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Assets/BestHTTP/SecureProtocol/math/ec/custom/djb/Curve25519.cs

@@ -0,0 +1,81 @@
+#if !BESTHTTP_DISABLE_ALTERNATE_SSL && (!UNITY_WEBGL || UNITY_EDITOR)
+
+using System;
+
+using Org.BouncyCastle.Math.Raw;
+using Org.BouncyCastle.Utilities.Encoders;
+
+namespace Org.BouncyCastle.Math.EC.Custom.Djb
+{
+    internal class Curve25519
+        : AbstractFpCurve
+    {
+        public static readonly BigInteger q = Nat256.ToBigInteger(Curve25519Field.P);
+
+        private const int Curve25519_DEFAULT_COORDS = COORD_JACOBIAN_MODIFIED;
+
+        protected readonly Curve25519Point m_infinity;
+
+        public Curve25519()
+            : base(q)
+        {
+            this.m_infinity = new Curve25519Point(this, null, null);
+
+            this.m_a = FromBigInteger(new BigInteger(1,
+                Hex.Decode("2AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA984914A144")));
+            this.m_b = FromBigInteger(new BigInteger(1,
+                Hex.Decode("7B425ED097B425ED097B425ED097B425ED097B425ED097B4260B5E9C7710C864")));
+            this.m_order = new BigInteger(1, Hex.Decode("1000000000000000000000000000000014DEF9DEA2F79CD65812631A5CF5D3ED"));
+            this.m_cofactor = BigInteger.ValueOf(8);
+            this.m_coord = Curve25519_DEFAULT_COORDS;
+        }
+
+        protected override ECCurve CloneCurve()
+        {
+            return new Curve25519();
+        }
+
+        public override bool SupportsCoordinateSystem(int coord)
+        {
+            switch (coord)
+            {
+            case COORD_JACOBIAN_MODIFIED:
+                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 Curve25519FieldElement(x);
+        }
+
+        protected internal override ECPoint CreateRawPoint(ECFieldElement x, ECFieldElement y, bool withCompression)
+        {
+            return new Curve25519Point(this, x, y, withCompression);
+        }
+
+        protected internal override ECPoint CreateRawPoint(ECFieldElement x, ECFieldElement y, ECFieldElement[] zs, bool withCompression)
+        {
+            return new Curve25519Point(this, x, y, zs, withCompression);
+        }
+    }
+}
+
+#endif

Assets/BestHTTP/SecureProtocol/math/ec/custom/djb/Curve25519.cs.meta

@@ -0,0 +1,11 @@
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+  defaultReferences: []
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+  assetBundleName: 
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Assets/BestHTTP/SecureProtocol/math/ec/custom/djb/Curve25519Field.cs

@@ -0,0 +1,257 @@
+#if !BESTHTTP_DISABLE_ALTERNATE_SSL && (!UNITY_WEBGL || UNITY_EDITOR)
+
+using System;
+using System.Diagnostics;
+
+using Org.BouncyCastle.Math.Raw;
+
+namespace Org.BouncyCastle.Math.EC.Custom.Djb
+{
+    internal class Curve25519Field
+    {
+        // 2^255 - 2^4 - 2^1 - 1
+        internal static readonly uint[] P = new uint[]{ 0xFFFFFFED, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF,
+            0xFFFFFFFF, 0x7FFFFFFF };
+        private const uint P7 = 0x7FFFFFFF;
+        private static readonly uint[] PExt = new uint[]{ 0x00000169, 0x00000000, 0x00000000, 0x00000000, 0x00000000,
+            0x00000000, 0x00000000, 0x00000000, 0xFFFFFFED, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF,
+            0xFFFFFFFF, 0x3FFFFFFF };
+        private const uint PInv = 0x13;
+
+        public static void Add(uint[] x, uint[] y, uint[] z)
+        {
+            Nat256.Add(x, y, z);
+            if (Nat256.Gte(z, P))
+            {
+                SubPFrom(z);
+            }
+        }
+
+        public static void AddExt(uint[] xx, uint[] yy, uint[] zz)
+        {
+            Nat.Add(16, xx, yy, zz);
