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-rw-r--r--crypto/src/math/ec/ECAlgorithms.cs31
-rw-r--r--crypto/src/math/ec/ECCurve.cs73
-rw-r--r--crypto/src/math/ec/ECFieldElement.cs94
-rw-r--r--crypto/src/math/ec/ECPoint.cs170
-rw-r--r--crypto/src/math/ec/custom/djb/Curve25519FieldElement.cs2
-rw-r--r--crypto/src/math/ec/custom/gm/SM2P256V1FieldElement.cs2
-rw-r--r--crypto/src/math/ec/custom/sec/SecP128R1FieldElement.cs2
-rw-r--r--crypto/src/math/ec/custom/sec/SecP160R1FieldElement.cs2
-rw-r--r--crypto/src/math/ec/custom/sec/SecP160R2FieldElement.cs2
-rw-r--r--crypto/src/math/ec/custom/sec/SecP192K1FieldElement.cs2
-rw-r--r--crypto/src/math/ec/custom/sec/SecP192R1FieldElement.cs2
-rw-r--r--crypto/src/math/ec/custom/sec/SecP224K1FieldElement.cs2
-rw-r--r--crypto/src/math/ec/custom/sec/SecP224R1FieldElement.cs2
-rw-r--r--crypto/src/math/ec/custom/sec/SecP256K1FieldElement.cs2
-rw-r--r--crypto/src/math/ec/custom/sec/SecP256R1FieldElement.cs2
-rw-r--r--crypto/src/math/ec/custom/sec/SecP384R1FieldElement.cs2
-rw-r--r--crypto/src/math/ec/custom/sec/SecP521R1FieldElement.cs2
-rw-r--r--crypto/src/math/ec/custom/sec/SecT113FieldElement.cs7
-rw-r--r--crypto/src/math/ec/custom/sec/SecT131FieldElement.cs7
-rw-r--r--crypto/src/math/ec/custom/sec/SecT163FieldElement.cs7
-rw-r--r--crypto/src/math/ec/custom/sec/SecT193FieldElement.cs7
-rw-r--r--crypto/src/math/ec/custom/sec/SecT233FieldElement.cs7
-rw-r--r--crypto/src/math/ec/custom/sec/SecT239FieldElement.cs7
-rw-r--r--crypto/src/math/ec/custom/sec/SecT283FieldElement.cs7
-rw-r--r--crypto/src/math/ec/custom/sec/SecT409FieldElement.cs7
-rw-r--r--crypto/src/math/ec/custom/sec/SecT571FieldElement.cs7
-rw-r--r--crypto/src/math/ec/multiplier/AbstractECMultiplier.cs7
-rw-r--r--crypto/src/math/ec/multiplier/FixedPointCombMultiplier.cs6
-rw-r--r--crypto/src/math/ec/multiplier/FixedPointPreCompInfo.cs14
-rw-r--r--crypto/src/math/ec/multiplier/FixedPointUtilities.cs63
-rw-r--r--crypto/src/math/ec/multiplier/IPreCompCallback.cs9
-rw-r--r--crypto/src/math/ec/multiplier/ValidityPreCompInfo.cs44
-rw-r--r--crypto/src/math/ec/multiplier/WNafUtilities.cs311
-rw-r--r--crypto/src/math/ec/multiplier/WTauNafMultiplier.cs47
-rw-r--r--crypto/src/math/ec/rfc7748/X25519.cs4
-rw-r--r--crypto/src/math/ec/rfc7748/X25519Field.cs147
-rw-r--r--crypto/src/math/ec/rfc7748/X448.cs8
-rw-r--r--crypto/src/math/ec/rfc7748/X448Field.cs123
-rw-r--r--crypto/src/math/ec/rfc8032/Ed25519.cs937
-rw-r--r--crypto/src/math/ec/rfc8032/Ed448.cs1067
-rw-r--r--crypto/src/math/raw/Interleave.cs71
-rw-r--r--crypto/src/math/raw/Nat.cs85
42 files changed, 3039 insertions, 361 deletions
diff --git a/crypto/src/math/ec/ECAlgorithms.cs b/crypto/src/math/ec/ECAlgorithms.cs
index 5d60de40f..b05c0201a 100644
--- a/crypto/src/math/ec/ECAlgorithms.cs
+++ b/crypto/src/math/ec/ECAlgorithms.cs
@@ -58,10 +58,10 @@ namespace Org.BouncyCastle.Math.EC
             GlvEndomorphism glvEndomorphism = c.GetEndomorphism() as GlvEndomorphism;
             if (glvEndomorphism != null)
             {
-                return ValidatePoint(ImplSumOfMultipliesGlv(imported, ks, glvEndomorphism));
+                return ImplCheckResult(ImplSumOfMultipliesGlv(imported, ks, glvEndomorphism));
             }
 
-            return ValidatePoint(ImplSumOfMultiplies(imported, ks));
+            return ImplCheckResult(ImplSumOfMultiplies(imported, ks));
         }
 
         public static ECPoint SumOfTwoMultiplies(ECPoint P, BigInteger a, ECPoint Q, BigInteger b)
@@ -74,18 +74,18 @@ namespace Org.BouncyCastle.Math.EC
                 AbstractF2mCurve f2mCurve = cp as AbstractF2mCurve;
                 if (f2mCurve != null && f2mCurve.IsKoblitz)
                 {
-                    return ValidatePoint(P.Multiply(a).Add(Q.Multiply(b)));
+                    return ImplCheckResult(P.Multiply(a).Add(Q.Multiply(b)));
                 }
             }
 
             GlvEndomorphism glvEndomorphism = cp.GetEndomorphism() as GlvEndomorphism;
             if (glvEndomorphism != null)
             {
-                return ValidatePoint(
+                return ImplCheckResult(
                     ImplSumOfMultipliesGlv(new ECPoint[] { P, Q }, new BigInteger[] { a, b }, glvEndomorphism));
             }
 
-            return ValidatePoint(ImplShamirsTrickWNaf(P, a, Q, b));
+            return ImplCheckResult(ImplShamirsTrickWNaf(P, a, Q, b));
         }
 
         /*
@@ -111,7 +111,7 @@ namespace Org.BouncyCastle.Math.EC
             ECCurve cp = P.Curve;
             Q = ImportPoint(cp, Q);
 
-            return ValidatePoint(ImplShamirsTrickJsf(P, k, Q, l));
+            return ImplCheckResult(ImplShamirsTrickJsf(P, k, Q, l));
         }
 
         public static ECPoint ImportPoint(ECCurve c, ECPoint p)
@@ -202,7 +202,24 @@ namespace Org.BouncyCastle.Math.EC
         public static ECPoint ValidatePoint(ECPoint p)
         {
             if (!p.IsValid())
-                throw new ArgumentException("Invalid point", "p");
+                throw new InvalidOperationException("Invalid point");
+
+            return p;
+        }
+
+        public static ECPoint CleanPoint(ECCurve c, ECPoint p)
+        {
+            ECCurve cp = p.Curve;
+            if (!c.Equals(cp))
+                throw new ArgumentException("Point must be on the same curve", "p");
+
+            return c.DecodePoint(p.GetEncoded(false));
+        }
+
+        internal static ECPoint ImplCheckResult(ECPoint p)
+        {
+            if (!p.IsValidPartial())
+                throw new InvalidOperationException("Invalid result");
 
             return p;
         }
diff --git a/crypto/src/math/ec/ECCurve.cs b/crypto/src/math/ec/ECCurve.cs
index 6a9342722..993b69149 100644
--- a/crypto/src/math/ec/ECCurve.cs
+++ b/crypto/src/math/ec/ECCurve.cs
@@ -161,15 +161,24 @@ namespace Org.BouncyCastle.Math.EC
         public virtual PreCompInfo GetPreCompInfo(ECPoint point, string name)
         {
             CheckPoint(point);
+
+            IDictionary table;
             lock (point)
             {
-                IDictionary table = point.m_preCompTable;
-                return table == null ? null : (PreCompInfo)table[name];
+                table = point.m_preCompTable;
+            }
+
+            if (null == table)
+                return null;
+
+            lock (table)
+            {
+                return (PreCompInfo)table[name];
             }
         }
 
         /**
-         * Adds <code>PreCompInfo</code> for a point on this curve, under a given name. Used by
+         * Compute a <code>PreCompInfo</code> for a point on this curve, under a given name. Used by
          * <code>ECMultiplier</code>s to save the precomputation for this <code>ECPoint</code> for use
          * by subsequent multiplication.
          * 
@@ -177,20 +186,34 @@ namespace Org.BouncyCastle.Math.EC
          *            The <code>ECPoint</code> to store precomputations for.
          * @param name
          *            A <code>String</code> used to index precomputations of different types.
-         * @param preCompInfo
-         *            The values precomputed by the <code>ECMultiplier</code>.
+         * @param callback
+         *            Called to calculate the <code>PreCompInfo</code>.
          */
-        public virtual void SetPreCompInfo(ECPoint point, string name, PreCompInfo preCompInfo)
+        public virtual PreCompInfo Precompute(ECPoint point, string name, IPreCompCallback callback)
         {
             CheckPoint(point);
+
+            IDictionary table;
             lock (point)
             {
-                IDictionary table = point.m_preCompTable;
+                table = point.m_preCompTable;
                 if (null == table)
                 {
                     point.m_preCompTable = table = Platform.CreateHashtable(4);
                 }
-                table[name] = preCompInfo;
+            }
+
+            lock (table)
+            {
+                PreCompInfo existing = (PreCompInfo)table[name];
+                PreCompInfo result = callback.Precompute(existing);
+
+                if (result != existing)
+                {
+                    table[name] = result;
+                }
+
+                return result;
             }
         }
 
@@ -208,7 +231,7 @@ namespace Org.BouncyCastle.Math.EC
             // TODO Default behaviour could be improved if the two curves have the same coordinate system by copying any Z coordinates.
             p = p.Normalize();
 
-            return ValidatePoint(p.XCoord.ToBigInteger(), p.YCoord.ToBigInteger(), p.IsCompressed);
+            return CreatePoint(p.XCoord.ToBigInteger(), p.YCoord.ToBigInteger(), p.IsCompressed);
         }
 
         /**
@@ -453,7 +476,7 @@ namespace Org.BouncyCastle.Math.EC
                     BigInteger X = new BigInteger(1, encoded, 1, expectedLength);
 
                     p = DecompressPoint(yTilde, X);
-                    if (!p.SatisfiesCofactor())
+                    if (!p.ImplIsValid(true, true))
                         throw new ArgumentException("Invalid point");
 
                     break;
@@ -588,6 +611,7 @@ namespace Org.BouncyCastle.Math.EC
         protected readonly BigInteger m_q, m_r;
         protected readonly FpPoint m_infinity;
 
+        [Obsolete("Use constructor taking order/cofactor")]
         public FpCurve(BigInteger q, BigInteger a, BigInteger b)
             : this(q, a, b, null, null)
         {
@@ -598,7 +622,7 @@ namespace Org.BouncyCastle.Math.EC
         {
             this.m_q = q;
             this.m_r = FpFieldElement.CalculateResidue(q);
-            this.m_infinity = new FpPoint(this, null, null);
+            this.m_infinity = new FpPoint(this, null, null, false);
 
             this.m_a = FromBigInteger(a);
             this.m_b = FromBigInteger(b);
@@ -607,6 +631,7 @@ namespace Org.BouncyCastle.Math.EC
             this.m_coord = FP_DEFAULT_COORDS;
         }
 
+        [Obsolete("Use constructor taking order/cofactor")]
         protected FpCurve(BigInteger q, BigInteger r, ECFieldElement a, ECFieldElement b)
             : this(q, r, a, b, null, null)
         {
@@ -617,7 +642,7 @@ namespace Org.BouncyCastle.Math.EC
         {
             this.m_q = q;
             this.m_r = r;
-            this.m_infinity = new FpPoint(this, null, null);
+            this.m_infinity = new FpPoint(this, null, null, false);
 
             this.m_a = a;
             this.m_b = b;
@@ -794,7 +819,7 @@ namespace Org.BouncyCastle.Math.EC
             else
             {
                 ECFieldElement beta = xp.Square().Invert().Multiply(B).Add(A).Add(xp);
-                ECFieldElement z = SolveQuadradicEquation(beta);
+                ECFieldElement z = SolveQuadraticEquation(beta);
 
                 if (z != null)
                 {
@@ -831,11 +856,11 @@ namespace Org.BouncyCastle.Math.EC
          * D.1.6) The other solution is <code>z + 1</code>.
          *
          * @param beta
-         *            The value to solve the qradratic equation for.
+         *            The value to solve the quadratic equation for.
          * @return the solution for <code>z<sup>2</sup> + z = beta</code> or
          *         <code>null</code> if no solution exists.
          */
-        private ECFieldElement SolveQuadradicEquation(ECFieldElement beta)
+        internal ECFieldElement SolveQuadraticEquation(ECFieldElement beta)
         {
             if (beta.IsZero)
                 return beta;
@@ -957,6 +982,7 @@ namespace Org.BouncyCastle.Math.EC
          * for non-supersingular elliptic curves over
          * <code>F<sub>2<sup>m</sup></sub></code>.
          */
+        [Obsolete("Use constructor taking order/cofactor")]
         public F2mCurve(
             int			m,
             int			k,
@@ -1014,6 +1040,7 @@ namespace Org.BouncyCastle.Math.EC
          * for non-supersingular elliptic curves over
          * <code>F<sub>2<sup>m</sup></sub></code>.
          */
+        [Obsolete("Use constructor taking order/cofactor")]
         public F2mCurve(
             int			m,
             int			k1,
@@ -1065,7 +1092,7 @@ namespace Org.BouncyCastle.Math.EC
             this.k3 = k3;
             this.m_order = order;
             this.m_cofactor = cofactor;
-            this.m_infinity = new F2mPoint(this, null, null);
+            this.m_infinity = new F2mPoint(this, null, null, false);
 
             if (k1 == 0)
                 throw new ArgumentException("k1 must be > 0");
@@ -1099,7 +1126,7 @@ namespace Org.BouncyCastle.Math.EC
             this.m_order = order;
             this.m_cofactor = cofactor;
 
-            this.m_infinity = new F2mPoint(this, null, null);
+            this.m_infinity = new F2mPoint(this, null, null, false);
             this.m_a = a;
             this.m_b = b;
             this.m_coord = F2M_DEFAULT_COORDS;
@@ -1188,18 +1215,6 @@ namespace Org.BouncyCastle.Math.EC
             get { return k3; }
         }
 
-        [Obsolete("Use 'Order' property instead")]
-        public BigInteger N
-        {
-            get { return m_order; }
-        }
-
-        [Obsolete("Use 'Cofactor' property instead")]
-        public BigInteger H
-        {
-            get { return m_cofactor; }
-        }
-
         public override ECLookupTable CreateCacheSafeLookupTable(ECPoint[] points, int off, int len)
         {
             int FE_LONGS = (m + 63) / 64;
diff --git a/crypto/src/math/ec/ECFieldElement.cs b/crypto/src/math/ec/ECFieldElement.cs
index 3676c81b1..350e8c6d4 100644
--- a/crypto/src/math/ec/ECFieldElement.cs
+++ b/crypto/src/math/ec/ECFieldElement.cs
@@ -101,9 +101,14 @@ namespace Org.BouncyCastle.Math.EC
         }
     }
 
