Add custom curve for secp384r1 (P-384)

5 files changed, 810 insertions, 0 deletions

diff --git a/crypto/src/math/ec/custom/sec/Nat384.cs b/crypto/src/math/ec/custom/sec/Nat384.cs
new file mode 100644
index 000000000..273ee2d65
--- /dev/null
+++ b/crypto/src/math/ec/custom/sec/Nat384.cs
@@ -0,0 +1,46 @@
+using System;
+using System.Diagnostics;
+
+namespace Org.BouncyCastle.Math.EC.Custom.Sec
+{
+    internal abstract class Nat384
+    {
+        public static void Mul(uint[] x, uint[] y, uint[] zz)
+        {
+            Nat192.Mul(x, y, zz);
+            Nat192.Mul(x, 6, y, 6, zz, 12);
+
+            uint c18 = Nat192.AddToEachOther(zz, 6, zz, 12);
+            uint c12 = c18 + Nat192.AddTo(zz, 0, zz, 6, 0);
+            c18 += Nat192.AddTo(zz, 18, zz, 12, c12);
+
+            uint[] dx = Nat192.Create(), dy = Nat192.Create();
+            bool neg = Nat192.Diff(x, 6, x, 0, dx, 0) != Nat192.Diff(y, 6, y, 0, dy, 0);
+
+            uint[] tt = Nat192.CreateExt();
+            Nat192.Mul(dx, dy, tt);
+
+            c18 += neg ? Nat.AddTo(12, tt, 0, zz, 6) : (uint)Nat.SubFrom(12, tt, 0, zz, 6);
+            Nat.AddWordExt(12, c18, zz, 18);
+        }
+
+        public static void Square(uint[] x, uint[] zz)
+        {
+            Nat192.Square(x, zz);
+            Nat192.Square(x, 6, zz, 12);
+
+            uint c18 = Nat192.AddToEachOther(zz, 6, zz, 12);
+            uint c12 = c18 + Nat192.AddTo(zz, 0, zz, 6, 0);
+            c18 += Nat192.AddTo(zz, 18, zz, 12, c12);
+
+            uint[] dx = Nat192.Create();
+            Nat192.Diff(x, 6, x, 0, dx, 0);
+
+            uint[] m = Nat192.CreateExt();
+            Nat192.Square(dx, m);
+
+            c18 += (uint)Nat.SubFrom(12, m, 0, zz, 6);
+            Nat.AddWordExt(12, c18, zz, 18);
+        }
+    }
+}
diff --git a/crypto/src/math/ec/custom/sec/SecP384R1Curve.cs b/crypto/src/math/ec/custom/sec/SecP384R1Curve.cs
new file mode 100644
index 000000000..9366232c6
--- /dev/null
+++ b/crypto/src/math/ec/custom/sec/SecP384R1Curve.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 SecP384R1Curve
+        : ECCurve
+    {
+        public static readonly BigInteger q = new BigInteger(1,
+            Hex.Decode("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFF"));
+
+        private const int SecP384R1_DEFAULT_COORDS = COORD_JACOBIAN;
+
+        protected readonly SecP384R1Point m_infinity;
+
+        public SecP384R1Curve()
+            : base(FiniteFields.GetPrimeField(q))
+        {
+            this.m_infinity = new SecP384R1Point(this, null, null);
+
+            this.m_a = FromBigInteger(new BigInteger(1,
+                Hex.Decode("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFC")));
+            this.m_b = FromBigInteger(new BigInteger(1,
+                Hex.Decode("B3312FA7E23EE7E4988E056BE3F82D19181D9C6EFE8141120314088F5013875AC656398D8A2ED19D2A85C8EDD3EC2AEF")));
+            this.m_order = new BigInteger(1, Hex.Decode("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC7634D81F4372DDF581A0DB248B0A77AECEC196ACCC52973"));
+            this.m_cofactor = BigInteger.One;
+            this.m_coord = SecP384R1_DEFAULT_COORDS;
+        }
+
+        protected override ECCurve CloneCurve()
+        {
+            return new SecP384R1Curve();
+        }
+
+        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 SecP384R1FieldElement(x);
+        }
+
+        protected internal override ECPoint CreateRawPoint(ECFieldElement x, ECFieldElement y, bool withCompression)
+        {
+            return new SecP384R1Point(this, x, y, withCompression);
+        }
+
+        protected override ECPoint DecompressPoint(int yTilde, BigInteger X1)
+        {
+            ECFieldElement x = FromBigInteger(X1);
+            ECFieldElement alpha = x.Square().Add(A).Multiply(x).Add(B);
+            ECFieldElement beta = alpha.Sqrt();
+
+            //
+            // if we can't find a sqrt we haven't got a point on the
+            // curve - run!