+            if (Nat.Gte(16, zz, PExt))
+            {
+                SubPExtFrom(zz);
+            }
+        }
+
+        public static void AddOne(uint[] x, uint[] z)
+        {
+            Nat.Inc(8, x, z);
+            if (Nat256.Gte(z, P))
+            {
+                SubPFrom(z);
+            }
+        }
+
+        public static uint[] FromBigInteger(BigInteger x)
+        {
+            uint[] z = Nat256.FromBigInteger(x);
+            while (Nat256.Gte(z, P))
+            {
+                Nat256.SubFrom(P, z);
+            }
+            return z;
+        }
+
+        public static void Half(uint[] x, uint[] z)
+        {
+            if ((x[0] & 1) == 0)
+            {
+                Nat.ShiftDownBit(8, x, 0, z);
+            }
+            else
+            {
+                Nat256.Add(x, P, z);
+                Nat.ShiftDownBit(8, z, 0);
+            }
+        }
+
+        public static void Multiply(uint[] x, uint[] y, uint[] z)
+        {
+            uint[] tt = Nat256.CreateExt();
+            Nat256.Mul(x, y, tt);
+            Reduce(tt, z);
+        }
+
+        public static void MultiplyAddToExt(uint[] x, uint[] y, uint[] zz)
+        {
+            Nat256.MulAddTo(x, y, zz);
+            if (Nat.Gte(16, zz, PExt))
+            {
+                SubPExtFrom(zz);
+            }
+        }
+
+        public static void Negate(uint[] x, uint[] z)
+        {
+            if (Nat256.IsZero(x))
+            {
+                Nat256.Zero(z);
+            }
+            else
+            {
+                Nat256.Sub(P, x, z);
+            }
+        }
+
+        public static void Reduce(uint[] xx, uint[] z)
+        {
+            Debug.Assert(xx[15] >> 30 == 0);
+
+            uint xx07 = xx[7];
+            Nat.ShiftUpBit(8, xx, 8, xx07, z, 0);
+            uint c = Nat256.MulByWordAddTo(PInv, xx, z) << 1;
+            uint z7 = z[7];
+            c += (z7 >> 31) - (xx07 >> 31);
+            z7 &= P7;
+            z7 += Nat.AddWordTo(7, c * PInv, z);
+            z[7] = z7;
+            if (z7 >= P7 && Nat256.Gte(z, P))
+            {
+                SubPFrom(z);
+            }
+        }
+
+        public static void Reduce27(uint x, uint[] z)
+        {
+            Debug.Assert(x >> 26 == 0);
+
+            uint z7 = z[7];
+            uint c = (x << 1 | z7 >> 31);
+            z7 &= P7;
+            z7 += Nat.AddWordTo(7, c * PInv, z);
+            z[7] = z7;
+            if (z7 >= P7 && Nat256.Gte(z, P))
+            {
+                SubPFrom(z);
+            }
+        }
+
+        public static void Square(uint[] x, uint[] z)
+        {
+            uint[] tt = Nat256.CreateExt();
+            Nat256.Square(x, tt);
+            Reduce(tt, z);
+        }
+
+        public static void SquareN(uint[] x, int n, uint[] z)
+        {
+            Debug.Assert(n > 0);
+
+            uint[] tt = Nat256.CreateExt();
+            Nat256.Square(x, tt);
+            Reduce(tt, z);
+
+            while (--n > 0)
+            {
+                Nat256.Square(z, tt);
+                Reduce(tt, z);
+            }
+        }
+
+        public static void Subtract(uint[] x, uint[] y, uint[] z)
+        {
+            int c = Nat256.Sub(x, y, z);
+            if (c != 0)
+            {
+                AddPTo(z);
+            }
+        }
+
+        public static void SubtractExt(uint[] xx, uint[] yy, uint[] zz)
+        {
+            int c = Nat.Sub(16, xx, yy, zz);
+            if (c != 0)
+            {
+                AddPExtTo(zz);
+            }
+        }
+
+        public static void Twice(uint[] x, uint[] z)
+        {
+            Nat.ShiftUpBit(8, x, 0, z);
+            if (Nat256.Gte(z, P))