-    public class FpFieldElement
+    public abstract class AbstractFpFieldElement
         : ECFieldElement
     {
+    }
+
+    public class FpFieldElement
+        : AbstractFpFieldElement
+    {
         private readonly BigInteger q, r, x;
 
         internal static BigInteger CalculateResidue(BigInteger p)
@@ -536,6 +541,45 @@ namespace Org.BouncyCastle.Math.EC
         }
     }
 
+    public abstract class AbstractF2mFieldElement
+        :   ECFieldElement
+    {
+        public virtual ECFieldElement HalfTrace()
+        {
+            int m = FieldSize;
+            if ((m & 1) == 0)
+                throw new InvalidOperationException("Half-trace only defined for odd m");
+
+            ECFieldElement fe = this;
+            ECFieldElement ht = fe;
+            for (int i = 2; i < m; i += 2)
+            {
+                fe = fe.SquarePow(2);
+                ht = ht.Add(fe);
+            }
+
+            return ht;
+        }
+
+        public virtual int Trace()
+        {
+            int m = FieldSize;
+            ECFieldElement fe = this;
+            ECFieldElement tr = fe;
+            for (int i = 1; i < m; ++i)
+            {
+                fe = fe.Square();
+                tr = tr.Add(fe);
+            }
+            if (tr.IsZero)
+                return 0;
+            if (tr.IsOne)
+                return 1;
+
+            throw new InvalidOperationException("Internal error in trace calculation");
+        }
+    }
+
     /**
      * Class representing the Elements of the finite field
      * <code>F<sub>2<sup>m</sup></sub></code> in polynomial basis (PB)
@@ -544,7 +588,7 @@ namespace Org.BouncyCastle.Math.EC
      * representation is not supported.
      */
     public class F2mFieldElement
-        : ECFieldElement
+        :   AbstractF2mFieldElement
     {
         /**
          * Indicates gaussian normal basis representation (GNB). Number chosen
@@ -582,20 +626,21 @@ namespace Org.BouncyCastle.Math.EC
         internal LongArray x;
 
         /**
-            * Constructor for Ppb.
-            * @param m  The exponent <code>m</code> of
-            * <code>F<sub>2<sup>m</sup></sub></code>.
-            * @param k1 The integer <code>k1</code> where <code>x<sup>m</sup> +
-            * x<sup>k3</sup> + x<sup>k2</sup> + x<sup>k1</sup> + 1</code>
-            * represents the reduction polynomial <code>f(z)</code>.
-            * @param k2 The integer <code>k2</code> where <code>x<sup>m</sup> +
-            * x<sup>k3</sup> + x<sup>k2</sup> + x<sup>k1</sup> + 1</code>
-            * represents the reduction polynomial <code>f(z)</code>.
-            * @param k3 The integer <code>k3</code> where <code>x<sup>m</sup> +
-            * x<sup>k3</sup> + x<sup>k2</sup> + x<sup>k1</sup> + 1</code>
-            * represents the reduction polynomial <code>f(z)</code>.
-            * @param x The BigInteger representing the value of the field element.
-            */
+         * Constructor for Ppb.
+         * @param m  The exponent <code>m</code> of
+         * <code>F<sub>2<sup>m</sup></sub></code>.
+         * @param k1 The integer <code>k1</code> where <code>x<sup>m</sup> +
+         * x<sup>k3</sup> + x<sup>k2</sup> + x<sup>k1</sup> + 1</code>
+         * represents the reduction polynomial <code>f(z)</code>.
+         * @param k2 The integer <code>k2</code> where <code>x<sup>m</sup> +
+         * x<sup>k3</sup> + x<sup>k2</sup> + x<sup>k1</sup> + 1</code>
+         * represents the reduction polynomial <code>f(z)</code>.
+         * @param k3 The integer <code>k3</code> where <code>x<sup>m</sup> +
+         * x<sup>k3</sup> + x<sup>k2</sup> + x<sup>k1</sup> + 1</code>
+         * represents the reduction polynomial <code>f(z)</code>.
+         * @param x The BigInteger representing the value of the field element.
+         */
+        [Obsolete("Use ECCurve.FromBigInteger to construct field elements")]
         public F2mFieldElement(
             int			m,
             int			k1,
@@ -627,14 +672,15 @@ namespace Org.BouncyCastle.Math.EC
         }
 
         /**
-            * Constructor for Tpb.
-            * @param m  The exponent <code>m</code> of
-            * <code>F<sub>2<sup>m</sup></sub></code>.
-            * @param k The integer <code>k</code> where <code>x<sup>m</sup> +
-            * x<sup>k</sup> + 1</code> represents the reduction
-            * polynomial <code>f(z)</code>.
-            * @param x The BigInteger representing the value of the field element.
-            */
+         * Constructor for Tpb.
+         * @param m  The exponent <code>m</code> of
+         * <code>F<sub>2<sup>m</sup></sub></code>.
+         * @param k The integer <code>k</code> where <code>x<sup>m</sup> +
+         * x<sup>k</sup> + 1</code> represents the reduction
+         * polynomial <code>f(z)</code>.
+         * @param x The BigInteger representing the value of the field element.
+         */
+        [Obsolete("Use ECCurve.FromBigInteger to construct field elements")]
         public F2mFieldElement(
             int			m,
             int			k,
diff --git a/crypto/src/math/ec/ECPoint.cs b/crypto/src/math/ec/ECPoint.cs
index a5ba515c5..2acc9f5c0 100644
--- a/crypto/src/math/ec/ECPoint.cs
+++ b/crypto/src/math/ec/ECPoint.cs
@@ -67,13 +67,19 @@ namespace Org.BouncyCastle.Math.EC
             this.m_withCompression = withCompression;
         }
 
-        protected internal bool SatisfiesCofactor()
+        protected abstract bool SatisfiesCurveEquation();
+
+        protected virtual bool SatisfiesOrder()
         {
-            BigInteger h = Curve.Cofactor;
-            return h == null || h.Equals(BigInteger.One) || !ECAlgorithms.ReferenceMultiply(this, h).IsInfinity;
-        }
+            if (BigInteger.One.Equals(Curve.Cofactor))
+                return true;
 
-        protected abstract bool SatisfiesCurveEquation();
+            BigInteger n = Curve.Order;
+
+            // TODO Require order to be available for all curves
+
+            return n == null || ECAlgorithms.ReferenceMultiply(this, n).IsInfinity;
+        }
 
         public ECPoint GetDetachedPoint()
         {
@@ -97,30 +103,6 @@ namespace Org.BouncyCastle.Math.EC
         }
 
         /**
-         * Normalizes this point, and then returns the affine x-coordinate.
-         * 
-         * Note: normalization can be expensive, this method is deprecated in favour
-         * of caller-controlled normalization.
-         */
-        [Obsolete("Use AffineXCoord, or Normalize() and XCoord, instead")]
-        public virtual ECFieldElement X
-        {
-            get { return Normalize().XCoord; }
-        }
-
-        /**
-         * Normalizes this point, and then returns the affine y-coordinate.
-         * 
-         * Note: normalization can be expensive, this method is deprecated in favour
-         * of caller-controlled normalization.
-         */
-        [Obsolete("Use AffineYCoord, or Normalize() and YCoord, instead")]
-        public virtual ECFieldElement Y
-        {
-            get { return Normalize().YCoord; }
-        }
-
-        /**
          * Returns the affine x-coordinate after checking that this point is normalized.
          * 
          * @return The affine x-coordinate of this point
@@ -299,22 +281,22 @@ namespace Org.BouncyCastle.Math.EC
 
         public bool IsValid()
         {
-            if (IsInfinity)
-                return true;
-
-            // TODO Sanity-check the field elements
+            return ImplIsValid(false, true);
+        }
 
-            ECCurve curve = Curve;
-            if (curve != null)
-            {
-                if (!SatisfiesCurveEquation())
-                    return false;
+        internal bool IsValidPartial()
+        {
+            return ImplIsValid(false, false);
+        }
 
-                if (!SatisfiesCofactor())
-                    return false;
-            }
+        internal bool ImplIsValid(bool decompressed, bool checkOrder)
+        {
+            if (IsInfinity)
+                return true;
 
-            return true;
+            ValidityCallback callback = new ValidityCallback(this, decompressed, checkOrder);
+            ValidityPreCompInfo validity = (ValidityPreCompInfo)Curve.Precompute(this, ValidityPreCompInfo.PRECOMP_NAME, callback);
+            return !validity.HasFailed();
         }
 
         public virtual ECPoint ScaleX(ECFieldElement scale)
@@ -462,6 +444,52 @@ namespace Org.BouncyCastle.Math.EC
         {
             return TwicePlus(this);
         }
+
+        private class ValidityCallback
+            : IPreCompCallback
+        {
+            private readonly ECPoint m_outer;
+            private readonly bool m_decompressed, m_checkOrder;
+
+            internal ValidityCallback(ECPoint outer, bool decompressed, bool checkOrder)
+            {
+                this.m_outer = outer;
+                this.m_decompressed = decompressed;
+                this.m_checkOrder = checkOrder;
+            }
+
+            public PreCompInfo Precompute(PreCompInfo existing)
+            {
+                ValidityPreCompInfo info = existing as ValidityPreCompInfo;
+                if (info == null)
+                {
+                    info = new ValidityPreCompInfo();
+                }
+
+                if (info.HasFailed())
+                    return info;
+
+                if (!info.HasCurveEquationPassed())
+                {
+                    if (!m_decompressed && !m_outer.SatisfiesCurveEquation())
+                    {
+                        info.ReportFailed();
+                        return info;
+                    }
+                    info.ReportCurveEquationPassed();
+                }
+                if (m_checkOrder && !info.HasOrderPassed())
+                {
+                    if (!m_outer.SatisfiesOrder())
+                    {
+                        info.ReportFailed();
+                        return info;
+                    }
+                    info.ReportOrderPassed();
+                }
+                return info;
+            }
+        }
     }
 
     public abstract class ECPointBase
@@ -608,6 +636,7 @@ namespace Org.BouncyCastle.Math.EC
          * @param x affine x co-ordinate
          * @param y affine y co-ordinate
          */
+        [Obsolete("Use ECCurve.CreatePoint to construct points")]
         public FpPoint(ECCurve curve, ECFieldElement x, ECFieldElement y)
             : this(curve, x, y, false)
         {
@@ -621,6 +650,7 @@ namespace Org.BouncyCastle.Math.EC
          * @param y affine y co-ordinate
          * @param withCompression if true encode with point compression
          */
+        [Obsolete("Per-point compression property will be removed, see GetEncoded(bool)")]
         public FpPoint(ECCurve curve, ECFieldElement x, ECFieldElement y, bool withCompression)
             : base(curve, x, y, withCompression)
         {
@@ -635,7 +665,7 @@ namespace Org.BouncyCastle.Math.EC
 
         protected override ECPoint Detach()
         {
-            return new FpPoint(null, AffineXCoord, AffineYCoord);
+            return new FpPoint(null, AffineXCoord, AffineYCoord, false);
         }
 
         public override ECFieldElement GetZCoord(int index)
@@ -1384,6 +1414,46 @@ namespace Org.BouncyCastle.Math.EC
             return lhs.Equals(rhs);
         }
 
+        protected override bool SatisfiesOrder()
+        {
+            ECCurve curve = Curve;
+            BigInteger cofactor = curve.Cofactor;
+            if (BigInteger.Two.Equals(cofactor))
+            {
+                /*
+                 *  Check that the trace of (X + A) is 0, then there exists a solution to L^2 + L = X + A,
+                 *  and so a halving is possible, so this point is the double of another.  
+                 */
+                ECPoint N = this.Normalize();
+                ECFieldElement X = N.AffineXCoord;
+                ECFieldElement rhs = X.Add(curve.A);
+                return ((AbstractF2mFieldElement)rhs).Trace() == 0;
+            }
+            if (BigInteger.ValueOf(4).Equals(cofactor))
+            {
+                /*
+                 * Solve L^2 + L = X + A to find the half of this point, if it exists (fail if not).
+                 * Generate both possibilities for the square of the half-point's x-coordinate (w),
+                 * and check if Tr(w + A) == 0 for at least one; then a second halving is possible
+                 * (see comments for cofactor 2 above), so this point is four times another.
+                 * 
+                 * Note: Tr(x^2) == Tr(x). 
+                 */
+                ECPoint N = this.Normalize();
+                ECFieldElement X = N.AffineXCoord;
+                ECFieldElement lambda = ((AbstractF2mCurve)curve).SolveQuadraticEquation(X.Add(curve.A));
+                if (lambda == null)
+                    return false;
+
+                ECFieldElement w = X.Multiply(lambda).Add(N.AffineYCoord);
+                ECFieldElement t = w.Add(curve.A);
+                return ((AbstractF2mFieldElement)t).Trace() == 0
+                    || ((AbstractF2mFieldElement)(t.Add(X))).Trace() == 0;
+            }
+
+            return base.SatisfiesOrder();
+        }
+
         public override ECPoint ScaleX(ECFieldElement scale)
         {
             if (this.IsInfinity)
@@ -1529,6 +1599,7 @@ namespace Org.BouncyCastle.Math.EC
          * @param x x point
          * @param y y point
          */
+        [Obsolete("Use ECCurve.CreatePoint to construct points")]
         public F2mPoint(
             ECCurve			curve,
             ECFieldElement	x,
@@ -1543,6 +1614,7 @@ namespace Org.BouncyCastle.Math.EC
          * @param y y point
          * @param withCompression true if encode with point compression.
          */
+        [Obsolete("Per-point compression property will be removed, see GetEncoded(bool)")]
         public F2mPoint(
             ECCurve			curve,
             ECFieldElement	x,
@@ -1573,19 +1645,9 @@ namespace Org.BouncyCastle.Math.EC
         {
         }
 
