Port custom curve for secp256r1 from Java

6 files changed, 758 insertions, 1 deletions

diff --git a/crypto/crypto.csproj b/crypto/crypto.csproj
index 0d4ca0e30..e89330bc2 100644
--- a/crypto/crypto.csproj
+++ b/crypto/crypto.csproj
@@ -4704,6 +4704,26 @@
                     BuildAction = "Compile"
                 />
                 <File
+                    RelPath = "src\math\ec\custom\sec\SecP256R1Curve.cs"
+                    SubType = "Code"
+                    BuildAction = "Compile"
+                />
+                <File
+                    RelPath = "src\math\ec\custom\sec\SecP256R1Field.cs"
+                    SubType = "Code"
+                    BuildAction = "Compile"
+                />
+                <File
+                    RelPath = "src\math\ec\custom\sec\SecP256R1FieldElement.cs"
+                    SubType = "Code"
+                    BuildAction = "Compile"
+                />
+                <File
+                    RelPath = "src\math\ec\custom\sec\SecP256R1Point.cs"
+                    SubType = "Code"
+                    BuildAction = "Compile"
+                />
+                <File
                     RelPath = "src\math\ec\multiplier\ECMultiplier.cs"
                     SubType = "Code"
                     BuildAction = "Compile"
diff --git a/crypto/src/crypto/ec/CustomNamedCurves.cs b/crypto/src/crypto/ec/CustomNamedCurves.cs
index 16badbe97..3cc9fe342 100644
--- a/crypto/src/crypto/ec/CustomNamedCurves.cs
+++ b/crypto/src/crypto/ec/CustomNamedCurves.cs
@@ -46,13 +46,37 @@ namespace Org.BouncyCastle.Crypto.EC
                 ECPoint G = curve.DecodePoint(Hex.Decode("04"
                     + "79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798"
                     + "483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8"));
-                //return new X9ECParameters(curve, G, curve.getOrder(), curve.getCofactor(), S);
+                //return new X9ECParameters(curve, G, curve.Order, curve.Cofactor, S);
                 BigInteger n = FromHex("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141");
                 BigInteger h = BigInteger.ValueOf(1);
                 return new X9ECParameters(curve, G, n, h, S);
             }
         }
 
+        /*
+         * secp256r1
+         */
+        internal class Secp256r1Holder
+            : X9ECParametersHolder
+        {
+            private Secp256r1Holder() {}
+
+            internal static readonly X9ECParametersHolder Instance = new Secp256r1Holder();
+
+            protected override X9ECParameters CreateParameters()
+            {
+                byte[] S = Hex.Decode("C49D360886E704936A6678E1139D26B7819F7E90");
+                ECCurve curve = ConfigureCurve(new SecP256R1Curve());
+                ECPoint G = curve.DecodePoint(Hex.Decode("04"
+                    + "6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296"
+                    + "4FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5"));
+                //return new X9ECParameters(curve, G, curve.Order, curve.Cofactor, S);
+                BigInteger n = FromHex("FFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E84F3B9CAC2FC632551");
+                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();
@@ -67,6 +91,9 @@ namespace Org.BouncyCastle.Crypto.EC
         static CustomNamedCurves()
         {
             DefineCurve("secp256k1", SecObjectIdentifiers.SecP256k1, Secp256k1Holder.Instance);
+            DefineCurve("secp256r1", SecObjectIdentifiers.SecP256r1, Secp256r1Holder.Instance);
+
+            objIds.Add(Platform.ToLowerInvariant("P-256"), SecObjectIdentifiers.SecP256r1);
         }
 
         public static X9ECParameters GetByName(string name)