+            //
+            if (beta == null)
+                throw new ArithmeticException("Invalid point compression");
+
+            if (beta.TestBitZero() != (yTilde == 1))
+            {
+                // Use the other root
+                beta = beta.Negate();
+            }
+
+            return new SecP384R1Point(this, x, beta, true);
+        }
+    }
+}
diff --git a/crypto/src/math/ec/custom/sec/SecP384R1Field.cs b/crypto/src/math/ec/custom/sec/SecP384R1Field.cs
new file mode 100644
index 000000000..8f9094b5b
--- /dev/null
+++ b/crypto/src/math/ec/custom/sec/SecP384R1Field.cs
@@ -0,0 +1,227 @@
+using System;
+using System.Diagnostics;
+
+namespace Org.BouncyCastle.Math.EC.Custom.Sec
+{
+    internal class SecP384R1Field
+    {
+            // 2^384 - 2^128 - 2^96 + 2^32 - 1
+        internal static readonly uint[] P = new uint[]{ 0xFFFFFFFF, 0x00000000, 0x00000000, 0xFFFFFFFF, 0xFFFFFFFE, 0xFFFFFFFF,
+            0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF };
+        private const uint P11 = 0xFFFFFFFF;
+        private static readonly uint[] PExt = new uint[]{ 0x00000001, 0xFFFFFFFE, 0x00000000, 0x00000002, 0x00000000, 0xFFFFFFFE,
+            0x00000000, 0x00000002, 0x00000001, 0x00000000, 0x00000000, 0x00000000, 0xFFFFFFFE, 0x00000001, 0x00000000,
+            0xFFFFFFFE, 0xFFFFFFFD, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF };
+        private const uint PExt23 = 0xFFFFFFFF;
+
+        public static void Add(uint[] x, uint[] y, uint[] z)
+        {
+            uint c = Nat.Add(12, x, y, z);
+            if (c != 0 || (z[11] == P11 && Nat.Gte(12, z, P)))
+            {
+                Nat.Sub(12, z, P, z);
+            }
+        }
+
+        public static void AddExt(uint[] xx, uint[] yy, uint[] zz)
+        {
+            uint c = Nat.Add(24, xx, yy, zz);
+            if (c != 0 || (zz[23] == PExt23 && Nat.Gte(24, zz, PExt)))
+            {
+                Nat.Sub(24, zz, PExt, zz);
+            }
+        }
+
+        public static void AddOne(uint[] x, uint[] z)
+        {
+            Nat.Copy(12, x, z);
+            uint c = Nat.Inc(12, z, 0);
+            if (c != 0 || (z[11] == P11 && Nat.Gte(12, z, P)))
+            {
+                Nat.Sub(12, z, P, z);
+            }
+        }
+
+        public static uint[] FromBigInteger(BigInteger x)
+        {
+            uint[] z = Nat.FromBigInteger(384, x);
+            if (z[11] == P11 && Nat.Gte(12, z, P))
+            {
+                Nat.Sub(12, z, P, z);
+            }
+            return z;
+        }
+
+        public static void Half(uint[] x, uint[] z)
+        {
+            if ((x[0] & 1) == 0)
+            {
+                Nat.ShiftDownBit(12, x, 0, z);
+            }
+            else
+            {
+                uint c = Nat.Add(12, x, P, z);
+                Nat.ShiftDownBit(12, z, c);
+            }
+        }
+
+        public static void Multiply(uint[] x, uint[] y, uint[] z)
+        {
+            uint[] tt = Nat.Create(24);
+            Nat384.Mul(x, y, tt);
+            Reduce(tt, z);
+        }
+
+        public static void Negate(uint[] x, uint[] z)
+        {
+            if (Nat.IsZero(12, x))
+            {
+                Nat.Zero(12, z);
+            }
+            else
+            {
+                Nat.Sub(12, P, x, z);
+            }
+        }
+
+        public static void Reduce(uint[] xx, uint[] z)
+        {
+            long xx12 = xx[12], xx13 = xx[13], xx14 = xx[14], xx15 = xx[15];
+            long xx16 = xx[16], xx17 = xx[17], xx18 = xx[18], xx19 = xx[19];
+            long xx20 = xx[20], xx21 = xx[21], xx22 = xx[22], xx23 = xx[23];
+
+            long cc = 0;
+            cc += (long)xx[0] + xx12 + xx20 + xx21 - xx23;
+            z[0] = (uint)cc;
+            cc >>= 32;
+            cc += (long)xx[1] + xx13 + xx22 + xx23 - xx12 - xx20;
