * y_4 + zz[i + 4];
+                zz[i + 4] = (uint)c;
+                c >>= 32;
+                c += x_i * y_5 + zz[i + 5];
+                zz[i + 5] = (uint)c;
+                c >>= 32;
+                c += x_i * y_6 + zz[i + 6];
+                zz[i + 6] = (uint)c;
+                c >>= 32;
+                c += x_i * y_7 + zz[i + 7];
+                zz[i + 7] = (uint)c;
+                c >>= 32;
+                zz[i + 8] = (uint)c;
+            }
+        }
+
+        public static uint MulWordAddExt(uint x, uint[] yy, int yyOff, uint[] zz, int zzOff)
+        {
+            Debug.Assert(yyOff <= 8);
+            Debug.Assert(zzOff <= 8);
+            ulong c = 0, xVal = x;
+            int i = 0;
+            do
+            {
+                c += xVal * yy[yyOff + i] + zz[zzOff + i];
+                zz[zzOff + i] = (uint)c;
+                c >>= 32;
+            }
+            while (++i < 8);
+            return (uint)c;
+        }
+
+        public static uint MulWordDwordAdd(uint x, ulong y, uint[] z, int zOff)
+        {
+            Debug.Assert(zOff < 5);
+            ulong c = 0, xVal = x;
+            c += xVal * y + z[zOff + 0];
+            z[zOff + 0] = (uint)c;
+            c >>= 32;
+            c += xVal * (y >> 32) + z[zOff + 1];
+            z[zOff + 1] = (uint)c;
+            c >>= 32;
+            c += z[zOff + 2];
+            z[zOff + 2] = (uint)c;
+            c >>= 32;
+            return c == 0 ? 0 : Inc(z, zOff + 3);
+        }
+
+        public static uint MulWordExt(uint x, uint[] y, uint[] zz, int zzOff)
+        {
+            Debug.Assert(zzOff <= 8);
+            ulong c = 0, xVal = x;
+            int i = 0;
+            do
+            {
+                c += xVal * y[i];
+                zz[zzOff + i] = (uint)c;
+                c >>= 32;
+            }
+            while (++i < 8);
+            return (uint)c;
+        }
+
+        public static uint ShiftDownBit(uint[] x, int xLen, uint c)
+        {
+            int i = xLen;
+            while (--i >= 0)
+            {
+                uint next = x[i];
+                x[i] = (next >> 1) | (c << 31);
+                c = next;
+            }
+            return c << 31;
+        }
+
+        public static uint ShiftDownBit(uint[] x, uint c, uint[] z)
+        {
+            int i = 8;
+            while (--i >= 0)
+            {
+                uint next = x[i];
+                z[i] = (next >> 1) | (c << 31);
+                c = next;
+            }
+            return c << 31;
+        }
+
+        public static uint ShiftDownBits(uint[] x, int xLen, int bits, uint c)
+        {
+            Debug.Assert(bits > 0 && bits < 32);
+            int i = xLen;
+            while (--i >= 0)
+            {
+                uint next = x[i];
+                x[i] = (next >> bits) | (c << -bits);
+                c = next;
+            }
+            return c << -bits;
+        }
+
+        public static uint ShiftDownWord(uint[] x, int xLen, uint c)
+        {
+            int i = xLen;
+            while (--i >= 0)
+            {
+                uint next = x[i];
+                x[i] = c;
+                c = next;
+            }
+            return c;
+        }
+
+        public static uint ShiftUpBit(uint[] x, int xLen, uint c)
+        {
+            for (int i = 0; i < xLen; ++i)
+            {
+                uint next = x[i];
+                x[i] = (next << 1) | (c >> 31);