+            {
+                SubPFrom(z);
+            }
+        }
+
+        private static uint AddPTo(uint[] z)
+        {
+            long c = (long)z[0] - PInv;
+            z[0] = (uint)c;
+            c >>= 32;
+            if (c != 0)
+            {
+                c = Nat.DecAt(7, z, 1);
+            }
+            c += (long)z[7] + (P7 + 1);
+            z[7] = (uint)c;
+            c >>= 32;
+            return (uint)c;
+        }
+
+        private static uint AddPExtTo(uint[] zz)
+        {
+            long c = (long)zz[0] + PExt[0];
+            zz[0] = (uint)c;
+            c >>= 32;
+            if (c != 0)
+            {
+                c = Nat.IncAt(8, zz, 1);
+            }
+            c += (long)zz[8] - PInv;
+            zz[8] = (uint)c;
+            c >>= 32;
+            if (c != 0)
+            {
+                c = Nat.DecAt(15, zz, 9);
+            }
+            c += (long)zz[15] + (PExt[15] + 1);
+            zz[15] = (uint)c;
+            c >>= 32;
+            return (uint)c;
+        }
+
+        private static int SubPFrom(uint[] z)
+        {
+            long c = (long)z[0] + PInv;
+            z[0] = (uint)c;
+            c >>= 32;
+            if (c != 0)
+            {
+                c = Nat.IncAt(7, z, 1);
+            }
+            c += (long)z[7] - (P7 + 1);
+            z[7] = (uint)c;
+            c >>= 32;
+            return (int)c;
+        }
+
+        private static int SubPExtFrom(uint[] zz)
+        {
+            long c = (long)zz[0] - PExt[0];
+            zz[0] = (uint)c;
+            c >>= 32;
+            if (c != 0)
+            {
+                c = Nat.DecAt(8, zz, 1);
+            }
+            c += (long)zz[8] + PInv;
+            zz[8] = (uint)c;
+            c >>= 32;
+            if (c != 0)
+            {
+                c = Nat.IncAt(15, zz, 9);
+            }
+            c += (long)zz[15] - (PExt[15] + 1);
+            zz[15] = (uint)c;
+            c >>= 32;
+            return (int)c;
+        }
+    }
+}
+
+#endif

Assets/BestHTTP/SecureProtocol/math/ec/custom/djb/Curve25519Field.cs.meta

@@ -0,0 +1,11 @@
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Assets/BestHTTP/SecureProtocol/math/ec/custom/djb/Curve25519FieldElement.cs

@@ -0,0 +1,237 @@
+#if !BESTHTTP_DISABLE_ALTERNATE_SSL && (!UNITY_WEBGL || UNITY_EDITOR)
+
+using System;
+
+using Org.BouncyCastle.Math.Raw;
+using Org.BouncyCastle.Utilities;
+
+namespace Org.BouncyCastle.Math.EC.Custom.Djb
+{
+    internal class Curve25519FieldElement
+        :   ECFieldElement
+    {
+        public static readonly BigInteger Q = Curve25519.q;
+
+        // Calculated as ECConstants.TWO.modPow(Q.shiftRight(2), Q)
+        private static readonly uint[] PRECOMP_POW2 = new uint[]{ 0x4a0ea0b0, 0xc4ee1b27, 0xad2fe478, 0x2f431806,
+            0x3dfbd7a7, 0x2b4d0099, 0x4fc1df0b, 0x2b832480 };
+
+        protected internal readonly uint[] x;
+
+        public Curve25519FieldElement(BigInteger x)
+        {
+            if (x == null || x.SignValue < 0 || x.CompareTo(Q) >= 0)
+                throw new ArgumentException("value invalid for Curve25519FieldElement", "x");
+
+            this.x = Curve25519Field.FromBigInteger(x);
+        }
+
+        public Curve25519FieldElement()
+        {
+            this.x = Nat256.Create();
+        }
+
+        protected internal Curve25519FieldElement(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 "Curve25519Field"; }
+        }
+
+        public override int FieldSize
+        {
+            get { return Q.BitLength; }
+        }
+
+        public override ECFieldElement Add(ECFieldElement b)
+        {
+            uint[] z = Nat256.Create();