-        /**
-         * Constructor for point at infinity
-         */
-        [Obsolete("Use ECCurve.Infinity property")]
-        public F2mPoint(
-            ECCurve curve)
-            : this(curve, null, null)
-        {
-        }
-
         protected override ECPoint Detach()
         {
-            return new F2mPoint(null, AffineXCoord, AffineYCoord);
+            return new F2mPoint(null, AffineXCoord, AffineYCoord, false);
         }
 
         public override ECFieldElement YCoord
diff --git a/crypto/src/math/ec/custom/djb/Curve25519FieldElement.cs b/crypto/src/math/ec/custom/djb/Curve25519FieldElement.cs
index 732e9e468..37256a550 100644
--- a/crypto/src/math/ec/custom/djb/Curve25519FieldElement.cs
+++ b/crypto/src/math/ec/custom/djb/Curve25519FieldElement.cs
@@ -6,7 +6,7 @@ using Org.BouncyCastle.Utilities;
 namespace Org.BouncyCastle.Math.EC.Custom.Djb
 {
     internal class Curve25519FieldElement
-        :   ECFieldElement
+        : AbstractFpFieldElement
     {
         public static readonly BigInteger Q = Curve25519.q;
 
diff --git a/crypto/src/math/ec/custom/gm/SM2P256V1FieldElement.cs b/crypto/src/math/ec/custom/gm/SM2P256V1FieldElement.cs
index 4f6428f9e..087a040f2 100644
--- a/crypto/src/math/ec/custom/gm/SM2P256V1FieldElement.cs
+++ b/crypto/src/math/ec/custom/gm/SM2P256V1FieldElement.cs
@@ -6,7 +6,7 @@ using Org.BouncyCastle.Utilities;
 namespace Org.BouncyCastle.Math.EC.Custom.GM
 {
     internal class SM2P256V1FieldElement
-        : ECFieldElement
+        : AbstractFpFieldElement
     {
         public static readonly BigInteger Q = SM2P256V1Curve.q;
 
diff --git a/crypto/src/math/ec/custom/sec/SecP128R1FieldElement.cs b/crypto/src/math/ec/custom/sec/SecP128R1FieldElement.cs
index fa7951d5d..5912a87e8 100644
--- a/crypto/src/math/ec/custom/sec/SecP128R1FieldElement.cs
+++ b/crypto/src/math/ec/custom/sec/SecP128R1FieldElement.cs
@@ -6,7 +6,7 @@ using Org.BouncyCastle.Utilities;
 namespace Org.BouncyCastle.Math.EC.Custom.Sec
 {
     internal class SecP128R1FieldElement
-        : ECFieldElement
+        : AbstractFpFieldElement
     {
         public static readonly BigInteger Q = SecP128R1Curve.q;
 
diff --git a/crypto/src/math/ec/custom/sec/SecP160R1FieldElement.cs b/crypto/src/math/ec/custom/sec/SecP160R1FieldElement.cs
index d1fc75644..3ab11bdae 100644
--- a/crypto/src/math/ec/custom/sec/SecP160R1FieldElement.cs
+++ b/crypto/src/math/ec/custom/sec/SecP160R1FieldElement.cs
@@ -6,7 +6,7 @@ using Org.BouncyCastle.Utilities;
 namespace Org.BouncyCastle.Math.EC.Custom.Sec
 {
     internal class SecP160R1FieldElement
-        : ECFieldElement
+        : AbstractFpFieldElement
     {
         public static readonly BigInteger Q = SecP160R1Curve.q;
 
diff --git a/crypto/src/math/ec/custom/sec/SecP160R2FieldElement.cs b/crypto/src/math/ec/custom/sec/SecP160R2FieldElement.cs
index bdb5245b2..9d8131857 100644
--- a/crypto/src/math/ec/custom/sec/SecP160R2FieldElement.cs
+++ b/crypto/src/math/ec/custom/sec/SecP160R2FieldElement.cs
@@ -6,7 +6,7 @@ using Org.BouncyCastle.Utilities;
 namespace Org.BouncyCastle.Math.EC.Custom.Sec
 {
     internal class SecP160R2FieldElement
-        : ECFieldElement
+        : AbstractFpFieldElement
     {
         public static readonly BigInteger Q = SecP160R2Curve.q;
 
diff --git a/crypto/src/math/ec/custom/sec/SecP192K1FieldElement.cs b/crypto/src/math/ec/custom/sec/SecP192K1FieldElement.cs
index dce377035..54b72573c 100644
--- a/crypto/src/math/ec/custom/sec/SecP192K1FieldElement.cs
+++ b/crypto/src/math/ec/custom/sec/SecP192K1FieldElement.cs
@@ -7,7 +7,7 @@ using Org.BouncyCastle.Utilities;
 namespace Org.BouncyCastle.Math.EC.Custom.Sec
 {
     internal class SecP192K1FieldElement
-        : ECFieldElement
+        : AbstractFpFieldElement
     {
         public static readonly BigInteger Q = SecP192K1Curve.q;
 
diff --git a/crypto/src/math/ec/custom/sec/SecP192R1FieldElement.cs b/crypto/src/math/ec/custom/sec/SecP192R1FieldElement.cs
index 45bcb00f0..f3e12b542 100644
--- a/crypto/src/math/ec/custom/sec/SecP192R1FieldElement.cs
+++ b/crypto/src/math/ec/custom/sec/SecP192R1FieldElement.cs
@@ -6,7 +6,7 @@ using Org.BouncyCastle.Utilities;
 namespace Org.BouncyCastle.Math.EC.Custom.Sec
 {
     internal class SecP192R1FieldElement
-        : ECFieldElement
+        : AbstractFpFieldElement
     {
         public static readonly BigInteger Q = SecP192R1Curve.q;
 
diff --git a/crypto/src/math/ec/custom/sec/SecP224K1FieldElement.cs b/crypto/src/math/ec/custom/sec/SecP224K1FieldElement.cs
index fec07436a..ef53a88d6 100644
--- a/crypto/src/math/ec/custom/sec/SecP224K1FieldElement.cs
+++ b/crypto/src/math/ec/custom/sec/SecP224K1FieldElement.cs
@@ -7,7 +7,7 @@ using Org.BouncyCastle.Utilities;
 namespace Org.BouncyCastle.Math.EC.Custom.Sec
 {
     internal class SecP224K1FieldElement
-        : ECFieldElement
+        : AbstractFpFieldElement
     {
         public static readonly BigInteger Q = SecP224K1Curve.q;
 
diff --git a/crypto/src/math/ec/custom/sec/SecP224R1FieldElement.cs b/crypto/src/math/ec/custom/sec/SecP224R1FieldElement.cs
index 2b9a06564..5780b7481 100644
--- a/crypto/src/math/ec/custom/sec/SecP224R1FieldElement.cs
+++ b/crypto/src/math/ec/custom/sec/SecP224R1FieldElement.cs
@@ -6,7 +6,7 @@ using Org.BouncyCastle.Utilities;
 namespace Org.BouncyCastle.Math.EC.Custom.Sec
 {
     internal class SecP224R1FieldElement
-        : ECFieldElement
+        : AbstractFpFieldElement
     {
         public static readonly BigInteger Q = SecP224R1Curve.q;
 
diff --git a/crypto/src/math/ec/custom/sec/SecP256K1FieldElement.cs b/crypto/src/math/ec/custom/sec/SecP256K1FieldElement.cs
index 473113d0f..9a604bdb7 100644
--- a/crypto/src/math/ec/custom/sec/SecP256K1FieldElement.cs
+++ b/crypto/src/math/ec/custom/sec/SecP256K1FieldElement.cs
@@ -7,7 +7,7 @@ using Org.BouncyCastle.Utilities;
 namespace Org.BouncyCastle.Math.EC.Custom.Sec
 {
     internal class SecP256K1FieldElement
-        : ECFieldElement
+        : AbstractFpFieldElement
     {
         public static readonly BigInteger Q = SecP256K1Curve.q;
 
diff --git a/crypto/src/math/ec/custom/sec/SecP256R1FieldElement.cs b/crypto/src/math/ec/custom/sec/SecP256R1FieldElement.cs
index d7838aead..808e99ea6 100644
--- a/crypto/src/math/ec/custom/sec/SecP256R1FieldElement.cs
+++ b/crypto/src/math/ec/custom/sec/SecP256R1FieldElement.cs
@@ -6,7 +6,7 @@ using Org.BouncyCastle.Utilities;
 namespace Org.BouncyCastle.Math.EC.Custom.Sec
 {
     internal class SecP256R1FieldElement
-        : ECFieldElement
+        : AbstractFpFieldElement
     {
         public static readonly BigInteger Q = SecP256R1Curve.q;
 
diff --git a/crypto/src/math/ec/custom/sec/SecP384R1FieldElement.cs b/crypto/src/math/ec/custom/sec/SecP384R1FieldElement.cs
index 18d48a57d..7eedccae6 100644
--- a/crypto/src/math/ec/custom/sec/SecP384R1FieldElement.cs
+++ b/crypto/src/math/ec/custom/sec/SecP384R1FieldElement.cs
@@ -6,7 +6,7 @@ using Org.BouncyCastle.Utilities;
 namespace Org.BouncyCastle.Math.EC.Custom.Sec
 {
     internal class SecP384R1FieldElement
-        : ECFieldElement
+        : AbstractFpFieldElement
     {
         public static readonly BigInteger Q = SecP384R1Curve.q;
 
diff --git a/crypto/src/math/ec/custom/sec/SecP521R1FieldElement.cs b/crypto/src/math/ec/custom/sec/SecP521R1FieldElement.cs
index 6f02a7eb5..96658a8e5 100644
--- a/crypto/src/math/ec/custom/sec/SecP521R1FieldElement.cs
+++ b/crypto/src/math/ec/custom/sec/SecP521R1FieldElement.cs
@@ -6,7 +6,7 @@ using Org.BouncyCastle.Utilities;
 namespace Org.BouncyCastle.Math.EC.Custom.Sec
 {
     internal class SecP521R1FieldElement
-        : ECFieldElement
+        : AbstractFpFieldElement
     {
         public static readonly BigInteger Q = SecP521R1Curve.q;
 
diff --git a/crypto/src/math/ec/custom/sec/SecT113FieldElement.cs b/crypto/src/math/ec/custom/sec/SecT113FieldElement.cs
index 9ba25d987..bb87b00fc 100644
--- a/crypto/src/math/ec/custom/sec/SecT113FieldElement.cs
+++ b/crypto/src/math/ec/custom/sec/SecT113FieldElement.cs
@@ -6,7 +6,7 @@ using Org.BouncyCastle.Utilities;
 namespace Org.BouncyCastle.Math.EC.Custom.Sec
 {
     internal class SecT113FieldElement
-        : ECFieldElement
+        : AbstractF2mFieldElement
     {
         protected internal readonly ulong[] x;
 
@@ -150,6 +150,11 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             return new SecT113FieldElement(z);
         }
 
+        public override int Trace()
+        {
+            return (int)SecT113Field.Trace(x);
+        }
+
         public override ECFieldElement Invert()
         {
             ulong[] z = Nat128.Create64();
diff --git a/crypto/src/math/ec/custom/sec/SecT131FieldElement.cs b/crypto/src/math/ec/custom/sec/SecT131FieldElement.cs
index c38e8eb0a..f96c7ca39 100644
--- a/crypto/src/math/ec/custom/sec/SecT131FieldElement.cs
+++ b/crypto/src/math/ec/custom/sec/SecT131FieldElement.cs
@@ -6,7 +6,7 @@ using Org.BouncyCastle.Utilities;
 namespace Org.BouncyCastle.Math.EC.Custom.Sec
 {
     internal class SecT131FieldElement
-        : ECFieldElement
+        : AbstractF2mFieldElement
     {
         protected internal readonly ulong[] x;
 
@@ -150,6 +150,11 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             return new SecT131FieldElement(z);
         }
 
+        public override int Trace()
+        {
+            return (int)SecT131Field.Trace(x);
+        }
+
         public override ECFieldElement Invert()
         {
             ulong[] z = Nat192.Create64();
diff --git a/crypto/src/math/ec/custom/sec/SecT163FieldElement.cs b/crypto/src/math/ec/custom/sec/SecT163FieldElement.cs
index 07bd07652..903645999 100644
--- a/crypto/src/math/ec/custom/sec/SecT163FieldElement.cs
+++ b/crypto/src/math/ec/custom/sec/SecT163FieldElement.cs
@@ -6,7 +6,7 @@ using Org.BouncyCastle.Utilities;
 namespace Org.BouncyCastle.Math.EC.Custom.Sec
 {
     internal class SecT163FieldElement
-        : ECFieldElement
+        : AbstractF2mFieldElement
     {
         protected internal readonly ulong[] x;
 
@@ -150,6 +150,11 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             return new SecT163FieldElement(z);
         }
 
+        public override int Trace()
+        {
+            return (int)SecT163Field.Trace(x);
+        }
+
         public override ECFieldElement Invert()
         {
             ulong[] z = Nat192.Create64();
diff --git a/crypto/src/math/ec/custom/sec/SecT193FieldElement.cs b/crypto/src/math/ec/custom/sec/SecT193FieldElement.cs
index d04e68d3f..9813bcb01 100644
--- a/crypto/src/math/ec/custom/sec/SecT193FieldElement.cs
+++ b/crypto/src/math/ec/custom/sec/SecT193FieldElement.cs
@@ -6,7 +6,7 @@ using Org.BouncyCastle.Utilities;
 namespace Org.BouncyCastle.Math.EC.Custom.Sec
 {
     internal class SecT193FieldElement
-        : ECFieldElement
+        : AbstractF2mFieldElement
     {
         protected internal readonly ulong[] x;
 
@@ -150,6 +150,11 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             return new SecT193FieldElement(z);
         }
 
+        public override int Trace()
+        {
+            return (int)SecT193Field.Trace(x);
+        }
+
         public override ECFieldElement Invert()
         {
             ulong[] z = Nat256.Create64();
diff --git a/crypto/src/math/ec/custom/sec/SecT233FieldElement.cs b/crypto/src/math/ec/custom/sec/SecT233FieldElement.cs
index 64d09bd6d..fbfe35e13 100644
--- a/crypto/src/math/ec/custom/sec/SecT233FieldElement.cs
+++ b/crypto/src/math/ec/custom/sec/SecT233FieldElement.cs
@@ -6,7 +6,7 @@ using Org.BouncyCastle.Utilities;
 namespace Org.BouncyCastle.Math.EC.Custom.Sec
 {
     internal class SecT233FieldElement
-        : ECFieldElement
+        : AbstractF2mFieldElement
     {
         protected internal readonly ulong[] x;
 
@@ -150,6 +150,11 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             return new SecT233FieldElement(z);
         }
 
+        public override int Trace()
+        {
+            return (int)SecT233Field.Trace(x);
+        }
+
         public override ECFieldElement Invert()
         {
             ulong[] z = Nat256.Create64();
diff --git a/crypto/src/math/ec/custom/sec/SecT239FieldElement.cs b/crypto/src/math/ec/custom/sec/SecT239FieldElement.cs
index 18563f746..b1b58e89b 100644
--- a/crypto/src/math/ec/custom/sec/SecT239FieldElement.cs
+++ b/crypto/src/math/ec/custom/sec/SecT239FieldElement.cs
@@ -6,7 +6,7 @@ using Org.BouncyCastle.Utilities;
 namespace Org.BouncyCastle.Math.EC.Custom.Sec
 {
     internal class SecT239FieldElement
-        : ECFieldElement
+        : AbstractF2mFieldElement
     {
         protected internal readonly ulong[] x;
 
@@ -150,6 +150,11 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             return new SecT239FieldElement(z);
         }
 