diff --git a/crypto/src/math/ec/custom/sec/SecP256R1Curve.cs b/crypto/src/math/ec/custom/sec/SecP256R1Curve.cs
new file mode 100644
index 000000000..252ec345f
--- /dev/null
+++ b/crypto/src/math/ec/custom/sec/SecP256R1Curve.cs
@@ -0,0 +1,95 @@
+using System;
+
+using Org.BouncyCastle.Math.Field;
+using Org.BouncyCastle.Utilities.Encoders;
+
+namespace Org.BouncyCastle.Math.EC.Custom.Sec
+{
+    internal class SecP256R1Curve
+        : ECCurve
+    {
+        public static readonly BigInteger q = new BigInteger(1,
+            Hex.Decode("FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF"));
+
+        private const int SecP256R1_DEFAULT_COORDS = COORD_JACOBIAN;
+
+        protected readonly SecP256R1Point m_infinity;
+
+        public SecP256R1Curve()
+            : base(FiniteFields.GetPrimeField(q))
+        {
+            this.m_infinity = new SecP256R1Point(this, null, null);
+
+            this.m_a = FromBigInteger(new BigInteger(1,
+                Hex.Decode("FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFC")));
+            this.m_b = FromBigInteger(new BigInteger(1,
+                Hex.Decode("5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B")));
+            //this.order = new BigInteger(1, Hex.decode("FFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E84F3B9CAC2FC632551"));
+            //this.cofactor = BigInteger.valueOf(1);
+            this.m_coord = SecP256R1_DEFAULT_COORDS;
+        }
+
+        protected override ECCurve CloneCurve()
+        {
+            return new SecP256R1Curve();
+        }
+
+        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 SecP256R1FieldElement(x);
+        }
+
+        protected internal override ECPoint CreateRawPoint(ECFieldElement x, ECFieldElement y, bool withCompression)
+        {
+            return new SecP256R1Point(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 SecP256R1Point(this, x, beta, true);
+        }
+    }
+}
diff --git a/crypto/src/math/ec/custom/sec/SecP256R1Field.cs b/crypto/src/math/ec/custom/sec/SecP256R1Field.cs
new file mode 100644
index 000000000..baea02dd0
--- /dev/null
+++ b/crypto/src/math/ec/custom/sec/SecP256R1Field.cs
@@ -0,0 +1,175 @@
+using System;
+using System.Diagnostics;
+
+namespace Org.BouncyCastle.Math.EC.Custom.Sec
+{
+    internal class SecP256R1Field
+    {
+        // 2^256 - 2^224 + 2^192 + 2^96 - 1
+        internal static readonly uint[] P = new uint[]{ 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0x00000000, 0x00000000, 0x00000000,
+            0x00000001, 0xFFFFFFFF };
+        private const uint P7 = 0xFFFFFFFF;
+        private static readonly uint[] PExt = new uint[]{ 0x00000001, 0x00000000, 0x00000000, 0xFFFFFFFE, 0xFFFFFFFF,
+            0xFFFFFFFF, 0xFFFFFFFE, 0x00000001, 0xFFFFFFFE, 0x00000001, 0xFFFFFFFE, 0x00000001, 0x00000001, 0xFFFFFFFE,
+            0x00000002, 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)))
+            {
+                Nat256.Sub(z, P, z);
+            }
+        }
+
+        public static void AddExt(uint[] xx, uint[] yy, uint[] zz)
+        {
+            uint c = Nat256.AddExt(xx, yy, zz);
+            if (c != 0 || 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.Sub(z, P, z);
+            }
+        }
+
+        public static uint[] FromBigInteger(BigInteger x)
+        {
+            uint[] z = Nat256.FromBigInteger(x);
+            if (z[7] == P7 && Nat256.Gte(z, P))
+            {
+                Nat256.Sub(z, P, z);
+            }
+            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 t08 = tt[8], t09 = tt[9], t10 = tt[10], t11 = tt[11];
+            long t12 = tt[12], t13 = tt[13], t14 = tt[14], t15 = tt[15];
+
+            long cc = 0;