+            z[1] = (uint)cc;
+            cc >>= 32;
+            cc += (long)xx[2] + xx14 + xx23 - xx13 - xx21;
+            z[2] = (uint)cc;
+            cc >>= 32;
+            cc += (long)xx[3] + xx12 + xx15 + xx20 + xx21 - xx14 - xx22 - xx23;
+            z[3] = (uint)cc;
+            cc >>= 32;
+            cc += (long)xx[4] + xx12 + xx13 + xx16 + xx20 + ((xx21 - xx23) << 1) + xx22 - xx15;
+            z[4] = (uint)cc;
+            cc >>= 32;
+            cc += (long)xx[5] + xx13 + xx14 + xx17 + xx21 + (xx22 << 1) + xx23 - xx16;
+            z[5] = (uint)cc;
+            cc >>= 32;
+            cc += (long)xx[6] + xx14 + xx15 + xx18 + xx22 + (xx23 << 1) - xx17;
+            z[6] = (uint)cc;
+            cc >>= 32;
+            cc += (long)xx[7] + xx15 + xx16 + xx19 + xx23 - xx18;
+            z[7] = (uint)cc;
+            cc >>= 32;
+            cc += (long)xx[8] + xx16 + xx17 + xx20 - xx19;
+            z[8] = (uint)cc;
+            cc >>= 32;
+            cc += (long)xx[9] + xx17 + xx18 + xx21 - xx20;
+            z[9] = (uint)cc;
+            cc >>= 32;
+            cc += (long)xx[10] + xx18 + xx19 + xx22 - xx21;
+            z[10] = (uint)cc;
+            cc >>= 32;
+            cc += (long)xx[11] + xx19 + xx20 + xx23 - xx22;
+            z[11] = (uint)cc;
+            cc >>= 32;
+
+            int c = (int)cc;
+            if (c > 0)
+            {
+                Reduce32((uint)c, z);
+            }
+            else
+            {
+                while (c < 0)
+                {
+                    c += (int)Nat256.Add(z, P, z);
+                }
+            }
+        }
+
+        public static void Reduce32(uint x, uint[] z)
+        {
+            long xx12 = x;
+
+            long cc = 0;
+            cc += (long)z[0] + xx12;
+            z[0] = (uint)cc;
+            cc >>= 32;
+            cc += (long)z[1] - xx12;
+            z[1] = (uint)cc;
+            cc >>= 32;
+            cc += (long)z[2];
+            z[2] = (uint)cc;
+            cc >>= 32;
+            cc += (long)z[3] + xx12;
+            z[3] = (uint)cc;
+            cc >>= 32;
+            cc += (long)z[4] + xx12;
+            z[4] = (uint)cc;
+            cc >>= 32;
+
+            Debug.Assert(cc >= 0);
+
+            if (cc > 0)
+            {
+                uint c = Nat.AddWord(12, (uint)cc, z, 5);
+                if (c != 0 || (z[11] == P11 && Nat.Gte(12, z, P)))
+                {
+                    Nat.Sub(12, z, P, z);
+                }
+            }
+        }
+
+        public static void Square(uint[] x, uint[] z)
+        {
+            uint[] tt = Nat.Create(24);
+            Nat384.Square(x, tt);
+            Reduce(tt, z);
+        }
+
+        public static void SquareN(uint[] x, int n, uint[] z)
+        {
+            Debug.Assert(n > 0);
+
+            uint[] tt = Nat.Create(24);
+            Nat384.Square(x, tt);
+            Reduce(tt, z);
+
+            while (--n > 0)
+            {
+                Nat384.Square(z, tt);
+                Reduce(tt, z);
+            }
+        }
+
+        public static void Subtract(uint[] x, uint[] y, uint[] z)
+        {
+            int c = Nat.Sub(12, x, y, z);
+            if (c != 0)
+            {
+                Nat.Add(12, z, P, z);
+            }
+        }
+
+        public static void SubtractExt(uint[] xx, uint[] yy, uint[] zz)
+        {
+            int c = Nat.Sub(24, xx, yy, zz);
+            if (c != 0)
+            {
+                Nat.Add(24, zz, PExt, zz);
+            }
+        }
+
+        public static void Twice(uint[] x, uint[] z)
+        {
+            uint c = Nat.ShiftUpBit(12, x, 0, z);
+            if (c != 0 || (z[11] == P11 && Nat.Gte(12, z, P)))
+            {
+                Nat.Sub(12, z, P, z);
+            }
+        }
+    }
+}