+                c = next;
+            }
+            return c >> 31;
+        }
+
+        public static uint ShiftUpBit(uint[] x, uint c, uint[] z)
+        {
+            for (int i = 0; i < 8; ++i)
+            {
+                uint next = x[i];
+                z[i] = (next << 1) | (c >> 31);
+                c = next;
+            }
+            return c >> 31;
+        }
+
+        public static void Square(uint[] x, uint[] zz)
+        {
+            ulong x_0 = x[0];
+            ulong zz_1;
+
+            {
+                uint c = 0;
+                int i = 7, j = 16;
+                do
+                {
+                    ulong xVal = x[i--];
+                    ulong p = xVal * xVal;
+                    zz[--j] = (c << 31) | (uint)(p >> 33);
+                    zz[--j] = (uint)(p >> 1);
+                    c = (uint)p;
+                }
+                while (i > 0);
+
+                {
+                    ulong p = x_0 * x_0;
+                    zz_1 = (ulong)(c << 31) | (p >> 33);
+                    zz[0] = (uint)(p >> 1);
+                }
+            }
+
+            ulong x_1 = x[1];
+            ulong zz_2 = zz[2];
+
+            {
+                zz_1 += x_1 * x_0;
+                zz[1] = (uint)zz_1;
+                zz_2 += zz_1 >> 32;
+            }
+
+            ulong x_2 = x[2];
+            ulong zz_3 = zz[3];
+            ulong zz_4 = zz[4];
+            {
+                zz_2 += x_2 * x_0;
+                zz[2] = (uint)zz_2;
+                zz_3 += (zz_2 >> 32) + x_2 * x_1;
+                zz_4 += zz_3 >> 32;
+                zz_3 &= M;
+            }
+
+            ulong x_3 = x[3];
+            ulong zz_5 = zz[5];
+            ulong zz_6 = zz[6];
+            {
+                zz_3 += x_3 * x_0;
+                zz[3] = (uint)zz_3;
+                zz_4 += (zz_3 >> 32) + x_3 * x_1;
+                zz_5 += (zz_4 >> 32) + x_3 * x_2;
+                zz_4 &= M;
+                zz_6 += zz_5 >> 32;
+                zz_5 &= M;
+            }
+
+            ulong x_4 = x[4];
+            ulong zz_7 = zz[7];
+            ulong zz_8 = zz[8];
+            {
+                zz_4 += x_4 * x_0;
+                zz[4] = (uint)zz_4;
+                zz_5 += (zz_4 >> 32) + x_4 * x_1;
+                zz_6 += (zz_5 >> 32) + x_4 * x_2;
+                zz_5 &= M;
+                zz_7 += (zz_6 >> 32) + x_4 * x_3;
+                zz_6 &= M;
+                zz_8 += zz_7 >> 32;
+                zz_7 &= M;
+            }
+
+            ulong x_5 = x[5];
+            ulong zz_9 = zz[9];
+            ulong zz_10 = zz[10];
+            {
+                zz_5 += x_5 * x_0;
+                zz[5] = (uint)zz_5;
+                zz_6 += (zz_5 >> 32) + x_5 * x_1;
+                zz_7 += (zz_6 >> 32) + x_5 * x_2;
+                zz_6 &= M;
+                zz_8 += (zz_7 >> 32) + x_5 * x_3;
+                zz_7 &= M;
+                zz_9 += (zz_8 >> 32) + x_5 * x_4;
+                zz_8 &= M;
+                zz_10 += zz_9 >> 32;
+                zz_9 &= M;
+            }
+
+            ulong x_6 = x[6];
+            ulong zz_11 = zz[11];
+            ulong zz_12 = zz[12];
+            {
+                zz_6 += x_6 * x_0;
+                zz[6] = (uint)zz_6;
+                zz_7 += (zz_6 >> 32) + x_6 * x_1;
+                zz_8 += (zz_7 >> 32) + x_6 * x_2;
+                zz_7 &= M;
+                zz_9 += (zz_8 >> 32) + x_6 * x_3;