+        public override int Trace()
+        {
+            return (int)SecT239Field.Trace(x);
+        }
+
         public override ECFieldElement Invert()
         {
             ulong[] z = Nat256.Create64();
diff --git a/crypto/src/math/ec/custom/sec/SecT283FieldElement.cs b/crypto/src/math/ec/custom/sec/SecT283FieldElement.cs
index b054bedfb..c1bb2e30c 100644
--- a/crypto/src/math/ec/custom/sec/SecT283FieldElement.cs
+++ b/crypto/src/math/ec/custom/sec/SecT283FieldElement.cs
@@ -6,7 +6,7 @@ using Org.BouncyCastle.Utilities;
 namespace Org.BouncyCastle.Math.EC.Custom.Sec
 {
     internal class SecT283FieldElement
-        : ECFieldElement
+        : AbstractF2mFieldElement
     {
         protected internal readonly ulong[] x;
 
@@ -150,6 +150,11 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             return new SecT283FieldElement(z);
         }
 
+        public override int Trace()
+        {
+            return (int)SecT283Field.Trace(x);
+        }
+
         public override ECFieldElement Invert()
         {
             ulong[] z = Nat320.Create64();
diff --git a/crypto/src/math/ec/custom/sec/SecT409FieldElement.cs b/crypto/src/math/ec/custom/sec/SecT409FieldElement.cs
index 7076905bb..68a63312d 100644
--- a/crypto/src/math/ec/custom/sec/SecT409FieldElement.cs
+++ b/crypto/src/math/ec/custom/sec/SecT409FieldElement.cs
@@ -6,7 +6,7 @@ using Org.BouncyCastle.Utilities;
 namespace Org.BouncyCastle.Math.EC.Custom.Sec
 {
     internal class SecT409FieldElement
-        : ECFieldElement
+        : AbstractF2mFieldElement
     {
         protected internal readonly ulong[] x;
 
@@ -150,6 +150,11 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             return new SecT409FieldElement(z);
         }
 
+        public override int Trace()
+        {
+            return (int)SecT409Field.Trace(x);
+        }
+
         public override ECFieldElement Invert()
         {
             ulong[] z = Nat448.Create64();
diff --git a/crypto/src/math/ec/custom/sec/SecT571FieldElement.cs b/crypto/src/math/ec/custom/sec/SecT571FieldElement.cs
index 5f28c01be..c9f3aa5c0 100644
--- a/crypto/src/math/ec/custom/sec/SecT571FieldElement.cs
+++ b/crypto/src/math/ec/custom/sec/SecT571FieldElement.cs
@@ -6,7 +6,7 @@ using Org.BouncyCastle.Utilities;
 namespace Org.BouncyCastle.Math.EC.Custom.Sec
 {
     internal class SecT571FieldElement
-        : ECFieldElement
+        : AbstractF2mFieldElement
     {
         protected internal readonly ulong[] x;
 
@@ -150,6 +150,11 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             return new SecT571FieldElement(z);
         }
 
+        public override int Trace()
+        {
+            return (int)SecT571Field.Trace(x);
+        }
+
         public override ECFieldElement Invert()
         {
             ulong[] z = Nat576.Create64();
diff --git a/crypto/src/math/ec/multiplier/AbstractECMultiplier.cs b/crypto/src/math/ec/multiplier/AbstractECMultiplier.cs
index 517881323..c2580c852 100644
--- a/crypto/src/math/ec/multiplier/AbstractECMultiplier.cs
+++ b/crypto/src/math/ec/multiplier/AbstractECMultiplier.cs
@@ -16,9 +16,14 @@
              * Although the various multipliers ought not to produce invalid output under normal
              * circumstances, a final check here is advised to guard against fault attacks.
              */
-            return ECAlgorithms.ValidatePoint(result);
+            return CheckResult(result);
         }
 
         protected abstract ECPoint MultiplyPositive(ECPoint p, BigInteger k);
+
+        protected virtual ECPoint CheckResult(ECPoint p)
+        {
+            return ECAlgorithms.ImplCheckResult(p);
+        }
     }
 }
diff --git a/crypto/src/math/ec/multiplier/FixedPointCombMultiplier.cs b/crypto/src/math/ec/multiplier/FixedPointCombMultiplier.cs
index adaedb809..505832442 100644
--- a/crypto/src/math/ec/multiplier/FixedPointCombMultiplier.cs
+++ b/crypto/src/math/ec/multiplier/FixedPointCombMultiplier.cs
@@ -52,11 +52,5 @@ namespace Org.BouncyCastle.Math.EC.Multiplier
 
             return R.Add(info.Offset);
         }
-
-        [Obsolete("Is no longer used; remove any overrides in subclasses.")]
-        protected virtual int GetWidthForCombSize(int combSize)
-        {
-            return combSize > 257 ? 6 : 5;
-        }
     }
 }
diff --git a/crypto/src/math/ec/multiplier/FixedPointPreCompInfo.cs b/crypto/src/math/ec/multiplier/FixedPointPreCompInfo.cs
index 4c0b404df..5d6af9e5d 100644
--- a/crypto/src/math/ec/multiplier/FixedPointPreCompInfo.cs
+++ b/crypto/src/math/ec/multiplier/FixedPointPreCompInfo.cs
@@ -11,13 +11,6 @@ namespace Org.BouncyCastle.Math.EC.Multiplier
         protected ECPoint m_offset = null;
 
         /**
-         * Array holding the precomputed <code>ECPoint</code>s used for a fixed
-         * point multiplication.
-         */
-        [Obsolete("Will be removed")]
-		protected ECPoint[] m_preComp = null;
-
-        /**
          * Lookup table for the precomputed <code>ECPoint</code>s used for a fixed point multiplication.
          */
         protected ECLookupTable m_lookupTable = null;
@@ -41,13 +34,6 @@ namespace Org.BouncyCastle.Math.EC.Multiplier
 			set { this.m_offset = value; }
 		}
 
-        [Obsolete("Use 'LookupTable' property instead.")]
-        public virtual ECPoint[] PreComp
-        {
-            get { return m_preComp; }
-            set { this.m_preComp = value; }
-        }
-
         public virtual int Width
         {
             get { return m_width; }
diff --git a/crypto/src/math/ec/multiplier/FixedPointUtilities.cs b/crypto/src/math/ec/multiplier/FixedPointUtilities.cs
index cc7203314..88f178e24 100644
--- a/crypto/src/math/ec/multiplier/FixedPointUtilities.cs
+++ b/crypto/src/math/ec/multiplier/FixedPointUtilities.cs
@@ -14,36 +14,40 @@ namespace Org.BouncyCastle.Math.EC.Multiplier
 
         public static FixedPointPreCompInfo GetFixedPointPreCompInfo(PreCompInfo preCompInfo)
         {
-            if ((preCompInfo != null) && (preCompInfo is FixedPointPreCompInfo))
-            {
-                return (FixedPointPreCompInfo)preCompInfo;
-            }
-
-            return new FixedPointPreCompInfo();
+            return preCompInfo as FixedPointPreCompInfo;
         }
 
-        [Obsolete("Use 'Precompute(ECPoint)' instead, as minWidth parameter is now ignored")]
-        public static FixedPointPreCompInfo Precompute(ECPoint p, int minWidth)
+        public static FixedPointPreCompInfo Precompute(ECPoint p)
         {
-            return Precompute(p);
+            return (FixedPointPreCompInfo)p.Curve.Precompute(p, PRECOMP_NAME, new FixedPointCallback(p));
         }
 
-        public static FixedPointPreCompInfo Precompute(ECPoint p)
+        private class FixedPointCallback
+            : IPreCompCallback
         {
-            ECCurve c = p.Curve;
-            int minWidth = GetCombSize(c) > 257 ? 6 : 5;
+            private readonly ECPoint m_p;
 
-            int n = 1 << minWidth;
-            FixedPointPreCompInfo info = GetFixedPointPreCompInfo(c.GetPreCompInfo(p, PRECOMP_NAME));
-            ECPoint[] lookupTable = info.PreComp;
+            internal FixedPointCallback(ECPoint p)
+            {
+                this.m_p = p;
+            }
 
-            if (lookupTable == null || lookupTable.Length < n)
+            public PreCompInfo Precompute(PreCompInfo existing)
             {
-                int bits = GetCombSize(c);
+                FixedPointPreCompInfo existingFP = (existing is FixedPointPreCompInfo) ? (FixedPointPreCompInfo)existing : null;
+
+                ECCurve c = m_p.Curve;
+                int bits = FixedPointUtilities.GetCombSize(c);
+                int minWidth = bits > 250 ? 6 : 5;
+                int n = 1 << minWidth;
+
+                if (CheckExisting(existingFP, n))
+                    return existingFP;
+
                 int d = (bits + minWidth - 1) / minWidth;
 
                 ECPoint[] pow2Table = new ECPoint[minWidth + 1];
-                pow2Table[0] = p;
+                pow2Table[0] = m_p;
                 for (int i = 1; i < minWidth; ++i)
                 {
                     pow2Table[i] = pow2Table[i - 1].TimesPow2(d);
@@ -53,8 +57,8 @@ namespace Org.BouncyCastle.Math.EC.Multiplier
                 pow2Table[minWidth] = pow2Table[0].Subtract(pow2Table[1]);
 
                 c.NormalizeAll(pow2Table);
-    
-                lookupTable = new ECPoint[n];
+
+                ECPoint[] lookupTable = new ECPoint[n];
                 lookupTable[0] = pow2Table[0];
 
                 for (int bit = minWidth - 1; bit >= 0; --bit)
@@ -70,15 +74,22 @@ namespace Org.BouncyCastle.Math.EC.Multiplier
 
                 c.NormalizeAll(lookupTable);
 
-                info.LookupTable = c.CreateCacheSafeLookupTable(lookupTable, 0, lookupTable.Length);
-                info.Offset = pow2Table[minWidth];
-                info.PreComp = lookupTable;
-                info.Width = minWidth;
+                FixedPointPreCompInfo result = new FixedPointPreCompInfo();
+                result.LookupTable = c.CreateCacheSafeLookupTable(lookupTable, 0, lookupTable.Length);
+                result.Offset = pow2Table[minWidth];
+                result.Width = minWidth;
+                return result;
+            }
 
-                c.SetPreCompInfo(p, PRECOMP_NAME, info);
+            private bool CheckExisting(FixedPointPreCompInfo existingFP, int n)
+            {
+                return existingFP != null && CheckTable(existingFP.LookupTable, n);
             }
 
-            return info;
+            private bool CheckTable(ECLookupTable table, int n)
+            {
+                return table != null && table.Size >= n;
+            }
         }
     }
 }
diff --git a/crypto/src/math/ec/multiplier/IPreCompCallback.cs b/crypto/src/math/ec/multiplier/IPreCompCallback.cs
new file mode 100644
index 000000000..e64ae834d
--- /dev/null
+++ b/crypto/src/math/ec/multiplier/IPreCompCallback.cs
@@ -0,0 +1,9 @@
+using System;
+
+namespace Org.BouncyCastle.Math.EC.Multiplier
+{
+    public interface IPreCompCallback
+    {
+        PreCompInfo Precompute(PreCompInfo existing);
+    }
+}
diff --git a/crypto/src/math/ec/multiplier/ValidityPreCompInfo.cs b/crypto/src/math/ec/multiplier/ValidityPreCompInfo.cs
new file mode 100644
index 000000000..7ec2cbb95
--- /dev/null
+++ b/crypto/src/math/ec/multiplier/ValidityPreCompInfo.cs
@@ -0,0 +1,44 @@
+using System;
+
+namespace Org.BouncyCastle.Math.EC.Multiplier
+{
+    internal class ValidityPreCompInfo
+        : PreCompInfo
+    {
+        internal static readonly string PRECOMP_NAME = "bc_validity";
+
+        private bool failed = false;
+        private bool curveEquationPassed = false;
+        private bool orderPassed = false;
+
+        internal bool HasFailed()
+        {
+            return failed;
+        }
+
+        internal void ReportFailed()
+        {
+            failed = true;
+        }
+
+        internal bool HasCurveEquationPassed()
+        {
+            return curveEquationPassed;
+        }
+
+        internal void ReportCurveEquationPassed()
+        {
+            curveEquationPassed = true;
+        }
+
+        internal bool HasOrderPassed()
+        {
+            return orderPassed;
+        }
+
+        internal void ReportOrderPassed()
+        {
+            orderPassed = true;
+        }
+    }
+}
diff --git a/crypto/src/math/ec/multiplier/WNafUtilities.cs b/crypto/src/math/ec/multiplier/WNafUtilities.cs
index 7d565dfbd..e893abd49 100644
--- a/crypto/src/math/ec/multiplier/WNafUtilities.cs
+++ b/crypto/src/math/ec/multiplier/WNafUtilities.cs
@@ -287,12 +287,7 @@ namespace Org.BouncyCastle.Math.EC.Multiplier
 
         public static WNafPreCompInfo GetWNafPreCompInfo(PreCompInfo preCompInfo)
         {
-            if ((preCompInfo != null) && (preCompInfo is WNafPreCompInfo))
-            {
-                return (WNafPreCompInfo)preCompInfo;
-            }
-
-            return new WNafPreCompInfo();
+            return preCompInfo as WNafPreCompInfo;
         }
 
         /**
@@ -333,106 +328,178 @@ namespace Org.BouncyCastle.Math.EC.Multiplier
             WNafPreCompInfo wnafPreCompP = Precompute(p, width, includeNegated);
 
             ECPoint q = pointMap.Map(p);
-            WNafPreCompInfo wnafPreCompQ = GetWNafPreCompInfo(c.GetPreCompInfo(q, PRECOMP_NAME));
+            c.Precompute(q, PRECOMP_NAME, new MapPointCallback(wnafPreCompP, includeNegated, pointMap));
+            return q;
+        }
 
-            ECPoint twiceP = wnafPreCompP.Twice;
-            if (twiceP != null)
-            {
-                ECPoint twiceQ = pointMap.Map(twiceP);
-                wnafPreCompQ.Twice = twiceQ;
-            }
+        public static WNafPreCompInfo Precompute(ECPoint p, int width, bool includeNegated)
+        {
+            return (WNafPreCompInfo)p.Curve.Precompute(p, PRECOMP_NAME, new WNafCallback(p, width, includeNegated));
+        }
+
+        private static byte[] Trim(byte[] a, int length)
+        {
+            byte[] result = new byte[length];
+            Array.Copy(a, 0, result, 0, result.Length);
+            return result;
+        }
+
+        private static int[] Trim(int[] a, int length)
+        {
+            int[] result = new int[length];
+            Array.Copy(a, 0, result, 0, result.Length);
+            return result;
+        }
+
+        private static ECPoint[] ResizeTable(ECPoint[] a, int length)
+        {
+            ECPoint[] result = new ECPoint[length];
+            Array.Copy(a, 0, result, 0, a.Length);
+            return result;
+        }
+
+        private class MapPointCallback
+            : IPreCompCallback
+        {
+            private readonly WNafPreCompInfo m_wnafPreCompP;
+            private readonly bool m_includeNegated;
+            private readonly ECPointMap m_pointMap;
 