+            Curve25519Field.Add(x, ((Curve25519FieldElement)b).x, z);
+            return new Curve25519FieldElement(z);
+        }
+
+        public override ECFieldElement AddOne()
+        {
+            uint[] z = Nat256.Create();
+            Curve25519Field.AddOne(x, z);
+            return new Curve25519FieldElement(z);
+        }
+
+        public override ECFieldElement Subtract(ECFieldElement b)
+        {
+            uint[] z = Nat256.Create();
+            Curve25519Field.Subtract(x, ((Curve25519FieldElement)b).x, z);
+            return new Curve25519FieldElement(z);
+        }
+
+        public override ECFieldElement Multiply(ECFieldElement b)
+        {
+            uint[] z = Nat256.Create();
+            Curve25519Field.Multiply(x, ((Curve25519FieldElement)b).x, z);
+            return new Curve25519FieldElement(z);
+        }
+
+        public override ECFieldElement Divide(ECFieldElement b)
+        {
+            //return Multiply(b.Invert());
+            uint[] z = Nat256.Create();
+            Mod.Invert(Curve25519Field.P, ((Curve25519FieldElement)b).x, z);
+            Curve25519Field.Multiply(z, x, z);
+            return new Curve25519FieldElement(z);
+        }
+
+        public override ECFieldElement Negate()
+        {
+            uint[] z = Nat256.Create();
+            Curve25519Field.Negate(x, z);
+            return new Curve25519FieldElement(z);
+        }
+
+        public override ECFieldElement Square()
+        {
+            uint[] z = Nat256.Create();
+            Curve25519Field.Square(x, z);
+            return new Curve25519FieldElement(z);
+        }
+
+        public override ECFieldElement Invert()
+        {
+            //return new Curve25519FieldElement(ToBigInteger().ModInverse(Q));
+            uint[] z = Nat256.Create();
+            Mod.Invert(Curve25519Field.P, x, z);
+            return new Curve25519FieldElement(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()
+        {
+            /*
+             * Q == 8m + 5, so we use Pocklington's method for this case.
+             *
+             * First, raise this element to the exponent 2^252 - 2^1 (i.e. m + 1)
+             * 
+             * Breaking up the exponent's binary representation into "repunits", we get:
+             * { 251 1s } { 1 0s }
+             * 
+             * Therefore we need an addition chain containing 251 (the lengths of the repunits)
+             * We use: 1, 2, 3, 4, 7, 11, 15, 30, 60, 120, 131, [251]
+             */
+
+            uint[] x1 = this.x;
+            if (Nat256.IsZero(x1) || Nat256.IsOne(x1))
+                return this;
+
+            uint[] x2 = Nat256.Create();
+            Curve25519Field.Square(x1, x2);
+            Curve25519Field.Multiply(x2, x1, x2);
+            uint[] x3 = x2;
+            Curve25519Field.Square(x2, x3);
+            Curve25519Field.Multiply(x3, x1, x3);
+            uint[] x4 = Nat256.Create();
+            Curve25519Field.Square(x3, x4);
+            Curve25519Field.Multiply(x4, x1, x4);
+            uint[] x7 = Nat256.Create();
+            Curve25519Field.SquareN(x4, 3, x7);
+            Curve25519Field.Multiply(x7, x3, x7);
+            uint[] x11 = x3;
+            Curve25519Field.SquareN(x7, 4, x11);
+            Curve25519Field.Multiply(x11, x4, x11);
+            uint[] x15 = x7;
+            Curve25519Field.SquareN(x11, 4, x15);
+            Curve25519Field.Multiply(x15, x4, x15);
+            uint[] x30 = x4;
+            Curve25519Field.SquareN(x15, 15, x30);
+            Curve25519Field.Multiply(x30, x15, x30);
+            uint[] x60 = x15;
+            Curve25519Field.SquareN(x30, 30, x60);
+            Curve25519Field.Multiply(x60, x30, x60);