+                zz_8 &= M;
+                zz_10 += (zz_9 >> 32) + x_6 * x_4;
+                zz_9 &= M;
+                zz_11 += (zz_10 >> 32) + x_6 * x_5;
+                zz_10 &= M;
+                zz_12 += zz_11 >> 32;
+                zz_11 &= M;
+            }
+
+            ulong x_7 = x[7];
+            ulong zz_13 = zz[13];
+            ulong zz_14 = zz[14];
+            {
+                zz_7 += x_7 * x_0;
+                zz[7] = (uint)zz_7;
+                zz_8 += (zz_7 >> 32) + x_7 * x_1;
+                zz_9 += (zz_8 >> 32) + x_7 * x_2;
+                zz_10 += (zz_9 >> 32) + x_7 * x_3;
+                zz_11 += (zz_10 >> 32) + x_7 * x_4;
+                zz_12 += (zz_11 >> 32) + x_7 * x_5;
+                zz_13 += (zz_12 >> 32) + x_7 * x_6;
+                zz_14 += zz_13 >> 32;
+            }
+
+            zz[8] = (uint)zz_8;
+            zz[9] = (uint)zz_9;
+            zz[10] = (uint)zz_10;
+            zz[11] = (uint)zz_11;
+            zz[12] = (uint)zz_12;
+            zz[13] = (uint)zz_13;
+            zz[14] = (uint)zz_14;
+            zz[15] += (uint)(zz_14 >> 32);
+
+            ShiftUpBit(zz, 16, (uint)x_0 << 31);
+        }
+
+        public static uint SquareWordAddExt(uint[] x, int xPos, uint[] zz)
+        {
+            Debug.Assert(xPos > 0 && xPos < 8);
+            ulong c = 0, xVal = x[xPos];
+            int i = 0;
+            do
+            {
+                c += xVal * x[i] + zz[xPos + i];
+                zz[xPos + i] = (uint)c;
+                c >>= 32;
+            }
+            while (++i < xPos);
+            return (uint)c;
+        }
+
+        public static int Sub(uint[] x, uint[] y, uint[] z)
+        {
+            long c = 0;
+            c += (long)x[0] - y[0];
+            z[0] = (uint)c;
+            c >>= 32;
+            c += (long)x[1] - y[1];
+            z[1] = (uint)c;
+            c >>= 32;
+            c += (long)x[2] - y[2];
+            z[2] = (uint)c;
+            c >>= 32;
+            c += (long)x[3] - y[3];
+            z[3] = (uint)c;
+            c >>= 32;
+            c += (long)x[4] - y[4];
+            z[4] = (uint)c;
+            c >>= 32;
+            c += (long)x[5] - y[5];
+            z[5] = (uint)c;
+            c >>= 32;
+            c += (long)x[6] - y[6];
+            z[6] = (uint)c;
+            c >>= 32;
+            c += (long)x[7] - y[7];
+            z[7] = (uint)c;
+            c >>= 32;
+            return (int)c;
+        }
+
+        public static int SubBothFrom(uint[] x, uint[] y, uint[] z)
+        {
+            long c = 0;
+            c += (long)z[0] - x[0] - y[0];
+            z[0] = (uint)c;
+            c >>= 32;
+            c += (long)z[1] - x[1] - y[1];
+            z[1] = (uint)c;
+            c >>= 32;
+            c += (long)z[2] - x[2] - y[2];
+            z[2] = (uint)c;
+            c >>= 32;
+            c += (long)z[3] - x[3] - y[3];
+            z[3] = (uint)c;
+            c >>= 32;
+            c += (long)z[4] - x[4] - y[4];
+            z[4] = (uint)c;
+            c >>= 32;
+            c += (long)z[5] - x[5] - y[5];
+            z[5] = (uint)c;
+            c >>= 32;
+            c += (long)z[6] - x[6] - y[6];
+            z[6] = (uint)c;
+            c >>= 32;
+            c += (long)z[7] - x[7] - y[7];
+            z[7] = (uint)c;
+            c >>= 32;
+            return (int)c;
+        }
+
+        // TODO Re-write to allow full range for x?