-            ECPoint[] preCompP = wnafPreCompP.PreComp;
-            ECPoint[] preCompQ = new ECPoint[preCompP.Length];
-            for (int i = 0; i < preCompP.Length; ++i)
+            internal MapPointCallback(WNafPreCompInfo wnafPreCompP, bool includeNegated, ECPointMap pointMap)
             {
-                preCompQ[i] = pointMap.Map(preCompP[i]);
+                this.m_wnafPreCompP = wnafPreCompP;
+                this.m_includeNegated = includeNegated;
+                this.m_pointMap = pointMap;
             }
-            wnafPreCompQ.PreComp = preCompQ;
 
-            if (includeNegated)
+            public PreCompInfo Precompute(PreCompInfo existing)
             {
-                ECPoint[] preCompNegQ = new ECPoint[preCompQ.Length];
-                for (int i = 0; i < preCompNegQ.Length; ++i)
+                WNafPreCompInfo result = new WNafPreCompInfo();
+
+                ECPoint twiceP = m_wnafPreCompP.Twice;
+                if (twiceP != null)
                 {
-                    preCompNegQ[i] = preCompQ[i].Negate();
+                    ECPoint twiceQ = m_pointMap.Map(twiceP);
+                    result.Twice = twiceQ;
                 }
-                wnafPreCompQ.PreCompNeg = preCompNegQ;
-            }
 
-            c.SetPreCompInfo(q, PRECOMP_NAME, wnafPreCompQ);
+                ECPoint[] preCompP = m_wnafPreCompP.PreComp;
+                ECPoint[] preCompQ = new ECPoint[preCompP.Length];
+                for (int i = 0; i < preCompP.Length; ++i)
+                {
+                    preCompQ[i] = m_pointMap.Map(preCompP[i]);
+                }
+                result.PreComp = preCompQ;
 
-            return q;
+                if (m_includeNegated)
+                {
+                    ECPoint[] preCompNegQ = new ECPoint[preCompQ.Length];
+                    for (int i = 0; i < preCompNegQ.Length; ++i)
+                    {
+                        preCompNegQ[i] = preCompQ[i].Negate();
+                    }
+                    result.PreCompNeg = preCompNegQ;
+                }
+
+                return result;
+            }
         }
 
-        public static WNafPreCompInfo Precompute(ECPoint p, int width, bool includeNegated)
+        private class WNafCallback
+            : IPreCompCallback
         {
-            ECCurve c = p.Curve;
-            WNafPreCompInfo wnafPreCompInfo = GetWNafPreCompInfo(c.GetPreCompInfo(p, PRECOMP_NAME));
+            private readonly ECPoint m_p;
+            private readonly int m_width;
+            private readonly bool m_includeNegated;
 
-            int iniPreCompLen = 0, reqPreCompLen = 1 << System.Math.Max(0, width - 2);
-
-            ECPoint[] preComp = wnafPreCompInfo.PreComp;
-            if (preComp == null)
+            internal WNafCallback(ECPoint p, int width, bool includeNegated)
             {
-                preComp = EMPTY_POINTS;
-            }
-            else
-            {
-                iniPreCompLen = preComp.Length;
+                this.m_p = p;
+                this.m_width = width;
+                this.m_includeNegated = includeNegated;
             }
 
-            if (iniPreCompLen < reqPreCompLen)
+            public PreCompInfo Precompute(PreCompInfo existing)
             {
-                preComp = ResizeTable(preComp, reqPreCompLen);
+                WNafPreCompInfo existingWNaf = existing as WNafPreCompInfo;
+
+                int reqPreCompLen = 1 << System.Math.Max(0, m_width - 2);
+
+                if (CheckExisting(existingWNaf, reqPreCompLen, m_includeNegated))
+                    return existingWNaf;
 
-                if (reqPreCompLen == 1)
+                ECCurve c = m_p.Curve;
+                ECPoint[] preComp = null, preCompNeg = null;
+                ECPoint twiceP = null;
+
+                if (existingWNaf != null)
+                {
+                    preComp = existingWNaf.PreComp;
+                    preCompNeg = existingWNaf.PreCompNeg;
+                    twiceP = existingWNaf.Twice;
+                }
+
+                int iniPreCompLen = 0;
+                if (preComp == null)
                 {
-                    preComp[0] = p.Normalize();
+                    preComp = EMPTY_POINTS;
                 }
                 else
                 {
-                    int curPreCompLen = iniPreCompLen;
-                    if (curPreCompLen == 0)
-                    {
-                        preComp[0] = p;
-                        curPreCompLen = 1;
-                    }
+                    iniPreCompLen = preComp.Length;
+                }
 
-                    ECFieldElement iso = null;
+                if (iniPreCompLen < reqPreCompLen)
+                {
+                    preComp = WNafUtilities.ResizeTable(preComp, reqPreCompLen);
 
-                    if (reqPreCompLen == 2)
+                    if (reqPreCompLen == 1)
                     {
-                        preComp[1] = p.ThreeTimes();
+                        preComp[0] = m_p.Normalize();
                     }
                     else
                     {
-                        ECPoint twiceP = wnafPreCompInfo.Twice, last = preComp[curPreCompLen - 1];
-                        if (twiceP == null)
+                        int curPreCompLen = iniPreCompLen;
+                        if (curPreCompLen == 0)
+                        {
+                            preComp[0] = m_p;
+                            curPreCompLen = 1;
+                        }
+
+                        ECFieldElement iso = null;
+
+                        if (reqPreCompLen == 2)
+                        {
+                            preComp[1] = m_p.ThreeTimes();
+                        }
+                        else
                         {
-                            twiceP = preComp[0].Twice();
-                            wnafPreCompInfo.Twice = twiceP;
-
-                            /*
-                             * For Fp curves with Jacobian projective coordinates, use a (quasi-)isomorphism
-                             * where 'twiceP' is "affine", so that the subsequent additions are cheaper. This
-                             * also requires scaling the initial point's X, Y coordinates, and reversing the
-                             * isomorphism as part of the subsequent normalization.
-                             * 
-                             *  NOTE: The correctness of this optimization depends on:
-                             *      1) additions do not use the curve's A, B coefficients.
-                             *      2) no special cases (i.e. Q +/- Q) when calculating 1P, 3P, 5P, ...
-                             */
-                            if (!twiceP.IsInfinity && ECAlgorithms.IsFpCurve(c) && c.FieldSize >= 64)
+                            ECPoint isoTwiceP = twiceP, last = preComp[curPreCompLen - 1];
+                            if (isoTwiceP == null)
                             {
-                                switch (c.CoordinateSystem)
+                                isoTwiceP = preComp[0].Twice();
+                                twiceP = isoTwiceP;
+
+                                /*
+                                 * For Fp curves with Jacobian projective coordinates, use a (quasi-)isomorphism
+                                 * where 'twiceP' is "affine", so that the subsequent additions are cheaper. This
+                                 * also requires scaling the initial point's X, Y coordinates, and reversing the
+                                 * isomorphism as part of the subsequent normalization.
+                                 * 
+                                 *  NOTE: The correctness of this optimization depends on:
+                                 *      1) additions do not use the curve's A, B coefficients.
+                                 *      2) no special cases (i.e. Q +/- Q) when calculating 1P, 3P, 5P, ...
+                                 */
+                                if (!twiceP.IsInfinity && ECAlgorithms.IsFpCurve(c) && c.FieldSize >= 64)
                                 {
+                                    switch (c.CoordinateSystem)
+                                    {
                                     case ECCurve.COORD_JACOBIAN:
                                     case ECCurve.COORD_JACOBIAN_CHUDNOVSKY:
                                     case ECCurve.COORD_JACOBIAN_MODIFIED:
                                     {
                                         iso = twiceP.GetZCoord(0);
-                                        twiceP = c.CreatePoint(twiceP.XCoord.ToBigInteger(),
+                                        isoTwiceP = c.CreatePoint(twiceP.XCoord.ToBigInteger(),
                                             twiceP.YCoord.ToBigInteger());
 
                                         ECFieldElement iso2 = iso.Square(), iso3 = iso2.Multiply(iso);
@@ -444,81 +511,69 @@ namespace Org.BouncyCastle.Math.EC.Multiplier
                                         }
                                         break;
                                     }
+                                    }
                                 }
                             }
-                        }
 
-                        while (curPreCompLen < reqPreCompLen)
-                        {
-                            /*
-                             * Compute the new ECPoints for the precomputation array. The values 1, 3,
-                             * 5, ..., 2^(width-1)-1 times p are computed
-                             */
-                            preComp[curPreCompLen++] = last = last.Add(twiceP);
+                            while (curPreCompLen < reqPreCompLen)
+                            {
+                                /*
+                                 * Compute the new ECPoints for the precomputation array. The values 1, 3,
+                                 * 5, ..., 2^(width-1)-1 times p are computed
+                                 */
+                                preComp[curPreCompLen++] = last = last.Add(isoTwiceP);
+                            }
                         }
-                    }
 
-                    /*
-                     * Having oft-used operands in affine form makes operations faster.
-                     */
-                    c.NormalizeAll(preComp, iniPreCompLen, reqPreCompLen - iniPreCompLen, iso);
+                        /*
+                         * Having oft-used operands in affine form makes operations faster.
+                         */
+                        c.NormalizeAll(preComp, iniPreCompLen, reqPreCompLen - iniPreCompLen, iso);
+                    }
                 }
-            }
-
-            wnafPreCompInfo.PreComp = preComp;
-
-            if (includeNegated)
-            {
-                ECPoint[] preCompNeg = wnafPreCompInfo.PreCompNeg;
 
-                int pos;
-                if (preCompNeg == null)
-                {
-                    pos = 0;
-                    preCompNeg = new ECPoint[reqPreCompLen]; 
-                }
-                else
+                if (m_includeNegated)
                 {
-                    pos = preCompNeg.Length;
-                    if (pos < reqPreCompLen)
+                    int pos;
+                    if (preCompNeg == null)
                     {
-                        preCompNeg = ResizeTable(preCompNeg, reqPreCompLen);
+                        pos = 0;
+                        preCompNeg = new ECPoint[reqPreCompLen]; 
+                    }
+                    else
+                    {
+                        pos = preCompNeg.Length;
+                        if (pos < reqPreCompLen)
+                        {
+                            preCompNeg = WNafUtilities.ResizeTable(preCompNeg, reqPreCompLen);
+                        }
                     }
-                }
 
-                while (pos < reqPreCompLen)
-                {
-                    preCompNeg[pos] = preComp[pos].Negate();
-                    ++pos;
+                    while (pos < reqPreCompLen)
+                    {
+                        preCompNeg[pos] = preComp[pos].Negate();
+                        ++pos;
+                    }
                 }
 
-                wnafPreCompInfo.PreCompNeg = preCompNeg;
+                WNafPreCompInfo result = new WNafPreCompInfo();
+                result.PreComp = preComp;
+                result.PreCompNeg = preCompNeg;
+                result.Twice = twiceP;
+                return result;
             }
 
-            c.SetPreCompInfo(p, PRECOMP_NAME, wnafPreCompInfo);
-
-            return wnafPreCompInfo;
-        }
-
-        private static byte[] Trim(byte[] a, int length)
-        {
-            byte[] result = new byte[length];
-            Array.Copy(a, 0, result, 0, result.Length);
-            return result;
-        }
-
-        private static int[] Trim(int[] a, int length)
-        {
-            int[] result = new int[length];
-            Array.Copy(a, 0, result, 0, result.Length);
-            return result;
-        }
+            private bool CheckExisting(WNafPreCompInfo existingWNaf, int reqPreCompLen, bool includeNegated)
+            {
+                return existingWNaf != null
+                    && CheckTable(existingWNaf.PreComp, reqPreCompLen)
+                    && (!includeNegated || CheckTable(existingWNaf.PreCompNeg, reqPreCompLen));
+            }
 
-        private static ECPoint[] ResizeTable(ECPoint[] a, int length)
-        {
-            ECPoint[] result = new ECPoint[length];
-            Array.Copy(a, 0, result, 0, a.Length);
-            return result;
+            private bool CheckTable(ECPoint[] table, int reqLen)
+            {
+                return table != null && table.Length >= reqLen;
+            }
         }
     }
 }
diff --git a/crypto/src/math/ec/multiplier/WTauNafMultiplier.cs b/crypto/src/math/ec/multiplier/WTauNafMultiplier.cs
index 1e7ddae91..4dce54440 100644
--- a/crypto/src/math/ec/multiplier/WTauNafMultiplier.cs
+++ b/crypto/src/math/ec/multiplier/WTauNafMultiplier.cs
@@ -36,7 +36,7 @@ namespace Org.BouncyCastle.Math.EC.Multiplier
 
             ZTauElement rho = Tnaf.PartModReduction(k, m, a, s, mu, (sbyte)10);
 
-            return MultiplyWTnaf(p, rho, curve.GetPreCompInfo(p, PRECOMP_NAME), a, mu);
+            return MultiplyWTnaf(p, rho, a, mu);
         }
 
         /**
@@ -50,7 +50,7 @@ namespace Org.BouncyCastle.Math.EC.Multiplier
         * @return <code>p</code> multiplied by <code>&#955;</code>.
         */
         private AbstractF2mPoint MultiplyWTnaf(AbstractF2mPoint p, ZTauElement lambda,
-            PreCompInfo preCompInfo, sbyte a, sbyte mu)
+            sbyte a, sbyte mu)
         {
             ZTauElement[] alpha = (a == 0) ? Tnaf.Alpha0 : Tnaf.Alpha1;
 
@@ -59,7 +59,7 @@ namespace Org.BouncyCastle.Math.EC.Multiplier
             sbyte[]u = Tnaf.TauAdicWNaf(mu, lambda, Tnaf.Width,
                 BigInteger.ValueOf(Tnaf.Pow2Width), tw, alpha);
 
-            return MultiplyFromWTnaf(p, u, preCompInfo);
+            return MultiplyFromWTnaf(p, u);
         }
         
         /**
@@ -71,24 +71,14 @@ namespace Org.BouncyCastle.Math.EC.Multiplier
         * @param u The the WTNAF of <code>&#955;</code>..
         * @return <code>&#955; * p</code>
         */
-        private static AbstractF2mPoint MultiplyFromWTnaf(AbstractF2mPoint p, sbyte[] u, PreCompInfo preCompInfo)
+        private static AbstractF2mPoint MultiplyFromWTnaf(AbstractF2mPoint p, sbyte[] u)
         {
             AbstractF2mCurve curve = (AbstractF2mCurve)p.Curve;
             sbyte a = (sbyte)curve.A.ToBigInteger().IntValue;
 