diff --git a/crypto/src/math/ec/custom/sec/SecP384R1FieldElement.cs b/crypto/src/math/ec/custom/sec/SecP384R1FieldElement.cs
new file mode 100644
index 000000000..bca260de9
--- /dev/null
+++ b/crypto/src/math/ec/custom/sec/SecP384R1FieldElement.cs
@@ -0,0 +1,155 @@
+using System;
+
+using Org.BouncyCastle.Utilities;
+
+namespace Org.BouncyCastle.Math.EC.Custom.Sec
+{
+    internal class SecP384R1FieldElement
+        : ECFieldElement
+    {
+        public static readonly BigInteger Q = SecP384R1Curve.q;
+
+        protected internal readonly uint[] x;
+
+        public SecP384R1FieldElement(BigInteger x)
+        {
+            if (x == null || x.SignValue < 0 || x.CompareTo(Q) >= 0)
+                throw new ArgumentException("value invalid for SecP384R1FieldElement", "x");
+
+            this.x = SecP384R1Field.FromBigInteger(x);
+        }
+
+        public SecP384R1FieldElement()
+        {
+            this.x = Nat.Create(12);
+        }
+
+        protected internal SecP384R1FieldElement(uint[] x)
+        {
+            this.x = x;
+        }
+
+        public override bool IsZero
+        {
+            get { return Nat.IsZero(12, x); }
+        }
+
+        public override bool IsOne
+        {
+            get { return Nat.IsOne(12, x); }
+        }
+
+        public override bool TestBitZero()
+        {
+            return Nat.GetBit(x, 0) == 1;
+        }
+
+        public override BigInteger ToBigInteger()
+        {
+            return Nat.ToBigInteger(12, x);
+        }
+
+        public override string FieldName
+        {
+            get { return "SecP384R1Field"; }
+        }
+
+        public override int FieldSize
+        {
+            get { return Q.BitLength; }
+        }
+
+        public override ECFieldElement Add(ECFieldElement b)
+        {
+            uint[] z = Nat.Create(12);
+            SecP384R1Field.Add(x, ((SecP384R1FieldElement)b).x, z);
+            return new SecP384R1FieldElement(z);
+        }
+
+        public override ECFieldElement AddOne()
+        {
+            uint[] z = Nat.Create(12);
+            SecP384R1Field.AddOne(x, z);
+            return new SecP384R1FieldElement(z);
+        }
+
+        public override ECFieldElement Subtract(ECFieldElement b)
+        {
+            uint[] z = Nat.Create(12);
+            SecP384R1Field.Subtract(x, ((SecP384R1FieldElement)b).x, z);
+            return new SecP384R1FieldElement(z);
+        }
+
+        public override ECFieldElement Multiply(ECFieldElement b)
+        {
+            uint[] z = Nat.Create(12);
+            SecP384R1Field.Multiply(x, ((SecP384R1FieldElement)b).x, z);
+            return new SecP384R1FieldElement(z);
+        }
+
+        public override ECFieldElement Divide(ECFieldElement b)
+        {
+            //return Multiply(b.Invert());
+            uint[] z = Nat.Create(12);
+            Mod.Invert(SecP384R1Field.P, ((SecP384R1FieldElement)b).x, z);
+            SecP384R1Field.Multiply(z, x, z);
+            return new SecP384R1FieldElement(z);
+        }
+
+        public override ECFieldElement Negate()
+        {
+            uint[] z = Nat.Create(12);
+            SecP384R1Field.Negate(x, z);
+            return new SecP384R1FieldElement(z);
+        }
+
+        public override ECFieldElement Square()
+        {
+            uint[] z = Nat.Create(12);
+            SecP384R1Field.Square(x, z);
+            return new SecP384R1FieldElement(z);
+        }
+
+        public override ECFieldElement Invert()
+        {
+            //return new SecP384R1FieldElement(ToBigInteger().ModInverse(Q));
+            uint[] z = Nat.Create(12);
+            Mod.Invert(SecP384R1Field.P, x, z);
+            return new SecP384R1FieldElement(z);
+        }
+
+        /**
+         * return a sqrt root - the routine verifies that the calculation returns the right value - if
+         * none exists it returns null.