+        public static int SubDWord(ulong x, uint[] z)
+        {
+            long c = -(long)x;
+            c += (long)z[0];
+            z[0] = (uint)c;
+            c >>= 32;
+            c += (long)z[1];
+            z[1] = (uint)c;
+            c >>= 32;
+            return c == 0 ? 0 : Dec(z, 2);
+        }
+
+        public static int SubExt(uint[] xx, uint[] yy, uint[] zz)
+        {
+            long c = 0;
+            for (int i = 0; i < 16; ++i)
+            {
+                c += (long)xx[i] - yy[i];
+                zz[i] = (uint)c;
+                c >>= 32;
+            }
+            return (int)c;
+        }
+
+        public static int SubFromExt(uint[] x, int xOff, uint[] zz, int zzOff)
+        {
+            Debug.Assert(zzOff <= 8);
+            long c = 0;
+            c += (long)zz[zzOff + 0] - x[xOff + 0];
+            zz[zzOff + 0] = (uint)c;
+            c >>= 32;
+            c += (long)zz[zzOff + 1] - x[xOff + 1];
+            zz[zzOff + 1] = (uint)c;
+            c >>= 32;
+            c += (long)zz[zzOff + 2] - x[xOff + 2];
+            zz[zzOff + 2] = (uint)c;
+            c >>= 32;
+            c += (long)zz[zzOff + 3] - x[xOff + 3];
+            zz[zzOff + 3] = (uint)c;
+            c >>= 32;
+            c += (long)zz[zzOff + 4] - x[xOff + 4];
+            zz[zzOff + 4] = (uint)c;
+            c >>= 32;
+            c += (long)zz[zzOff + 5] - x[xOff + 5];
+            zz[zzOff + 5] = (uint)c;
+            c >>= 32;
+            c += (long)zz[zzOff + 6] - x[xOff + 6];
+            zz[zzOff + 6] = (uint)c;
+            c >>= 32;
+            c += (long)zz[zzOff + 7] - x[xOff + 7];
+            zz[zzOff + 7] = (uint)c;
+            c >>= 32;
+            return (int)c;
+        }
+
+        public static BigInteger ToBigInteger(uint[] x)
+        {
+            byte[] bs = new byte[32];
+            for (int i = 0; i < 8; ++i)
+            {
+                uint x_i = x[i];
+                if (x_i != 0)
+                {
+                    Pack.UInt32_To_BE(x_i, bs, (7 - i) << 2);
+                }
+            }
+            return new BigInteger(1, bs);
+        }
+
+        public static void Zero(uint[] z)
+        {
+            z[0] = 0;
+            z[1] = 0;
+            z[2] = 0;
+            z[3] = 0;
+            z[4] = 0;
+            z[5] = 0;
+            z[6] = 0;
+            z[7] = 0;
+        }
+    }
+}
diff --git a/crypto/src/math/ec/custom/sec/SecP256K1Curve.cs b/crypto/src/math/ec/custom/sec/SecP256K1Curve.cs
new file mode 100644
index 000000000..2e0a4a5e4
--- /dev/null
+++ b/crypto/src/math/ec/custom/sec/SecP256K1Curve.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 SecP256K1Curve
+        : ECCurve
+    {
+        public static readonly BigInteger q = new BigInteger(1,
+            Hex.Decode("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F"));
+
+        private const int SECP256K1_DEFAULT_COORDS = COORD_JACOBIAN;
+
+        protected readonly SecP256K1Point m_infinity;
+
+        public SecP256K1Curve()
+            : base(FiniteFields.GetPrimeField(q))
+        {
+            this.m_infinity = new SecP256K1Point(this, null, null);
+
+            this.m_a = FromBigInteger(BigInteger.Zero);
+            this.m_b = FromBigInteger(BigInteger.ValueOf(7));
+            //this.order = new BigInteger(1, Hex.decode("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141"));
+            //this.cofactor = BigInteger.valueOf(1);
+            this.m_coord = SECP256K1_DEFAULT_COORDS;
+        }
+
+        protected override ECCurve CloneCurve()
+        {
+            return new SecP256K1Curve();
+        }
+
+        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 SecP256K1FieldElement(x);