-            AbstractF2mPoint[] pu;
-            if ((preCompInfo == null) || !(preCompInfo is WTauNafPreCompInfo))
-            {
-                pu = Tnaf.GetPreComp(p, a);
-
-                WTauNafPreCompInfo pre = new WTauNafPreCompInfo();
-                pre.PreComp = pu;
-                curve.SetPreCompInfo(p, PRECOMP_NAME, pre);
-            }
-            else
-            {
-                pu = ((WTauNafPreCompInfo)preCompInfo).PreComp;
-            }
+            WTauNafCallback callback = new WTauNafCallback(p, a);
+            WTauNafPreCompInfo preCompInfo = (WTauNafPreCompInfo)curve.Precompute(p, PRECOMP_NAME, callback);
+            AbstractF2mPoint[] pu = preCompInfo.PreComp;
 
             // TODO Include negations in precomp (optionally) and use from here
             AbstractF2mPoint[] puNeg = new AbstractF2mPoint[pu.Length];
@@ -121,5 +111,28 @@ namespace Org.BouncyCastle.Math.EC.Multiplier
             }
             return q;
         }
+
+        private class WTauNafCallback
+            : IPreCompCallback
+        {
+            private readonly AbstractF2mPoint m_p;
+            private readonly sbyte m_a;
+
+            internal WTauNafCallback(AbstractF2mPoint p, sbyte a)
+            {
+                this.m_p = p;
+                this.m_a = a;
+            }
+
+            public PreCompInfo Precompute(PreCompInfo existing)
+            {
+                if (existing is WTauNafPreCompInfo)
+                    return existing;
+
+                WTauNafPreCompInfo result = new WTauNafPreCompInfo();
+                result.PreComp = Tnaf.GetPreComp(m_p, m_a);
+                return result;
+            }
+        }
     }
 }
diff --git a/crypto/src/math/ec/rfc7748/X25519.cs b/crypto/src/math/ec/rfc7748/X25519.cs
index 8c52a21ac..38bc9c1f1 100644
--- a/crypto/src/math/ec/rfc7748/X25519.cs
+++ b/crypto/src/math/ec/rfc7748/X25519.cs
@@ -10,10 +10,10 @@ namespace Org.BouncyCastle.Math.EC.Rfc7748
         private const int C_A24 = (C_A + 2)/4;
 
         // 0x1
-        //private static readonly int[] S_x = new int[] { 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 };
+        //private static readonly int[] S_x = { 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 };
 
         // 0x215132111D8354CB52385F46DCA2B71D440F6A51EB4D1207816B1E0137D48290
-        private static readonly int[] PsubS_x = new int[]{ 0x03D48290, 0x02C7804D, 0x01207816, 0x028F5A68, 0x00881ED4, 0x00A2B71D,
+        private static readonly int[] PsubS_x = { 0x03D48290, 0x02C7804D, 0x01207816, 0x028F5A68, 0x00881ED4, 0x00A2B71D,
             0x0217D1B7, 0x014CB523, 0x0088EC1A, 0x0042A264 };
 
         private static int[] precompBase = null;
diff --git a/crypto/src/math/ec/rfc7748/X25519Field.cs b/crypto/src/math/ec/rfc7748/X25519Field.cs
index 282f41628..fd5599657 100644
--- a/crypto/src/math/ec/rfc7748/X25519Field.cs
+++ b/crypto/src/math/ec/rfc7748/X25519Field.cs
@@ -11,6 +11,9 @@ namespace Org.BouncyCastle.Math.EC.Rfc7748
         private const int M25 = 0x01FFFFFF;
         private const int M26 = 0x03FFFFFF;
 
+        private static readonly int[] RootNegOne = { 0x020EA0B0, 0x0386C9D2, 0x00478C4E, 0x0035697F, 0x005E8630,
+            0x01FBD7A7, 0x0340264F, 0x01F0B2B4, 0x00027E0E, 0x00570649 };
+
         private X25519Field() {}
 
         public static void Add(int[] x, int[] y, int[] z)
@@ -21,6 +24,16 @@ namespace Org.BouncyCastle.Math.EC.Rfc7748
             }
         }
 
+        public static void AddOne(int[] z)
+        {
+            z[0] += 1;
+        }
+
+        public static void AddOne(int[] z, int zOff)
+        {
+            z[zOff] += 1;
+        }
+
         public static void Apm(int[] x, int[] y, int[] zp, int[] zm)
         {
             for (int i = 0; i < Size; ++i)
@@ -54,6 +67,17 @@ namespace Org.BouncyCastle.Math.EC.Rfc7748
             z[5] = z5; z[6] = z6; z[7] = z7; z[8] = z8; z[9] = z9;
         }
 
+        public static void CNegate(int negate, int[] z)
+        {
+            Debug.Assert(negate >> 1 == 0);
+
+            int mask = 0 - negate;
+            for (int i = 0; i < Size; ++i)
+            {
+                z[i] = (z[i] ^ mask) - mask;
+            }
+        }
+
         public static void Copy(int[] x, int xOff, int[] z, int zOff)
         {
             for (int i = 0; i < Size; ++i)
@@ -67,6 +91,11 @@ namespace Org.BouncyCastle.Math.EC.Rfc7748
             return new int[Size];
         }
 
+        public static int[] CreateTable(int n)
+        {
+            return new int[Size * n];
+        }
+
         public static void CSwap(int swap, int[] a, int[] b)
         {
             Debug.Assert(swap >> 1 == 0);
@@ -143,24 +172,23 @@ namespace Org.BouncyCastle.Math.EC.Rfc7748
             // (250 1s) (1 0s) (1 1s) (1 0s) (2 1s)
             // Addition chain: [1] [2] 3 5 10 15 25 50 75 125 [250]
 
-            int[] x2 = Create();    Sqr(x, x2);             Mul(x, x2, x2);
-            int[] x3 = Create();    Sqr(x2, x3);            Mul(x, x3, x3);
-            int[] x5 = x3;          Sqr(x3, 2, x5);         Mul(x2, x5, x5);
-            int[] x10 = Create();   Sqr(x5, 5, x10);        Mul(x5, x10, x10);
-            int[] x15 = Create();   Sqr(x10, 5, x15);       Mul(x5, x15, x15);
-            int[] x25 = x5;         Sqr(x15, 10, x25);      Mul(x10, x25, x25);
-            int[] x50 = x10;        Sqr(x25, 25, x50);      Mul(x25, x50, x50);
-            int[] x75 = x15;        Sqr(x50, 25, x75);      Mul(x25, x75, x75);
-            int[] x125 = x25;       Sqr(x75, 50, x125);     Mul(x50, x125, x125);
-            int[] x250 = x50;       Sqr(x125, 125, x250);   Mul(x125, x250, x250);
-
-            int[] t = x125;
-            Sqr(x250, 2, t);
-            Mul(t, x, t);
+            int[] x2 = Create();
+            int[] t = Create();
+            PowPm5d8(x, x2, t);
             Sqr(t, 3, t);
             Mul(t, x2, z);
         }
 
+        public static bool IsZeroVar(int[] x)
+        {
+            int d = 0;
+            for (int i = 0; i < Size; ++i)
+            {
+                d |= x[i];
+            }
+            return d == 0;
+        }
+
         public static void Mul(int[] x, int y, int[] z)
         {
             int x0 = x[0], x1 = x[1], x2 = x[2], x3 = x[3], x4 = x[4];
@@ -345,6 +373,14 @@ namespace Org.BouncyCastle.Math.EC.Rfc7748
             z[9]     = z9 + (int)t;
         }
 
+        public static void Negate(int[] x, int[] z)
+        {
+            for (int i = 0; i < Size; ++i)
+            {
+                z[i] = -x[i];
+            }
+        }
+
         public static void Normalize(int[] z)
         {
             int x = (z[9] >> 23) & 1;
@@ -353,6 +389,37 @@ namespace Org.BouncyCastle.Math.EC.Rfc7748
             Debug.Assert(z[9] >> 24 == 0);
         }
 
+        public static void One(int[] z)
+        {
+            z[0] = 1;
+            for (int i = 1; i < Size; ++i)
+            {
+                z[i] = 0;
+            }
+        }
+
+        private static void PowPm5d8(int[] x, int[] rx2, int[] rz)
+        {
+            // z = x^((p-5)/8) = x^FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFD
+            // (250 1s) (1 0s) (1 1s)
+            // Addition chain: [1] 2 3 5 10 15 25 50 75 125 [250]
+
+            int[] x2 = rx2;         Sqr(x, x2);             Mul(x, x2, x2);
+            int[] x3 = Create();    Sqr(x2, x3);            Mul(x, x3, x3);
+            int[] x5 = x3;          Sqr(x3, 2, x5);         Mul(x2, x5, x5);
+            int[] x10 = Create();   Sqr(x5, 5, x10);        Mul(x5, x10, x10);
+            int[] x15 = Create();   Sqr(x10, 5, x15);       Mul(x5, x15, x15);
+            int[] x25 = x5;         Sqr(x15, 10, x25);      Mul(x10, x25, x25);
+            int[] x50 = x10;        Sqr(x25, 25, x50);      Mul(x25, x50, x50);
+            int[] x75 = x15;        Sqr(x50, 25, x75);      Mul(x25, x75, x75);
+            int[] x125 = x25;       Sqr(x75, 50, x125);     Mul(x50, x125, x125);
+            int[] x250 = x50;       Sqr(x125, 125, x250);   Mul(x125, x250, x250);
+
+            int[] t = x125;
+            Sqr(x250, 2, t);
+            Mul(t, x, rz);
+        }
+
         private static void Reduce(int[] z, int c)
         {
             int z9 = z[9], t = z9;
@@ -509,6 +576,45 @@ namespace Org.BouncyCastle.Math.EC.Rfc7748
             }
         }
 
+        public static bool SqrtRatioVar(int[] u, int[] v, int[] z)
+        {
+            int[] uv3 = Create();
+            int[] uv7 = Create();
+
+            Mul(u, v, uv3);
+            Sqr(v, uv7);
+            Mul(uv3, uv7, uv3);
+            Sqr(uv7, uv7);
+            Mul(uv7, uv3, uv7);
+
+            int[] t = Create();
+            int[] x = Create();
+            PowPm5d8(uv7, t, x);
+            Mul(x, uv3, x);
+
+            int[] vx2 = Create();
+            Sqr(x, vx2);
+            Mul(vx2, v, vx2);
+
+            Sub(vx2, u, t);
+            Normalize(t);
+            if (IsZeroVar(t))
+            {
+                Copy(x, 0, z, 0);
+                return true;
+            }
+
+            Add(vx2, u, t);
+            Normalize(t);
+            if (IsZeroVar(t))
+            {
+                Mul(x, RootNegOne, z);
+                return true;
+            }
+
+            return false;
+        }
+
         public static void Sub(int[] x, int[] y, int[] z)
         {
             for (int i = 0; i < Size; ++i)
@@ -516,5 +622,18 @@ namespace Org.BouncyCastle.Math.EC.Rfc7748
                 z[i] = x[i] - y[i];
             }
         }
+
+        public static void SubOne(int[] z)
+        {
+            z[0] -= 1;
+        }
+
+        public static void Zero(int[] z)
+        {
+            for (int i = 0; i < Size; ++i)
+            {
+                z[i] = 0;
+            }
+        }
     }
 }
diff --git a/crypto/src/math/ec/rfc7748/X448.cs b/crypto/src/math/ec/rfc7748/X448.cs
index 8ded25a06..4e6e32879 100644
--- a/crypto/src/math/ec/rfc7748/X448.cs
+++ b/crypto/src/math/ec/rfc7748/X448.cs
@@ -10,14 +10,14 @@ namespace Org.BouncyCastle.Math.EC.Rfc7748
         private const uint C_A24 = (C_A + 2)/4;
 
         // 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE
-        private static readonly uint[] S_x = new uint[]{ 0x0FFFFFFEU, 0x0FFFFFFFU, 0x0FFFFFFFU, 0x0FFFFFFFU, 0x0FFFFFFFU, 0x0FFFFFFFU,
+        private static readonly uint[] S_x = { 0x0FFFFFFEU, 0x0FFFFFFFU, 0x0FFFFFFFU, 0x0FFFFFFFU, 0x0FFFFFFFU, 0x0FFFFFFFU,
             0x0FFFFFFFU, 0x0FFFFFFFU, 0x0FFFFFFEU, 0x0FFFFFFFU, 0x0FFFFFFFU, 0x0FFFFFFFU, 0x0FFFFFFFU, 0x0FFFFFFFU, 0x0FFFFFFFU,
             0x0FFFFFFFU };
 
         // 0xF0FAB725013244423ACF03881AFFEB7BDACDD1031C81B9672954459D84C1F823F1BD65643ACE1B5123AC33FF1C69BAF8ACB1197DC99D2720
-        private static readonly uint[] PsubS_x = new uint[]{ 0x099d2720U, 0x0b1197dcU, 0x09baf8acU, 0x033ff1c6U, 0x0b5123acU,
-            0x0643ace1U, 0x03f1bd65U, 0x084c1f82U, 0x0954459dU, 0x081b9672U, 0x0dd1031cU, 0x0eb7bdacU, 0x03881affU, 0x0423acf0U,
-            0x05013244U, 0x0f0fab72U };
+        private static readonly uint[] PsubS_x = { 0x099D2720U, 0x0B1197DCU, 0x09BAF8ACU, 0x033FF1C6U, 0x0B5123ACU,
+            0x0643ACE1U, 0x03F1BD65U, 0x084C1F82U, 0x0954459DU, 0x081B9672U, 0x0DD1031CU, 0x0EB7BDACU, 0x03881AFFU, 0x0423ACF0U,
+            0x05013244U, 0x0F0FAB72U };
 
         private static uint[] precompBase = null;
 
diff --git a/crypto/src/math/ec/rfc7748/X448Field.cs b/crypto/src/math/ec/rfc7748/X448Field.cs
index 0c44f1eb5..5a682714d 100644
--- a/crypto/src/math/ec/rfc7748/X448Field.cs
+++ b/crypto/src/math/ec/rfc7748/X448Field.cs
@@ -1,6 +1,8 @@
 using System;
 using System.Diagnostics;
 
+using Org.BouncyCastle.Math.Raw;
+
 namespace Org.BouncyCastle.Math.EC.Rfc7748
 {
     [CLSCompliantAttribute(false)]
@@ -20,6 +22,16 @@ namespace Org.BouncyCastle.Math.EC.Rfc7748
             }
         }
 
+        public static void AddOne(uint[] z)
+        {
+            z[0] += 1;
+        }
+
+        public static void AddOne(uint[] z, int zOff)
+        {
+            z[zOff] += 1;
+        }
+
         //public static void Apm(int[] x, int[] y, int[] zp, int[] zm)
         //{
         //    for (int i = 0; i < Size; ++i)
@@ -62,6 +74,16 @@ namespace Org.BouncyCastle.Math.EC.Rfc7748
             z[8] = z8; z[9] = z9; z[10] = z10; z[11] = z11; z[12] = z12; z[13] = z13; z[14] = z14; z[15] = z15;
         }
 