+            uint[] x120 = x30;
+            Curve25519Field.SquareN(x60, 60, x120);
+            Curve25519Field.Multiply(x120, x60, x120);
+            uint[] x131 = x60;
+            Curve25519Field.SquareN(x120, 11, x131);
+            Curve25519Field.Multiply(x131, x11, x131);
+            uint[] x251 = x11;
+            Curve25519Field.SquareN(x131, 120, x251);
+            Curve25519Field.Multiply(x251, x120, x251);
+
+            uint[] t1 = x251;
+            Curve25519Field.Square(t1, t1);
+
+            uint[] t2 = x120;
+            Curve25519Field.Square(t1, t2);
+
+            if (Nat256.Eq(x1, t2))
+            {
+                return new Curve25519FieldElement(t1);
+            }
+
+            /*
+             * If the first guess is incorrect, we multiply by a precomputed power of 2 to get the second guess,
+             * which is ((4x)^(m + 1))/2 mod Q
+             */
+            Curve25519Field.Multiply(t1, PRECOMP_POW2, t1);
+
+            Curve25519Field.Square(t1, t2);
+
+            if (Nat256.Eq(x1, t2))
+            {
+                return new Curve25519FieldElement(t1);
+            }
+
+            return null;
+        }
+
+        public override bool Equals(object obj)
+        {
+            return Equals(obj as Curve25519FieldElement);
+        }
+
+        public override bool Equals(ECFieldElement other)
+        {
+            return Equals(other as Curve25519FieldElement);
+        }
+
+        public virtual bool Equals(Curve25519FieldElement other)
+        {
+            if (this == other)
+                return true;
+            if (null == other)
+                return false;
+            return Nat256.Eq(x, other.x);
+        }
+
+        public override int GetHashCode()
+        {
+            return Q.GetHashCode() ^ Arrays.GetHashCode(x, 0, 8);
+        }
+    }
+}
+
+#endif

Assets/BestHTTP/SecureProtocol/math/ec/custom/djb/Curve25519FieldElement.cs.meta

@@ -0,0 +1,11 @@
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Assets/BestHTTP/SecureProtocol/math/ec/custom/djb/Curve25519Point.cs

@@ -0,0 +1,317 @@
+#if !BESTHTTP_DISABLE_ALTERNATE_SSL && (!UNITY_WEBGL || UNITY_EDITOR)
+
+using System;
+
+using Org.BouncyCastle.Math.Raw;
+
+namespace Org.BouncyCastle.Math.EC.Custom.Djb
+{
+    internal class Curve25519Point
+        : AbstractFpPoint
+    {
+        /**
+         * Create a point which encodes with point compression.
+         * 
+         * @param curve the curve to use
+         * @param x affine x co-ordinate
+         * @param y affine y co-ordinate
+         * 
+         * @deprecated Use ECCurve.CreatePoint to construct points
+         */
+        public Curve25519Point(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 Curve25519Point(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 Curve25519Point(ECCurve curve, ECFieldElement x, ECFieldElement y, ECFieldElement[] zs, bool withCompression)
+            : base(curve, x, y, zs, withCompression)
+        {
+        }
+
+        protected override ECPoint Detach()
+        {
+            return new Curve25519Point(null, AffineXCoord, AffineYCoord);
+        }
+
+        public override ECFieldElement GetZCoord(int index)
+        {
+            if (index == 1)
+            {
+                return GetJacobianModifiedW();
+            }
+
+            return base.GetZCoord(index);
+        }
+
+        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;
+
+            Curve25519FieldElement X1 = (Curve25519FieldElement)this.RawXCoord, Y1 = (Curve25519FieldElement)this.RawYCoord,
+                Z1 = (Curve25519FieldElement)this.RawZCoords[0];