+        }
+
+        protected internal override ECPoint CreateRawPoint(ECFieldElement x, ECFieldElement y, bool withCompression)
+        {
+            return new SecP256K1Point(this, x, y, withCompression);
+        }
+
+        protected override ECPoint DecompressPoint(int yTilde, BigInteger X1)
+        {
+            ECFieldElement x = FromBigInteger(X1);
+            ECFieldElement alpha = x.Square().Add(m_a).Multiply(x).Add(m_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 SecP256K1Point(this, x, beta, true);
+        }
+    }
+}
diff --git a/crypto/src/math/ec/custom/sec/SecP256K1Field.cs b/crypto/src/math/ec/custom/sec/SecP256K1Field.cs
new file mode 100644
index 000000000..ec2c36e9f
--- /dev/null
+++ b/crypto/src/math/ec/custom/sec/SecP256K1Field.cs
@@ -0,0 +1,142 @@
+using System;
+using System.Diagnostics;
+
+namespace Org.BouncyCastle.Math.EC.Custom.Sec
+{
+    internal class SecP256K1Field
+    {
+        // 2^256 - 2^32 - 2^9 - 2^8 - 2^7 - 2^6 - 2^4 - 1
+        internal static readonly uint[] P = new uint[]{ 0xFFFFFC2F, 0xFFFFFFFE, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF,
+            0xFFFFFFFF, 0xFFFFFFFF };
+        private const uint P7 = 0xFFFFFFFF;
+        private static readonly uint[] PExt = new uint[]{ 0x000E90A1, 0x000007A2, 0x00000001, 0x00000000, 0x00000000,
+            0x00000000, 0x00000000, 0x00000000, 0xFFFFF85E, 0xFFFFFFFD, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF,
+            0xFFFFFFFF, 0xFFFFFFFF };
+        private const uint PExt15 = 0xFFFFFFFF;
+        private static readonly ulong PInv = 0x00000001000003D1UL;
+
+        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)))
+            {
+                Nat256.AddDWord(PInv, z, 0);
+            }
+        }
+
+        public static void AddExt(uint[] xx, uint[] yy, uint[] zz)
+        {
+            uint c = Nat256.AddExt(xx, yy, zz);
+            if (c != 0 || (zz[15] == PExt15 && Nat256.GteExt(zz, PExt)))
+            {
+                Nat256.SubExt(zz, PExt, zz);
+            }
+        }
+
+        public static void AddOne(uint[] x, uint[] z)
+        {
+            Array.Copy(x, 0, z, 0, 8);
+            uint c = Nat256.Inc(z, 0);
+            if (c != 0 || (z[7] == P7 && Nat256.Gte(z, P)))
+            {
+                Nat256.AddDWord(PInv, z, 0);
+            }
+        }
+
+        public static uint[] FromBigInteger(BigInteger x)
+        {
+            uint[] z = Nat256.FromBigInteger(x);
+            if (z[7] == P7 && Nat256.Gte(z, P))
+            {
+                Nat256.AddDWord(PInv, z, 0);
+            }
+            return z;
+        }
+
+        public static void Half(uint[] x, uint[] z)
+        {
+            if ((x[0] & 1) == 0)
+            {
+                Nat256.ShiftDownBit(x, 0, z);
+            }
+            else
+            {
+                uint c = Nat256.Add(x, P, z);
+                Nat256.ShiftDownBit(z, c, z);
+            }
+        }
+
+        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 Negate(uint[] x, uint[] z)
+        {
+            if (Nat256.IsZero(x))
+            {
+                Nat256.Zero(z);
+            }
+            else
+            {
+                Nat256.Sub(P, x, z);
+            }
+        }
+
+        public static void Reduce(uint[] tt, uint[] z)
+        {
+            long extra = -(long)tt[8];
+            extra += (long)Nat256.MulWordAddExt((uint)PInv, tt, 8, tt, 0);
+            extra += (long)Nat256.AddToExt(tt, 8, tt, 1) << 32;
+            extra += (long)tt[8];
+
+            ulong c = Nat256.MulWordDwordAdd((uint)PInv, (ulong)extra, tt, 0);
+            c += Nat256.AddDWord((ulong)extra, tt, 1);
+