+        public static void CNegate(int negate, uint[] z)
+        {
+            Debug.Assert(negate >> 1 == 0);
+
+            uint[] t = Create();
+            Sub(t, z, t);
+
+            Nat.CMov(Size, negate, t, 0, z, 0);
+        }
+
         public static void Copy(uint[] x, int xOff, uint[] z, int zOff)
         {
             for (int i = 0; i < Size; ++i)
@@ -166,25 +188,23 @@ namespace Org.BouncyCastle.Math.EC.Rfc7748
             // z = x^(p-2) = x^(2^448 - 2^224 - 3)
             // (223 1s) (1 0s) (222 1s) (1 0s) (1 1s)
             // Addition chain: [1] 2 3 6 9 18 19 37 74 111 [222] [223]
-            uint[] x2 = Create();    Sqr(x, x2);             Mul(x, x2, x2);
-            uint[] x3 = Create();    Sqr(x2, x3);            Mul(x, x3, x3);
-            uint[] x6 = Create();    Sqr(x3, 3, x6);         Mul(x3, x6, x6);
-            uint[] x9 = Create();    Sqr(x6, 3, x9);         Mul(x3, x9, x9);
-            uint[] x18 = Create();   Sqr(x9, 9, x18);        Mul(x9, x18, x18);
-            uint[] x19 = Create();   Sqr(x18, x19);          Mul(x, x19, x19);
-            uint[] x37 = Create();   Sqr(x19, 18, x37);      Mul(x18, x37, x37);
-            uint[] x74 = Create();   Sqr(x37, 37, x74);      Mul(x37, x74, x74);
-            uint[] x111 = Create();  Sqr(x74, 37, x111);     Mul(x37, x111, x111);
-            uint[] x222 = Create();  Sqr(x111, 111, x222);   Mul(x111, x222, x222);
-            uint[] x223 = Create();  Sqr(x222, x223);        Mul(x, x223, x223);
 
             uint[] t = Create();
-            Sqr(x223, 223, t);
-            Mul(t, x222, t);
+            PowPm3d4(x, t);
             Sqr(t, 2, t);
             Mul(t, x, z);
         }
 
+        public static bool IsZeroVar(uint[] x)
+        {
+            uint d = 0;
+            for (int i = 0; i < Size; ++i)
+            {
+                d |= x[i];
+            }
+            return d == 0U;
+        }
+
         public static void Mul(uint[] x, uint y, uint[] z)
         {
             uint x0 = x[0], x1 = x[1], x2 = x[2], x3 = x[3], x4 = x[4], x5 = x[5], x6 = x[6], x7 = x[7];
@@ -563,6 +583,12 @@ namespace Org.BouncyCastle.Math.EC.Rfc7748
             z[15] = z15;
         }
 
+        public static void Negate(uint[] x, uint[] z)
+        {
+            uint[] zero = Create();
+            Sub(zero, x, z);
+        }
+
         public static void Normalize(uint[] z)
         {
             //int x = (z[15] >> (28 - 1)) & 1;
@@ -571,6 +597,37 @@ namespace Org.BouncyCastle.Math.EC.Rfc7748
             Debug.Assert(z[15] >> 28 == 0U);
         }
 
+        public static void One(uint[] z)
+        {
+            z[0] = 1U;
+            for (int i = 1; i < Size; ++i)
+            {
+                z[i] = 0;
+            }
+        }
+
+        private static void PowPm3d4(uint[] x, uint[] z)
+        {
+            // z = x^((p-3)/4) = x^(2^446 - 2^222 - 1)
+            // (223 1s) (1 0s) (222 1s)
+            // Addition chain: 1 2 3 6 9 18 19 37 74 111 [222] [223]
+            uint[] x2 = Create();   Sqr(x, x2);             Mul(x, x2, x2);
+            uint[] x3 = Create();   Sqr(x2, x3);            Mul(x, x3, x3);
+            uint[] x6 = Create();   Sqr(x3, 3, x6);         Mul(x3, x6, x6);
+            uint[] x9 = Create();   Sqr(x6, 3, x9);         Mul(x3, x9, x9);
+            uint[] x18 = Create();  Sqr(x9, 9, x18);        Mul(x9, x18, x18);
+            uint[] x19 = Create();  Sqr(x18, x19);          Mul(x, x19, x19);
+            uint[] x37 = Create();  Sqr(x19, 18, x37);      Mul(x18, x37, x37);
+            uint[] x74 = Create();  Sqr(x37, 37, x74);      Mul(x37, x74, x74);
+            uint[] x111 = Create(); Sqr(x74, 37, x111);     Mul(x37, x111, x111);
+            uint[] x222 = Create(); Sqr(x111, 111, x222);   Mul(x111, x222, x222);
+            uint[] x223 = Create(); Sqr(x222, x223);        Mul(x, x223, x223);
+
+            uint[] t = Create();
+            Sqr(x223, 223, t);
+            Mul(t, x222, z);
+        }
+
         private static void Reduce(uint[] z, int c)
         {
             uint z15 = z[15];
@@ -836,6 +893,38 @@ namespace Org.BouncyCastle.Math.EC.Rfc7748
             }
         }
 