+            Curve25519FieldElement X2 = (Curve25519FieldElement)b.RawXCoord, Y2 = (Curve25519FieldElement)b.RawYCoord,
+                Z2 = (Curve25519FieldElement)b.RawZCoords[0];
+
+            uint c;
+            uint[] tt1 = Nat256.CreateExt();
+            uint[] t2 = Nat256.Create();
+            uint[] t3 = Nat256.Create();
+            uint[] t4 = Nat256.Create();
+
+            bool Z1IsOne = Z1.IsOne;
+            uint[] U2, S2;
+            if (Z1IsOne)
+            {
+                U2 = X2.x;
+                S2 = Y2.x;
+            }
+            else
+            {
+                S2 = t3;
+                Curve25519Field.Square(Z1.x, S2);
+
+                U2 = t2;
+                Curve25519Field.Multiply(S2, X2.x, U2);
+
+                Curve25519Field.Multiply(S2, Z1.x, S2);
+                Curve25519Field.Multiply(S2, Y2.x, S2);
+            }
+
+            bool Z2IsOne = Z2.IsOne;
+            uint[] U1, S1;
+            if (Z2IsOne)
+            {
+                U1 = X1.x;
+                S1 = Y1.x;
+            }
+            else
+            {
+                S1 = t4;
+                Curve25519Field.Square(Z2.x, S1);
+
+                U1 = tt1;
+                Curve25519Field.Multiply(S1, X1.x, U1);
+
+                Curve25519Field.Multiply(S1, Z2.x, S1);
+                Curve25519Field.Multiply(S1, Y1.x, S1);
+            }
+
+            uint[] H = Nat256.Create();
+            Curve25519Field.Subtract(U1, U2, H);
+
+            uint[] R = t2;
+            Curve25519Field.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 = Nat256.Create();
+            Curve25519Field.Square(H, HSquared);
+
+            uint[] G = Nat256.Create();
+            Curve25519Field.Multiply(HSquared, H, G);
+
+            uint[] V = t3;
+            Curve25519Field.Multiply(HSquared, U1, V);
+
+            Curve25519Field.Negate(G, G);
+            Nat256.Mul(S1, G, tt1);
+
+            c = Nat256.AddBothTo(V, V, G);
+            Curve25519Field.Reduce27(c, G);
+
+            Curve25519FieldElement X3 = new Curve25519FieldElement(t4);
+            Curve25519Field.Square(R, X3.x);
+            Curve25519Field.Subtract(X3.x, G, X3.x);
+
+            Curve25519FieldElement Y3 = new Curve25519FieldElement(G);
+            Curve25519Field.Subtract(V, X3.x, Y3.x);
+            Curve25519Field.MultiplyAddToExt(Y3.x, R, tt1);
+            Curve25519Field.Reduce(tt1, Y3.x);
+
+            Curve25519FieldElement Z3 = new Curve25519FieldElement(H);
+            if (!Z1IsOne)
+            {
+                Curve25519Field.Multiply(Z3.x, Z1.x, Z3.x);
+            }
+            if (!Z2IsOne)
+            {
+                Curve25519Field.Multiply(Z3.x, Z2.x, Z3.x);
+            }
+
+            uint[] Z3Squared = (Z1IsOne && Z2IsOne) ? HSquared : null;
+
+            // TODO If the result will only be used in a subsequent addition, we don't need W3
+            Curve25519FieldElement W3 = CalculateJacobianModifiedW((Curve25519FieldElement)Z3, Z3Squared);
+
+            ECFieldElement[] zs = new ECFieldElement[] { Z3, W3 };
+
+            return new Curve25519Point(curve, X3, Y3, zs, IsCompressed);
+        }
+
+        public override ECPoint Twice()
+        {
+            if (this.IsInfinity)
+                return this;
+
+            ECCurve curve = this.Curve;
+
+            ECFieldElement Y1 = this.RawYCoord;
+            if (Y1.IsZero)
+                return curve.Infinity;
+
+            return TwiceJacobianModified(true);
+        }
+
+        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 TwiceJacobianModified(false).Add(b);
+        }
+
+        public override ECPoint ThreeTimes()
+        {
+            if (this.IsInfinity || this.RawYCoord.IsZero)