+         */
+        public override ECFieldElement Sqrt()
+        {
+            ECFieldElement root = new FpFieldElement(Q, ToBigInteger()).Sqrt();
+            return root == null ? null : new SecP384R1FieldElement(root.ToBigInteger());
+        }
+
+        public override bool Equals(object obj)
+        {
+            return Equals(obj as SecP384R1FieldElement);
+        }
+
+        public override bool Equals(ECFieldElement other)
+        {
+            return Equals(other as SecP384R1FieldElement);
+        }
+
+        public virtual bool Equals(SecP384R1FieldElement 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/SecP384R1Point.cs b/crypto/src/math/ec/custom/sec/SecP384R1Point.cs
new file mode 100644
index 000000000..6547df20c
--- /dev/null
+++ b/crypto/src/math/ec/custom/sec/SecP384R1Point.cs
@@ -0,0 +1,287 @@
+using System;
+
+namespace Org.BouncyCastle.Math.EC.Custom.Sec
+{
+    internal class SecP384R1Point
+        : 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 SecP384R1Point(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 SecP384R1Point(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 SecP384R1Point(ECCurve curve, ECFieldElement x, ECFieldElement y, ECFieldElement[] zs, bool withCompression)
+            : base(curve, x, y, zs, withCompression)
+        {
+        }
+
+        protected override ECPoint Detach()
+        {
+            return new SecP384R1Point(null, AffineXCoord, AffineYCoord);
+        }
+
+        protected internal override bool CompressionYTilde
+        {
+            get { return this.AffineYCoord.TestBitZero(); }
+        }
+
+        public override ECPoint Add(ECPoint b)
+        {
+            if (this.IsInfinity)
+                return b;
+            if (b.IsInfinity)
+                return this;
+            if (this == b)
+                return Twice();
+
+            ECCurve curve = this.Curve;
+
+            SecP384R1FieldElement X1 = (SecP384R1FieldElement)this.RawXCoord, Y1 = (SecP384R1FieldElement)this.RawYCoord;
+            SecP384R1FieldElement X2 = (SecP384R1FieldElement)b.RawXCoord, Y2 = (SecP384R1FieldElement)b.RawYCoord;
+
+            SecP384R1FieldElement Z1 = (SecP384R1FieldElement)this.RawZCoords[0];
+            SecP384R1FieldElement Z2 = (SecP384R1FieldElement)b.RawZCoords[0];
+
+            uint[] tt1 = Nat.Create(24);
+            uint[] tt2 = Nat.Create(24);
+            uint[] t3 = Nat.Create(12);
+            uint[] t4 = Nat.Create(12);
+
+            bool Z1IsOne = Z1.IsOne;
+            uint[] U2, S2;
+            if (Z1IsOne)
+            {
+                U2 = X2.x;
+                S2 = Y2.x;
+            }
+            else
+            {
+                S2 = t3;
+                SecP384R1Field.Square(Z1.x, S2);
+
+                U2 = tt2;
+                SecP384R1Field.Multiply(S2, X2.x, U2);
+
+                SecP384R1Field.Multiply(S2, Z1.x, S2);
+                SecP384R1Field.Multiply(S2, Y2.x, S2);
+            }
+
+            bool Z2IsOne = Z2.IsOne;
+            uint[] U1, S1;
+            if (Z2IsOne)
+            {
+                U1 = X1.x;
+                S1 = Y1.x;
+            }
+            else
+            {
+                S1 = t4;
+                SecP384R1Field.Square(Z2.x, S1);
+
+                U1 = tt1;
+                SecP384R1Field.Multiply(S1, X1.x, U1);
+
+                SecP384R1Field.Multiply(S1, Z2.x, S1);
+                SecP384R1Field.Multiply(S1, Y1.x, S1);
+            }
+
+            uint[] H = Nat.Create(12);
+            SecP384R1Field.Subtract(U1, U2, H);
+
+            uint[] R = Nat.Create(12);// tt2;
+            SecP384R1Field.Subtract(S1, S2, R);
+
+            // Check if b == this or b == -this
+            if (Nat.IsZero(12, H))