+            Debug.Assert(c == 0 || c == 1);
+
+            if (c != 0 || (tt[7] == P7 && Nat256.Gte(tt, P)))
+            {
+                Nat256.AddDWord(PInv, tt, 0);
+            }
+
+            Array.Copy(tt, 0, z, 0, 8);
+        }
+
+        public static void Square(uint[] x, uint[] z)
+        {
+            uint[] tt = Nat256.CreateExt();
+            Nat256.Square(x, tt);
+            Reduce(tt, z);
+        }
+
+        public static void Subtract(uint[] x, uint[] y, uint[] z)
+        {
+            int c = Nat256.Sub(x, y, z);
+            if (c != 0)
+            {
+                Nat256.SubDWord(PInv, z);
+            }
+        }
+
+        public static void SubtractExt(uint[] xx, uint[] yy, uint[] zz)
+        {
+            int c = Nat256.SubExt(xx, yy, zz);
+            if (c != 0)
+            {
+                Nat256.AddExt(zz, PExt, zz);
+            }
+        }
+
+        public static void Twice(uint[] x, uint[] z)
+        {
+            uint c = Nat256.ShiftUpBit(x, 0, z);
+            if (c != 0 || (z[7] == P7 && Nat256.Gte(z, P)))
+            {
+                Nat256.AddDWord(PInv, z, 0);
+            }
+        }
+    }
+}
diff --git a/crypto/src/math/ec/custom/sec/SecP256K1FieldElement.cs b/crypto/src/math/ec/custom/sec/SecP256K1FieldElement.cs
new file mode 100644
index 000000000..4da1013d1
--- /dev/null
+++ b/crypto/src/math/ec/custom/sec/SecP256K1FieldElement.cs
@@ -0,0 +1,157 @@
+using System;
+using System.Diagnostics;
+
+using Org.BouncyCastle.Utilities;
+
+namespace Org.BouncyCastle.Math.EC.Custom.Sec
+{
+    internal class SecP256K1FieldElement
+        : ECFieldElement
+    {
+        public static readonly BigInteger Q = SecP256K1Curve.q;
+
+        protected internal readonly uint[] x;
+
+        public SecP256K1FieldElement(BigInteger x)
+        {
+            if (x == null || x.SignValue < 0 || x.CompareTo(Q) >= 0)
+                throw new ArgumentException("value invalid for SecP256K1FieldElement", "x");
+
+            this.x = SecP256K1Field.FromBigInteger(x);
+        }
+
+        public SecP256K1FieldElement()
+        {
+            this.x = Nat256.Create();
+        }
+
+        protected internal SecP256K1FieldElement(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 "SecP256K1Field"; }
+        }
+
+        public override int FieldSize
+        {
+            get { return Q.BitLength; }
+        }
+
+        public override ECFieldElement Add(ECFieldElement b)
+        {
+            uint[] z = Nat256.Create();
+            SecP256K1Field.Add(x, ((SecP256K1FieldElement)b).x, z);
+            return new SecP256K1FieldElement(z);
+        }
+
+        public override ECFieldElement AddOne()
+        {
+            uint[] z = Nat256.Create();
+            SecP256K1Field.AddOne(x, z);
+            return new SecP256K1FieldElement(z);
+        }
+
+        public override ECFieldElement Subtract(ECFieldElement b)
+        {
+            uint[] z = Nat256.Create();
+            SecP256K1Field.Subtract(x, ((SecP256K1FieldElement)b).x, z);
+            return new SecP256K1FieldElement(z);
+        }
+
+        public override ECFieldElement Multiply(ECFieldElement b)
+        {
+            uint[] z = Nat256.Create();
+            SecP256K1Field.Multiply(x, ((SecP256K1FieldElement)b).x, z);
+            return new SecP256K1FieldElement(z);
+        }
+
+        public override ECFieldElement Divide(ECFieldElement b)
+        {
+    //        return Multiply(b.Invert());
+            uint[] z = Nat256.Create();
+            Mod.Invert(SecP256K1Field.P, ((SecP256K1FieldElement)b).x, z);
+            SecP256K1Field.Multiply(z, x, z);
+            return new SecP256K1FieldElement(z);
+        }
+