+            cc += (long)tt[0] + t08 + t09 - t11 - t12 - t13 - t14;
+            z[0] = (uint)cc;
+            cc >>= 32;
+            cc += (long)tt[1] + t09 + t10 - t12 - t13 - t14 - t15;
+            z[1] = (uint)cc;
+            cc >>= 32;
+            cc += (long)tt[2] + t10 + t11 - t13 - t14 - t15;
+            z[2] = (uint)cc;
+            cc >>= 32;
+            cc += (long)tt[3] + ((t11 + t12) << 1) + t13 - t15 - t08 - t09;
+            z[3] = (uint)cc;
+            cc >>= 32;
+            cc += (long)tt[4] + ((t12 + t13) << 1) + t14 - t09 - t10;
+            z[4] = (uint)cc;
+            cc >>= 32;
+            cc += (long)tt[5] + ((t13 + t14) << 1) + t15 - t10 - t11;
+            z[5] = (uint)cc;
+            cc >>= 32;
+            cc += (long)tt[6] + ((t14 + t15) << 1) + t14 + t13 - t08 - t09;
+            z[6] = (uint)cc;
+            cc >>= 32;
+            cc += (long)tt[7] + (t15 << 1) + t15 + t08 - t10 - t11 - t12 - t13;
+            z[7] = (uint)cc;
+            cc >>= 32;
+
+            int c = (int)cc;
+            if (c > 0)
+            {
+                do
+                {
+                    c += Nat256.Sub(z, P, z);
+                }
+                while (c != 0);
+
+                if (z[7] == P7 && Nat256.Gte(z, P))
+                {
+                    Nat256.Sub(z, P, z);
+                }
+            }
+            else if (c < 0)
+            {
+                do
+                {
+                    c += (int)Nat256.Add(z, P, z);
+                }
+                while (c != 0);
+            }
+        }
+
+        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.Add(z, P, 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.Sub(z, P, z);
+            }
+        }
+    }
+}
diff --git a/crypto/src/math/ec/custom/sec/SecP256R1FieldElement.cs b/crypto/src/math/ec/custom/sec/SecP256R1FieldElement.cs
new file mode 100644
index 000000000..edb4754ba
--- /dev/null
+++ b/crypto/src/math/ec/custom/sec/SecP256R1FieldElement.cs
@@ -0,0 +1,157 @@
+using System;
+using System.Diagnostics;
+
+using Org.BouncyCastle.Utilities;
+
+namespace Org.BouncyCastle.Math.EC.Custom.Sec
+{
+    public class SecP256R1FieldElement
+        : ECFieldElement
+    {
+        public static readonly BigInteger Q = SecP256R1Curve.q;
+
+        protected internal readonly uint[] x;
+
+        public SecP256R1FieldElement(BigInteger x)
+        {
+            if (x == null || x.SignValue < 0 || x.CompareTo(Q) >= 0)
+                throw new ArgumentException("value invalid for SecP256R1FieldElement", "x");
+
+            this.x = SecP256R1Field.FromBigInteger(x);
+        }
+
+        public SecP256R1FieldElement()
+        {
+            this.x = Nat256.Create();
+        }
+
+        protected internal SecP256R1FieldElement(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 "SecP256R1Field"; }
+        }
+
+        public override int FieldSize
+        {
+            get { return Q.BitLength; }
+        }
+
+        public override ECFieldElement Add(ECFieldElement b)
+        {
+            uint[] z = Nat256.Create();
+            SecP256R1Field.Add(x, ((SecP256R1FieldElement)b).x, z);
+            return new SecP256R1FieldElement(z);
+        }
+
+        public override ECFieldElement AddOne()
+        {
+            uint[] z = Nat256.Create();
+            SecP256R1Field.AddOne(x, z);
+            return new SecP256R1FieldElement(z);
+        }
+
+        public override ECFieldElement Subtract(ECFieldElement b)
+        {
+            uint[] z = Nat256.Create();
+            SecP256R1Field.Subtract(x, ((SecP256R1FieldElement)b).x, z);
+            return new SecP256R1FieldElement(z);
+        }
+
+        public override ECFieldElement Multiply(ECFieldElement b)