+                return this;
+
+            return TwiceJacobianModified(false).Add(this);
+        }
+
+        public override ECPoint Negate()
+        {
+            if (IsInfinity)
+                return this;
+
+            return new Curve25519Point(Curve, RawXCoord, RawYCoord.Negate(), RawZCoords, IsCompressed);
+        }
+
+        protected virtual Curve25519FieldElement CalculateJacobianModifiedW(Curve25519FieldElement Z, uint[] ZSquared)
+        {
+            Curve25519FieldElement a4 = (Curve25519FieldElement)this.Curve.A;
+            if (Z.IsOne)
+                return a4;
+
+            Curve25519FieldElement W = new Curve25519FieldElement();
+            if (ZSquared == null)
+            {
+                ZSquared = W.x;
+                Curve25519Field.Square(Z.x, ZSquared);
+            }
+            Curve25519Field.Square(ZSquared, W.x);
+            Curve25519Field.Multiply(W.x, a4.x, W.x);
+            return W;
+        }
+
+        protected virtual Curve25519FieldElement GetJacobianModifiedW()
+        {
+            ECFieldElement[] ZZ = this.RawZCoords;
+            Curve25519FieldElement W = (Curve25519FieldElement)ZZ[1];
+            if (W == null)
+            {
+                // NOTE: Rarely, TwicePlus will result in the need for a lazy W1 calculation here
+                ZZ[1] = W = CalculateJacobianModifiedW((Curve25519FieldElement)ZZ[0], null);
+            }
+            return W;
+        }
+
+        protected virtual Curve25519Point TwiceJacobianModified(bool calculateW)
+        {
+            Curve25519FieldElement X1 = (Curve25519FieldElement)this.RawXCoord, Y1 = (Curve25519FieldElement)this.RawYCoord,
+                Z1 = (Curve25519FieldElement)this.RawZCoords[0], W1 = GetJacobianModifiedW();
+
+            uint c;
+
+            uint[] M = Nat256.Create();
+            Curve25519Field.Square(X1.x, M);
+            c = Nat256.AddBothTo(M, M, M);
+            c += Nat256.AddTo(W1.x, M);
+            Curve25519Field.Reduce27(c, M);
+
+            uint[] _2Y1 = Nat256.Create();
+            Curve25519Field.Twice(Y1.x, _2Y1);
+
+            uint[] _2Y1Squared = Nat256.Create();
+            Curve25519Field.Multiply(_2Y1, Y1.x, _2Y1Squared);
+
+            uint[] S = Nat256.Create();
+            Curve25519Field.Multiply(_2Y1Squared, X1.x, S);
+            Curve25519Field.Twice(S, S);
+
+            uint[] _8T = Nat256.Create();
+            Curve25519Field.Square(_2Y1Squared, _8T);
+            Curve25519Field.Twice(_8T, _8T);
+
+            Curve25519FieldElement X3 = new Curve25519FieldElement(_2Y1Squared);
+            Curve25519Field.Square(M, X3.x);
+            Curve25519Field.Subtract(X3.x, S, X3.x);
+            Curve25519Field.Subtract(X3.x, S, X3.x);
+
+            Curve25519FieldElement Y3 = new Curve25519FieldElement(S);
+            Curve25519Field.Subtract(S, X3.x, Y3.x);
+            Curve25519Field.Multiply(Y3.x, M, Y3.x);
+            Curve25519Field.Subtract(Y3.x, _8T, Y3.x);
+
+            Curve25519FieldElement Z3 = new Curve25519FieldElement(_2Y1);
+            if (!Nat256.IsOne(Z1.x))
+            {
+                Curve25519Field.Multiply(Z3.x, Z1.x, Z3.x);
+            }
+
+            Curve25519FieldElement W3 = null;
+            if (calculateW)
+            {
+                W3 = new Curve25519FieldElement(_8T);
+                Curve25519Field.Multiply(W3.x, W1.x, W3.x);
+                Curve25519Field.Twice(W3.x, W3.x);
+            }
+
+            return new Curve25519Point(this.Curve, X3, Y3, new ECFieldElement[] { Z3, W3 }, IsCompressed);
+        }
+    }
+}
+
+#endif

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