+        public override ECFieldElement Negate()
+        {
+            uint[] z = Nat256.Create();
+            SecP256K1Field.Negate(x, z);
+            return new SecP256K1FieldElement(z);
+        }
+
+        public override ECFieldElement Square()
+        {
+            uint[] z = Nat256.Create();
+            SecP256K1Field.Square(x, z);
+            return new SecP256K1FieldElement(z);
+        }
+
+        public override ECFieldElement Invert()
+        {
+    //        return new SecP256K1FieldElement(ToBigInteger().ModInverse(Q));
+            uint[] z = Nat256.Create();
+            Mod.Invert(SecP256K1Field.P, x, z);
+            return new SecP256K1FieldElement(z);
+        }
+
+        // D.1.4 91
+        /**
+         * 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 SecP256K1FieldElement(root.ToBigInteger());
+        }
+
+        public override bool Equals(object obj)
+        {
+            return Equals(obj as SecP256K1FieldElement);
+        }
+
+        public override bool Equals(ECFieldElement other)
+        {
+            return Equals(other as SecP256K1FieldElement);
+        }
+
+        public virtual bool Equals(SecP256K1FieldElement 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/SecP256K1Point.cs b/crypto/src/math/ec/custom/sec/SecP256K1Point.cs
new file mode 100644
index 000000000..e2a22fbe7
--- /dev/null
+++ b/crypto/src/math/ec/custom/sec/SecP256K1Point.cs
@@ -0,0 +1,275 @@
+using System;
+
+namespace Org.BouncyCastle.Math.EC.Custom.Sec
+{
+    internal class SecP256K1Point
+        : 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 SecP256K1Point(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 SecP256K1Point(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 SecP256K1Point(ECCurve curve, ECFieldElement x, ECFieldElement y, ECFieldElement[] zs,
+            bool withCompression)
+            : base(curve, x, y, zs, withCompression)
+        {
+        }
+
+        protected internal override bool CompressionYTilde
+        {
+            get { return this.AffineYCoord.TestBitZero(); }
+        }
+
+        // B.3 pg 62
+        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;
+
+            SecP256K1FieldElement X1 = (SecP256K1FieldElement)this.RawXCoord, Y1 = (SecP256K1FieldElement)this.RawYCoord;
+            SecP256K1FieldElement X2 = (SecP256K1FieldElement)b.RawXCoord, Y2 = (SecP256K1FieldElement)b.RawYCoord;
+
+            SecP256K1FieldElement Z1 = (SecP256K1FieldElement)this.RawZCoords[0];
+            SecP256K1FieldElement Z2 = (SecP256K1FieldElement)b.RawZCoords[0];
+
+            uint[] tt1 = Nat256.CreateExt();
+            uint[] tt2 = Nat256.CreateExt();
+            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;
+                SecP256K1Field.Square(Z1.x, S2);
+
+                U2 = tt2;
+                SecP256K1Field.Multiply(S2, X2.x, U2);
+
+                SecP256K1Field.Multiply(S2, Z1.x, S2);
+                SecP256K1Field.Multiply(S2, Y2.x, S2);
+            }
+
+            bool Z2IsOne = Z2.IsOne;
+            uint[] U1, S1;
+            if (Z2IsOne)
+            {
+                U1 = X1.x;
+                S1 = Y1.x;
+            }
+            else
+            {
+                S1 = t4;
+                SecP256K1Field.Square(Z2.x, S1);
+
+                U1 = tt1;
+                SecP256K1Field.Multiply(S1, X1.x, U1);
+
+                SecP256K1Field.Multiply(S1, Z2.x, S1);
+                SecP256K1Field.Multiply(S1, Y1.x, S1);
+            }
+
+            uint[] H = Nat256.Create();
+            SecP256K1Field.Subtract(U1, U2, H);
+
+            uint[] R = tt2;
+            SecP256K1Field.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;