+        {
+            uint[] z = Nat256.Create();
+            SecP256R1Field.Multiply(x, ((SecP256R1FieldElement)b).x, z);
+            return new SecP256R1FieldElement(z);
+        }
+
+        public override ECFieldElement Divide(ECFieldElement b)
+        {
+            //return Multiply(b.Invert());
+            uint[] z = Nat256.Create();
+            Mod.Invert(SecP256R1Field.P, ((SecP256R1FieldElement)b).x, z);
+            SecP256R1Field.Multiply(z, x, z);
+            return new SecP256R1FieldElement(z);
+        }
+
+        public override ECFieldElement Negate()
+        {
+            uint[] z = Nat256.Create();
+            SecP256R1Field.Negate(x, z);
+            return new SecP256R1FieldElement(z);
+        }
+
+        public override ECFieldElement Square()
+        {
+            uint[] z = Nat256.Create();
+            SecP256R1Field.Square(x, z);
+            return new SecP256R1FieldElement(z);
+        }
+
+        public override ECFieldElement Invert()
+        {
+            //return new SecP256R1FieldElement(ToBigInteger().ModInverse(Q));
+            uint[] z = Nat256.Create();
+            Mod.Invert(SecP256R1Field.P, x, z);
+            return new SecP256R1FieldElement(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 SecP256R1FieldElement(root.ToBigInteger());
+        }
+
+        public override bool Equals(object obj)
+        {
+            return Equals(obj as SecP256R1FieldElement);
+        }
+
+        public override bool Equals(ECFieldElement other)
+        {
+            return Equals(other as SecP256R1FieldElement);
+        }
+
+        public virtual bool Equals(SecP256R1FieldElement 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/SecP256R1Point.cs b/crypto/src/math/ec/custom/sec/SecP256R1Point.cs
new file mode 100644
index 000000000..11e79678f
--- /dev/null
+++ b/crypto/src/math/ec/custom/sec/SecP256R1Point.cs
@@ -0,0 +1,283 @@
+using System;
+
+namespace Org.BouncyCastle.Math.EC.Custom.Sec
+{
+    internal class SecP256R1Point
+        : 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 SecP256R1Point(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 SecP256R1Point(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 SecP256R1Point(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(); }
+        }
+
+        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;
+
+            SecP256R1FieldElement X1 = (SecP256R1FieldElement)this.RawXCoord, Y1 = (SecP256R1FieldElement)this.RawYCoord;
+            SecP256R1FieldElement X2 = (SecP256R1FieldElement)b.RawXCoord, Y2 = (SecP256R1FieldElement)b.RawYCoord;
+
+            SecP256R1FieldElement Z1 = (SecP256R1FieldElement)this.RawZCoords[0];
+            SecP256R1FieldElement Z2 = (SecP256R1FieldElement)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;
+                SecP256R1Field.Square(Z1.x, S2);
+
+                U2 = tt2;
+                SecP256R1Field.Multiply(S2, X2.x, U2);
+
+                SecP256R1Field.Multiply(S2, Z1.x, S2);
+                SecP256R1Field.Multiply(S2, Y2.x, S2);
+            }
+
+            bool Z2IsOne = Z2.IsOne;
+            uint[] U1, S1;
+            if (Z2IsOne)
+            {
+                U1 = X1.x;
+                S1 = Y1.x;
+            }
+            else
+            {
+                S1 = t4;
+                SecP256R1Field.Square(Z2.x, S1);
+
+                U1 = tt1;
+                SecP256R1Field.Multiply(S1, X1.x, U1);
+
+                SecP256R1Field.Multiply(S1, Z2.x, S1);
+                SecP256R1Field.Multiply(S1, Y1.x, S1);
+            }
+
+            uint[] H = Nat256.Create();
+            SecP256R1Field.Subtract(U1, U2, H);
+
+            uint[] R = tt2;