+            {
+                if (Nat.IsZero(12, 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;
+            SecP384R1Field.Square(H, HSquared);
+
+            uint[] G = Nat.Create(12);
+            SecP384R1Field.Multiply(HSquared, H, G);
+
+            uint[] V = t3;
+            SecP384R1Field.Multiply(HSquared, U1, V);
+
+            Nat384.Mul(S1, G, tt1);
+
+            SecP384R1FieldElement X3 = new SecP384R1FieldElement(t4);
+            SecP384R1Field.Square(R, X3.x);
+            SecP384R1Field.Add(X3.x, G, X3.x);
+            SecP384R1Field.Subtract(X3.x, V, X3.x);
+            SecP384R1Field.Subtract(X3.x, V, X3.x);
+
+            SecP384R1FieldElement Y3 = new SecP384R1FieldElement(G);
+            SecP384R1Field.Subtract(V, X3.x, Y3.x);
+            Nat384.Mul(Y3.x, R, tt2);
+            SecP384R1Field.SubtractExt(tt2, tt1, tt2);
+            SecP384R1Field.Reduce(tt2, Y3.x);
+
+            SecP384R1FieldElement Z3 = new SecP384R1FieldElement(H);
+            if (!Z1IsOne)
+            {
+                SecP384R1Field.Multiply(Z3.x, Z1.x, Z3.x);
+            }
+            if (!Z2IsOne)
+            {
+                SecP384R1Field.Multiply(Z3.x, Z2.x, Z3.x);
+            }
+
+            ECFieldElement[] zs = new ECFieldElement[] { Z3 };
+
+            return new SecP384R1Point(curve, X3, Y3, zs, IsCompressed);
+        }
+
+        public override ECPoint Twice()
+        {
+            if (this.IsInfinity)
+                return this;
+
+            ECCurve curve = this.Curve;
+
+            SecP384R1FieldElement Y1 = (SecP384R1FieldElement)this.RawYCoord;
+            if (Y1.IsZero)
+                return curve.Infinity;
+
+            SecP384R1FieldElement X1 = (SecP384R1FieldElement)this.RawXCoord, Z1 = (SecP384R1FieldElement)this.RawZCoords[0];
+
+            uint[] t1 = Nat.Create(12);
+            uint[] t2 = Nat.Create(12);
+
+            uint[] Y1Squared = Nat.Create(12);
+            SecP384R1Field.Square(Y1.x, Y1Squared);
+
+            uint[] T = Nat.Create(12);
+            SecP384R1Field.Square(Y1Squared, T);
+
+            bool Z1IsOne = Z1.IsOne;
+
+            uint[] Z1Squared = Z1.x;
+            if (!Z1IsOne)
+            {
+                Z1Squared = t2;
+                SecP384R1Field.Square(Z1.x, Z1Squared);
+            }
+
+            SecP384R1Field.Subtract(X1.x, Z1Squared, t1);
+
+            uint[] M = t2;
+            SecP384R1Field.Add(X1.x, Z1Squared, M);
+            SecP384R1Field.Multiply(M, t1, M);
+            SecP384R1Field.Twice(M, t1);
+            SecP384R1Field.Add(M, t1, M);
+
+            uint[] S = Y1Squared;
+            SecP384R1Field.Multiply(Y1Squared, X1.x, S);
+            uint c = Nat.ShiftUpBits(12, S, 2, 0);
+            SecP384R1Field.Reduce32(c, S);
+
+            c = Nat.ShiftUpBits(12, T, 3, 0, t1);
+            SecP384R1Field.Reduce32(c, t1);
+
+            SecP384R1FieldElement X3 = new SecP384R1FieldElement(T);
+            SecP384R1Field.Square(M, X3.x);
+            SecP384R1Field.Subtract(X3.x, S, X3.x);
+            SecP384R1Field.Subtract(X3.x, S, X3.x);
+
+            SecP384R1FieldElement Y3 = new SecP384R1FieldElement(S);
+            SecP384R1Field.Subtract(S, X3.x, Y3.x);
+            SecP384R1Field.Multiply(Y3.x, M, Y3.x);
+            SecP384R1Field.Subtract(Y3.x, t1, Y3.x);
+
+            SecP384R1FieldElement Z3 = new SecP384R1FieldElement(M);
+            SecP384R1Field.Twice(Y1.x, Z3.x);
+            if (!Z1IsOne)
+            {
+                SecP384R1Field.Multiply(Z3.x, Z1.x, Z3.x);
+            }
+
+            return new SecP384R1Point(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 SecP384R1Point(Curve, RawXCoord, RawYCoord.Negate(), RawZCoords, IsCompressed);
+        }
+    }
+}