+            SecP256K1Field.Square(H, HSquared);
+
+            uint[] G = Nat256.Create();
+            SecP256K1Field.Multiply(HSquared, H, G);
+
+            uint[] V = t3;
+            SecP256K1Field.Multiply(HSquared, U1, V);
+
+            Nat256.Mul(S1, G, tt1);
+
+            SecP256K1FieldElement X3 = new SecP256K1FieldElement(t4);
+            SecP256K1Field.Square(R, X3.x);
+            SecP256K1Field.Add(X3.x, G, X3.x);
+            SecP256K1Field.Subtract(X3.x, V, X3.x);
+            SecP256K1Field.Subtract(X3.x, V, X3.x);
+
+            SecP256K1FieldElement Y3 = new SecP256K1FieldElement(G);
+            SecP256K1Field.Subtract(V, X3.x, Y3.x);
+            Nat256.Mul(Y3.x, R, tt2);
+            SecP256K1Field.SubtractExt(tt2, tt1, tt2);
+            SecP256K1Field.Reduce(tt2, Y3.x);
+
+            SecP256K1FieldElement Z3 = new SecP256K1FieldElement(H);
+            if (!Z1IsOne)
+            {
+                SecP256K1Field.Multiply(Z3.x, Z1.x, Z3.x);
+            }
+            if (!Z2IsOne)
+            {
+                SecP256K1Field.Multiply(Z3.x, Z2.x, Z3.x);
+            }
+
+            ECFieldElement[] zs = new ECFieldElement[] { Z3 };
+
+            return new SecP256K1Point(curve, X3, Y3, zs, IsCompressed);
+        }
+
+        // B.3 pg 62
+        public override ECPoint Twice()
+        {
+            if (this.IsInfinity)
+                return this;
+
+            ECCurve curve = this.Curve;
+
+            SecP256K1FieldElement Y1 = (SecP256K1FieldElement)this.RawYCoord;
+            if (Y1.IsZero)
+                return curve.Infinity;
+
+            SecP256K1FieldElement X1 = (SecP256K1FieldElement)this.RawXCoord, Z1 = (SecP256K1FieldElement)this.RawZCoords[0];
+
+            uint[] Y1Squared = Nat256.Create();
+            SecP256K1Field.Square(Y1.x, Y1Squared);
+
+            uint[] T = Nat256.Create();
+            SecP256K1Field.Square(Y1Squared, T);
+
+            uint[] t1 = Nat256.Create();
+            SecP256K1Field.Square(X1.x, t1);
+
+            uint[] M = Nat256.Create();
+            SecP256K1Field.Twice(t1, M);
+            SecP256K1Field.Add(M, t1, M);
+
+            uint[] S = Y1Squared;
+            SecP256K1Field.Multiply(Y1Squared, X1.x, S);
+            SecP256K1Field.Twice(S, S);
+            SecP256K1Field.Twice(S, S);
+
+            SecP256K1Field.Twice(T, t1);
+            SecP256K1Field.Twice(t1, t1);
+            SecP256K1Field.Twice(t1, t1);
+
+            SecP256K1FieldElement X3 = new SecP256K1FieldElement(T);
+            SecP256K1Field.Square(M, X3.x);
+            SecP256K1Field.Subtract(X3.x, S, X3.x);
+            SecP256K1Field.Subtract(X3.x, S, X3.x);
+
+            SecP256K1FieldElement Y3 = new SecP256K1FieldElement(S);
+            SecP256K1Field.Subtract(S, X3.x, Y3.x);
+            SecP256K1Field.Multiply(Y3.x, M, Y3.x);
+            SecP256K1Field.Subtract(Y3.x, t1, Y3.x);
+
+            SecP256K1FieldElement Z3 = new SecP256K1FieldElement(M);
+            SecP256K1Field.Twice(Y1.x, Z3.x);
+            if (!Z1.IsOne)
+            {
+                SecP256K1Field.Multiply(Z3.x, Z1.x, Z3.x);
+            }
+
+            return new SecP256K1Point(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);
+        }
+
+        // D.3.2 pg 102 (see Note:)
+        public override ECPoint Subtract(ECPoint b)
+        {
+            if (b.IsInfinity)
+                return this;
+
+            // Add -b
+            return Add(b.Negate());
+        }
+
+        public override ECPoint Negate()
+        {
+            if (IsInfinity)
+                return this;
+
+            return new SecP256K1Point(Curve, RawXCoord, RawYCoord.Negate(), RawZCoords, IsCompressed);
+        }
+    }
+}