+            SecP256R1Field.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;
+            SecP256R1Field.Square(H, HSquared);
+
+            uint[] G = Nat256.Create();
+            SecP256R1Field.Multiply(HSquared, H, G);
+
+            uint[] V = t3;
+            SecP256R1Field.Multiply(HSquared, U1, V);
+
+            Nat256.Mul(S1, G, tt1);
+
+            SecP256R1FieldElement X3 = new SecP256R1FieldElement(t4);
+            SecP256R1Field.Square(R, X3.x);
+            SecP256R1Field.Add(X3.x, G, X3.x);
+            SecP256R1Field.Subtract(X3.x, V, X3.x);
+            SecP256R1Field.Subtract(X3.x, V, X3.x);
+
+            SecP256R1FieldElement Y3 = new SecP256R1FieldElement(G);
+            SecP256R1Field.Subtract(V, X3.x, Y3.x);
+            Nat256.Mul(Y3.x, R, tt2);
+            SecP256R1Field.SubtractExt(tt2, tt1, tt2);
+            SecP256R1Field.Reduce(tt2, Y3.x);
+
+            SecP256R1FieldElement Z3 = new SecP256R1FieldElement(H);
+            if (!Z1IsOne)
+            {
+                SecP256R1Field.Multiply(Z3.x, Z1.x, Z3.x);
+            }
+            if (!Z2IsOne)
+            {
+                SecP256R1Field.Multiply(Z3.x, Z2.x, Z3.x);
+            }
+
+            ECFieldElement[] zs = new ECFieldElement[]{ Z3 };
+
+            return new SecP256R1Point(curve, X3, Y3, zs, IsCompressed);
+        }
+
+        public override ECPoint Twice()
+        {
+            if (this.IsInfinity)
+                return this;
+
+            ECCurve curve = this.Curve;
+
+            SecP256R1FieldElement Y1 = (SecP256R1FieldElement)this.RawYCoord;
+            if (Y1.IsZero)
+                return curve.Infinity;
+
+            SecP256R1FieldElement X1 = (SecP256R1FieldElement)this.RawXCoord, Z1 = (SecP256R1FieldElement)this.RawZCoords[0];
+
+            uint[] t1 = Nat256.Create();
+            uint[] t2 = Nat256.Create();
+
+            uint[] Y1Squared = Nat256.Create();
+            SecP256R1Field.Square(Y1.x, Y1Squared);
+
+            uint[] T = Nat256.Create();
+            SecP256R1Field.Square(Y1Squared, T);
+
+            bool Z1IsOne = Z1.IsOne;
+
+            uint[] Z1Squared = Z1.x;
+            if (!Z1IsOne)
+            {
+                Z1Squared = t2;
+                SecP256R1Field.Square(Z1.x, Z1Squared);
+            }
+
+            SecP256R1Field.Subtract(X1.x, Z1Squared, t1);
+
+            uint[] M = t2;
+            SecP256R1Field.Add(X1.x, Z1Squared, M);
+            SecP256R1Field.Multiply(M, t1, M);
+            SecP256R1Field.Twice(M, t1);
+            SecP256R1Field.Add(M, t1, M);
+
+            uint[] S = Y1Squared;
+            SecP256R1Field.Multiply(Y1Squared, X1.x, S);
+            SecP256R1Field.Twice(S, S);
+            SecP256R1Field.Twice(S, S);
+
+            SecP256R1Field.Twice(T, t1);
+            SecP256R1Field.Twice(t1, t1);
+            SecP256R1Field.Twice(t1, t1);
+
+            SecP256R1FieldElement X3 = new SecP256R1FieldElement(T);
+            SecP256R1Field.Square(M, X3.x);
+            SecP256R1Field.Subtract(X3.x, S, X3.x);
+            SecP256R1Field.Subtract(X3.x, S, X3.x);
+
+            SecP256R1FieldElement Y3 = new SecP256R1FieldElement(S);
+            SecP256R1Field.Subtract(S, X3.x, Y3.x);
+            SecP256R1Field.Multiply(Y3.x, M, Y3.x);
+            SecP256R1Field.Subtract(Y3.x, t1, Y3.x);
+
+            SecP256R1FieldElement Z3 = new SecP256R1FieldElement(M);
+            SecP256R1Field.Twice(Y1.x, Z3.x);
+            if (!Z1IsOne)
+            {
+                SecP256R1Field.Multiply(Z3.x, Z1.x, Z3.x);
+            }
+
+            return new SecP256R1Point(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 SecP256R1Point(Curve, RawXCoord, RawYCoord.Negate(), RawZCoords, IsCompressed);
+        }
+    }
+}