+        public static bool SqrtRatioVar(uint[] u, uint[] v, uint[] z)
+        {
+            uint[] u3v = Create();
+            uint[] u5v3 = Create();
+
+            Sqr(u, u3v);
+            Mul(u3v, v, u3v);
+            Sqr(u3v, u5v3);
+            Mul(u3v, u, u3v);
+            Mul(u5v3, u, u5v3);
+            Mul(u5v3, v, u5v3);
+
+            uint[] x = Create();
+            PowPm3d4(u5v3, x);
+            Mul(x, u3v, x);
+
+            uint[] t = Create();
+            Sqr(x, t);
+            Mul(t, v, t);
+
+            Sub(u, t, t);
+            Normalize(t);
+
+            if (IsZeroVar(t))
+            {
+                Copy(x, 0, z, 0);
+                return true;
+            }
+
+            return false;
+        }
+
         public static void Sub(uint[] x, uint[] y, uint[] z)
         {
             uint x0 = x[0], x1 = x[1], x2 = x[2], x3 = x[3], x4 = x[4], x5 = x[5], x6 = x[6], x7 = x[7];
@@ -900,5 +989,13 @@ namespace Org.BouncyCastle.Math.EC.Rfc7748
             z[14] = z14;
             z[15] = z15;
         }
+
+        public static void Zero(uint[] z)
+        {
+            for (int i = 0; i < Size; ++i)
+            {
+                z[i] = 0;
+            }
+        }
     }
 }
diff --git a/crypto/src/math/ec/rfc8032/Ed25519.cs b/crypto/src/math/ec/rfc8032/Ed25519.cs
new file mode 100644
index 000000000..ff4587cb2
--- /dev/null
+++ b/crypto/src/math/ec/rfc8032/Ed25519.cs
@@ -0,0 +1,937 @@
+using System;
+using System.Diagnostics;
+using System.Runtime.CompilerServices;
+
+using Org.BouncyCastle.Crypto.Digests;
+using Org.BouncyCastle.Math.EC.Rfc7748;
+using Org.BouncyCastle.Math.Raw;
+using Org.BouncyCastle.Utilities;
+
+namespace Org.BouncyCastle.Math.EC.Rfc8032
+{
+    public abstract class Ed25519
+    {
+        private const long M28L = 0x0FFFFFFFL;
+        private const long M32L = 0xFFFFFFFFL;
+
+        private const int PointBytes = 32;
+        private const int ScalarUints = 8;
+        private const int ScalarBytes = ScalarUints * 4;
+
+        public static readonly int PublicKeySize = PointBytes;
+        public static readonly int SecretKeySize = 32;
+        public static readonly int SignatureSize = PointBytes + ScalarBytes;
+
+        //private static readonly byte[] Dom2Prefix = Strings.ToByteArray("SigEd25519 no Ed25519 collisions");
+
+        private static readonly uint[] P = { 0xFFFFFFEDU, 0xFFFFFFFFU, 0xFFFFFFFFU, 0xFFFFFFFFU, 0xFFFFFFFFU, 0xFFFFFFFFU, 0xFFFFFFFFU, 0x7FFFFFFFU };
+        private static readonly uint[] L = { 0x5CF5D3EDU, 0x5812631AU, 0xA2F79CD6U, 0x14DEF9DEU, 0x00000000U, 0x00000000U, 0x00000000U, 0x10000000U };
+
+        private const int L0 = unchecked((int)0xFCF5D3ED);  // L0:26/--
+        private const int L1 =                0x012631A6;   // L1:24/22
+        private const int L2 =                0x079CD658;   // L2:27/--
+        private const int L3 = unchecked((int)0xFF9DEA2F);  // L3:23/--
+        private const int L4 =                0x000014DF;   // L4:12/11
+
+        private static readonly int[] B_x = { 0x0325D51A, 0x018B5823, 0x007B2C95, 0x0304A92D, 0x00D2598E, 0x01D6DC5C,
+            0x01388C7F, 0x013FEC0A, 0x029E6B72, 0x0042D26D };
+        private static readonly int[] B_y = { 0x02666658, 0x01999999, 0x00666666, 0x03333333, 0x00CCCCCC, 0x02666666,
+            0x01999999, 0x00666666, 0x03333333, 0x00CCCCCC, };
+        private static readonly int[] C_d = { 0x035978A3, 0x02D37284, 0x018AB75E, 0x026A0A0E, 0x0000E014, 0x0379E898,
+            0x01D01E5D, 0x01E738CC, 0x03715B7F, 0x00A406D9 };
+        private static readonly int[] C_d2 = { 0x02B2F159, 0x01A6E509, 0x01156EBD, 0x00D4141D, 0x0001C029, 0x02F3D130,
+            0x03A03CBB, 0x01CE7198, 0x02E2B6FF, 0x00480DB3 };
+        private static readonly int[] C_d4 = { 0x0165E2B2, 0x034DCA13, 0x002ADD7A, 0x01A8283B, 0x00038052, 0x01E7A260,
+            0x03407977, 0x019CE331, 0x01C56DFF, 0x00901B67 };
+
+        private const int WnafWidthBase = 7;
+
+        private const int PrecompBlocks = 8;
+        private const int PrecompTeeth = 4;
+        private const int PrecompSpacing = 8;
+        private const int PrecompPoints = 1 << (PrecompTeeth - 1);
+        private const int PrecompMask = PrecompPoints - 1;
+
+        // TODO[ed25519] Convert to PointPrecomp
+        private static PointExt[] precompBaseTable = null;
+        private static int[] precompBase = null;
+
+        private class PointAccum
+        {
+            internal int[] x = X25519Field.Create();
+            internal int[] y = X25519Field.Create();
+            internal int[] z = X25519Field.Create();
+            internal int[] u = X25519Field.Create();
+            internal int[] v = X25519Field.Create();
+        }
+
+        private class PointExt
+        {
+            internal int[] x = X25519Field.Create();
+            internal int[] y = X25519Field.Create();
+            internal int[] z = X25519Field.Create();
+            internal int[] t = X25519Field.Create();
+        }
+
+        private class PointPrecomp
+        {
+            internal int[] ypx_h = X25519Field.Create();
+            internal int[] ymx_h = X25519Field.Create();
+            internal int[] xyd = X25519Field.Create();
+        }
+
+        private static byte[] CalculateS(byte[] r, byte[] k, byte[] s)
+        {
+            uint[] t = new uint[ScalarUints * 2];   DecodeScalar(r, 0, t);
+            uint[] u = new uint[ScalarUints];       DecodeScalar(k, 0, u);
+            uint[] v = new uint[ScalarUints];       DecodeScalar(s, 0, v);
+
+            Nat256.MulAddTo(u, v, t);
+
+            byte[] result = new byte[ScalarBytes * 2];
+            for (int i = 0; i < t.Length; ++i)
+            {
+                Encode32(t[i], result, i * 4);
+            }
+            return ReduceScalar(result);
+        }
+
+        private static bool CheckPointVar(byte[] p)
+        {
+            uint[] t = new uint[8];
+            Decode32(p, 0, t, 0, 8);
+            t[7] &= 0x7FFFFFFFU;
+            return !Nat256.Gte(t, P);
+        }
+
+        private static bool CheckScalarVar(byte[] s)
+        {
+            uint[] n = new uint[ScalarUints];
+            DecodeScalar(s, 0, n);
+            return !Nat256.Gte(n, L);
+        }
+
+        private static uint Decode24(byte[] bs, int off)
+        {
+            uint n = bs[off];
+            n |= (uint)bs[++off] << 8;
+            n |= (uint)bs[++off] << 16;
+            return n;
+        }
+
+        private static uint Decode32(byte[] bs, int off)
+        {
+            uint n = bs[off];
+            n |= (uint)bs[++off] << 8;
+            n |= (uint)bs[++off] << 16;
+            n |= (uint)bs[++off] << 24;
+            return n;
+        }
+
+        private static void Decode32(byte[] bs, int bsOff, uint[] n, int nOff, int nLen)
+        {
+            for (int i = 0; i < nLen; ++i)
+            {
+                n[nOff + i] = Decode32(bs, bsOff + i * 4);
+            }
+        }
+
+        private static bool DecodePointVar(byte[] p, int pOff, bool negate, PointExt r)
+        {
+            byte[] py = Arrays.CopyOfRange(p, pOff, pOff + PointBytes);
+            if (!CheckPointVar(py))
+            {
+                return false;
+            }
+
+            int x_0 = (py[PointBytes - 1] & 0x80) >> 7;
+            py[PointBytes - 1] &= 0x7F;
+
+            X25519Field.Decode(py, 0, r.y);
+
+            int[] u = X25519Field.Create();
+            int[] v = X25519Field.Create();
+
+            X25519Field.Sqr(r.y, u);
+            X25519Field.Mul(C_d, u, v);
+            X25519Field.SubOne(u);
+            X25519Field.AddOne(v);
+
+            if (!X25519Field.SqrtRatioVar(u, v, r.x))
+            {
+                return false;
+            }
+
+            X25519Field.Normalize(r.x);
+            if (x_0 == 1 && X25519Field.IsZeroVar(r.x))
+            {
+                return false;
+            }
+
+            if (negate ^ (x_0 != (r.x[0] & 1)))
+            {
+                X25519Field.Negate(r.x, r.x);
+            }
+
+            PointExtendXY(r);
+            return true;
+        }
+
+        private static void DecodeScalar(byte[] k, int kOff, uint[] n)
+        {
+            Decode32(k, kOff, n, 0, ScalarUints);
+        }
+
+        private static void Encode24(uint n, byte[] bs, int off)
+        {
+            bs[off] = (byte)(n);
+            bs[++off] = (byte)(n >> 8);
+            bs[++off] = (byte)(n >> 16);
+        }
+
+        private static void Encode32(uint n, byte[] bs, int off)
+        {
+            bs[off] = (byte)(n);
+            bs[++off] = (byte)(n >> 8);
+            bs[++off] = (byte)(n >> 16);
+            bs[++off] = (byte)(n >> 24);
+        }
+
+        private static void Encode56(ulong n, byte[] bs, int off)
+        {
+            Encode32((uint)n, bs, off);
+            Encode24((uint)(n >> 32), bs, off + 4);
+        }
+
+        private static void EncodePoint(PointAccum p, byte[] r, int rOff)
+        {
+            int[] x = X25519Field.Create();
+            int[] y = X25519Field.Create();
+
+            X25519Field.Inv(p.z, y);
+            X25519Field.Mul(p.x, y, x);
+            X25519Field.Mul(p.y, y, y);
+            X25519Field.Normalize(x);
+            X25519Field.Normalize(y);
+
+            X25519Field.Encode(y, r, rOff);
+            r[rOff + PointBytes - 1] |= (byte)((x[0] & 1) << 7);
+        }
+
+        public static void GeneratePublicKey(byte[] sk, int skOff, byte[] pk, int pkOff)
+        {
+            Sha512Digest d = new Sha512Digest();
+            byte[] h = new byte[d.GetDigestSize()];
+
+            d.BlockUpdate(sk, skOff, SecretKeySize);
+            d.DoFinal(h, 0);
+
+            byte[] s = new byte[ScalarBytes];
+            PruneScalar(h, 0, s);
+
+            ScalarMultBaseEncoded(s, pk, pkOff);
+        }
+
+        private static sbyte[] GetWnaf(uint[] n, int width)
+        {
+            Debug.Assert(n[ScalarUints - 1] >> 31 == 0);
+
+            uint[] t = new uint[ScalarUints * 2];
+            {
+                uint c = 0;
+                int tPos = t.Length, i = ScalarUints;
+                while (--i >= 0)
+                {
+                    uint next = n[i];
+                    t[--tPos] = (next >> 16) | (c << 16);
+                    t[--tPos] = c = next;
+                }
+            }
+
+            sbyte[] ws = new sbyte[256];
+
+            uint pow2 = 1U << width;
+            uint mask = pow2 - 1U;
+            uint sign = pow2 >> 1;
+
+            uint carry = 0U;
+            int j = 0;
+            for (int i = 0; i < t.Length; ++i, j -= 16)
+            {
+                uint word = t[i];
+                while (j < 16)
+                {
+                    uint word16 = word >> j;
+                    uint bit = word16 & 1U;
+
+                    if (bit == carry)
+                    {
+                        ++j;
+                        continue;
+                    }
+
+                    uint digit = (word16 & mask) + carry;
+                    carry = digit & sign;
+                    digit -= (carry << 1);
+                    carry >>= (width - 1);
+
+                    ws[(i << 4) + j] = (sbyte)digit;
+
+                    j += width;
+                }
+            }
+
+            Debug.Assert(carry == 0);
+
+            return ws;
+        }
+
+        private static void ImplSign(Sha512Digest d, byte[] h, byte[] s, byte[] pk, int pkOff, byte[] m, int mOff, int mLen, byte[] sig, int sigOff)
+        {
+            d.BlockUpdate(h, ScalarBytes, ScalarBytes);
+            d.BlockUpdate(m, mOff, mLen);
+            d.DoFinal(h, 0);
+
+            byte[] r = ReduceScalar(h);
+            byte[] R = new byte[PointBytes];
+            ScalarMultBaseEncoded(r, R, 0);
+
+            d.BlockUpdate(R, 0, PointBytes);
+            d.BlockUpdate(pk, 0, PointBytes);
+            d.BlockUpdate(m, mOff, mLen);
+            d.DoFinal(h, 0);
+
+            byte[] k = ReduceScalar(h);
+            byte[] S = CalculateS(r, k, s);
+
+            Array.Copy(R, 0, sig, sigOff, PointBytes);
+            Array.Copy(S, 0, sig, sigOff + PointBytes, ScalarBytes);
+        }
+
+        private static void PointAddVar(bool negate, PointExt p, PointAccum r)
+        {
+            int[] A = X25519Field.Create();
+            int[] B = X25519Field.Create();
+            int[] C = X25519Field.Create();
+            int[] D = X25519Field.Create();
+            int[] E = r.u;
+            int[] F = X25519Field.Create();
+            int[] G = X25519Field.Create();
+            int[] H = r.v;
+
+            int[] c, d, f, g;
+            if (negate)
+            {
+                c = D; d = C; f = G; g = F;
+            }
+            else
+            {
+                c = C; d = D; f = F; g = G;
+            }
+
+            X25519Field.Apm(r.y, r.x, B, A);
+            X25519Field.Apm(p.y, p.x, d, c);
+            X25519Field.Mul(A, C, A);
+            X25519Field.Mul(B, D, B);
+            X25519Field.Mul(r.u, r.v, C);
+            X25519Field.Mul(C, p.t, C);
+            X25519Field.Mul(C, C_d2, C);
+            X25519Field.Mul(r.z, p.z, D);
+            X25519Field.Add(D, D, D);
+            X25519Field.Apm(B, A, H, E);
+            X25519Field.Apm(D, C, g, f);
+            X25519Field.Carry(g);
+            X25519Field.Mul(E, F, r.x);
+            X25519Field.Mul(G, H, r.y);
+            X25519Field.Mul(F, G, r.z);
+        }
+
+        private static void PointAddVar(bool negate, PointExt p, PointExt q, PointExt r)
+        {
+            int[] A = X25519Field.Create();
+            int[] B = X25519Field.Create();
+            int[] C = X25519Field.Create();
+            int[] D = X25519Field.Create();
+            int[] E = X25519Field.Create();
+            int[] F = X25519Field.Create();
+            int[] G = X25519Field.Create();
+            int[] H = X25519Field.Create();
+
+            int[] c, d, f, g;
+            if (negate)
+            {
+                c = D; d = C; f = G; g = F;
+            }
+            else
+            {
+                c = C; d = D; f = F; g = G;
+            }
+
+            X25519Field.Apm(p.y, p.x, B, A);
+            X25519Field.Apm(q.y, q.x, d, c);
+            X25519Field.Mul(A, C, A);
+            X25519Field.Mul(B, D, B);
+            X25519Field.Mul(p.t, q.t, C);
+            X25519Field.Mul(C, C_d2, C);
+            X25519Field.Mul(p.z, q.z, D);
+            X25519Field.Add(D, D, D);
+            X25519Field.Apm(B, A, H, E);
+            X25519Field.Apm(D, C, g, f);
+            X25519Field.Carry(g);
+            X25519Field.Mul(E, F, r.x);
+            X25519Field.Mul(G, H, r.y);
+            X25519Field.Mul(F, G, r.z);
+            X25519Field.Mul(E, H, r.t);
+        }
+
+        private static void PointAddPrecomp(PointPrecomp p, PointAccum r)
+        {
+            int[] A = X25519Field.Create();
+            int[] B = X25519Field.Create();
+            int[] C = X25519Field.Create();
+            int[] E = r.u;
+            int[] F = X25519Field.Create();
+            int[] G = X25519Field.Create();
+            int[] H = r.v;
+
+            X25519Field.Apm(r.y, r.x, B, A);
+            X25519Field.Mul(A, p.ymx_h, A);
+            X25519Field.Mul(B, p.ypx_h, B);
+            X25519Field.Mul(r.u, r.v, C);
+            X25519Field.Mul(C, p.xyd, C);
+            X25519Field.Apm(B, A, H, E);
+            X25519Field.Apm(r.z, C, G, F);
+            X25519Field.Carry(G);
+            X25519Field.Mul(E, F, r.x);
+            X25519Field.Mul(G, H, r.y);
+            X25519Field.Mul(F, G, r.z);
+        }
+
+        private static PointExt PointCopy(PointAccum p)
+        {
+            PointExt r = new PointExt();
+            X25519Field.Copy(p.x, 0, r.x, 0);
+            X25519Field.Copy(p.y, 0, r.y, 0);
+            X25519Field.Copy(p.z, 0, r.z, 0);
+            X25519Field.Mul(p.u, p.v, r.t);
+            return r;
+        }
+
+        private static PointExt PointCopy(PointExt p)
+        {
+            PointExt r = new PointExt();
+            X25519Field.Copy(p.x, 0, r.x, 0);
+            X25519Field.Copy(p.y, 0, r.y, 0);
+            X25519Field.Copy(p.z, 0, r.z, 0);
+            X25519Field.Copy(p.t, 0, r.t, 0);
+            return r;
+        }
+
+        private static void PointDouble(PointAccum r)
+        {
+            int[] A = X25519Field.Create();
+            int[] B = X25519Field.Create();
+            int[] C = X25519Field.Create();
+            int[] E = r.u;
+            int[] F = X25519Field.Create();
+            int[] G = X25519Field.Create();
+            int[] H = r.v;
+
+            X25519Field.Sqr(r.x, A);
+            X25519Field.Sqr(r.y, B);
+            X25519Field.Sqr(r.z, C);
+            X25519Field.Add(C, C, C);
+            X25519Field.Apm(A, B, H, G);
+            X25519Field.Add(r.x, r.y, E);
+            X25519Field.Sqr(E, E);
+            X25519Field.Sub(H, E, E);
+            X25519Field.Add(C, G, F);
+            X25519Field.Carry(F);
+            X25519Field.Mul(E, F, r.x);
+            X25519Field.Mul(G, H, r.y);
+            X25519Field.Mul(F, G, r.z);
+        }
+
+        private static void PointExtendXY(PointAccum p)
+        {
+            X25519Field.One(p.z);
+            X25519Field.Copy(p.x, 0, p.u, 0);
+            X25519Field.Copy(p.y, 0, p.v, 0);
+        }
+
+        private static void PointExtendXY(PointExt p)
+        {
+            X25519Field.One(p.z);
+            X25519Field.Mul(p.x, p.y, p.t);
+        }
+
+        private static void PointLookup(int block, int index, PointPrecomp p)
+        {
+            Debug.Assert(0 <= block && block < PrecompBlocks);
+            Debug.Assert(0 <= index && index < PrecompPoints);
+
+            int off = block * PrecompPoints * 3 * X25519Field.Size;
+
+            for (int i = 0; i < PrecompPoints; ++i)
+            {
+                int mask = ((i ^ index) - 1) >> 31;
+                Nat.CMov(X25519Field.Size, mask, precompBase, off, p.ypx_h, 0); off += X25519Field.Size;
+                Nat.CMov(X25519Field.Size, mask, precompBase, off, p.ymx_h, 0); off += X25519Field.Size;
+                Nat.CMov(X25519Field.Size, mask, precompBase, off, p.xyd, 0);   off += X25519Field.Size;
+            }
+        }
+
+        private static PointExt[] PointPrecompVar(PointExt p, int count)
+        {
+            Debug.Assert(count > 0);
+
+            PointExt d = new PointExt();
+            PointAddVar(false, p, p, d);
+
+            PointExt[] table = new PointExt[count];
+            table[0] = PointCopy(p);
+            for (int i = 1; i < count; ++i)
+            {
+                PointAddVar(false, table[i - 1], d, table[i] = new PointExt());
+            }
+            return table;
+        }
+
+        private static void PointSetNeutral(PointAccum p)
+        {
+            X25519Field.Zero(p.x);
+            X25519Field.One(p.y);
+            X25519Field.One(p.z);
+            X25519Field.Zero(p.u);
+            X25519Field.One(p.v);
+        }
+
+        private static void PointSetNeutral(PointExt p)
+        {
+            X25519Field.Zero(p.x);
+            X25519Field.One(p.y);
+            X25519Field.One(p.z);
+            X25519Field.Zero(p.t);
+        }
+
+        [MethodImpl(MethodImplOptions.Synchronized)]
+        public static void Precompute()
+        {
+            if (precompBase != null)
+            {
+                return;
+            }
+
+            // Precomputed table for the base point in verification ladder
+            {
+                PointExt b = new PointExt();
+                X25519Field.Copy(B_x, 0, b.x, 0);
+                X25519Field.Copy(B_y, 0, b.y, 0);
+                PointExtendXY(b);
+
+                precompBaseTable = PointPrecompVar(b, 1 << (WnafWidthBase - 2));
+            }
+
+            PointAccum p = new PointAccum();
+            X25519Field.Copy(B_x, 0, p.x, 0);
+            X25519Field.Copy(B_y, 0, p.y, 0);
+            PointExtendXY(p);
+
+            precompBase = new int[PrecompBlocks * PrecompPoints * 3 * X25519Field.Size];
+
+            int off = 0;
+            for (int b = 0; b < PrecompBlocks; ++b)
+            {
+                PointExt[] ds = new PointExt[PrecompTeeth];
+
+                PointExt sum = new PointExt();
+                PointSetNeutral(sum);
+
+                for (int t = 0; t < PrecompTeeth; ++t)
+                {
+                    PointExt q = PointCopy(p);
+                    PointAddVar(true, sum, q, sum);
+                    PointDouble(p);
+
+                    ds[t] = PointCopy(p);
+
+                    for (int s = 1; s < PrecompSpacing; ++s)
+                    {
+                        PointDouble(p);
+                    }
+                }
+
+                PointExt[] points = new PointExt[PrecompPoints];
+                int k = 0;
+                points[k++] = sum;
+
+                for (int t = 0; t < (PrecompTeeth - 1); ++t)
+                {
+                    int size = 1 << t;
+                    for (int j = 0; j < size; ++j, ++k)
+                    {
+                        PointAddVar(false, points[k - size], ds[t], points[k] = new PointExt());
+                    }
+                }
+
+                Debug.Assert(k == PrecompPoints);
+
+                for (int i = 0; i < PrecompPoints; ++i)
+                {
+                    PointExt q = points[i];
+
+                    int[] x = X25519Field.Create();
+                    int[] y = X25519Field.Create();
+
+                    X25519Field.Add(q.z, q.z, x);
+                    // TODO[ed25519] Batch inversion
+                    X25519Field.Inv(x, y);
+                    X25519Field.Mul(q.x, y, x);
+                    X25519Field.Mul(q.y, y, y);
+
+                    PointPrecomp r = new PointPrecomp();
+                    X25519Field.Apm(y, x, r.ypx_h, r.ymx_h);
+                    X25519Field.Mul(x, y, r.xyd);
+                    X25519Field.Mul(r.xyd, C_d4, r.xyd);
+
+                    X25519Field.Normalize(r.ypx_h);
+                    X25519Field.Normalize(r.ymx_h);
+                    //X25519Field.Normalize(r.xyd);
+
+                    X25519Field.Copy(r.ypx_h, 0, precompBase, off); off += X25519Field.Size;
+                    X25519Field.Copy(r.ymx_h, 0, precompBase, off); off += X25519Field.Size;
+                    X25519Field.Copy(r.xyd, 0, precompBase, off);   off += X25519Field.Size;
+                }
+            }
+
+            Debug.Assert(off == precompBase.Length);
+        }
+
+        private static void PruneScalar(byte[] n, int nOff, byte[] r)
+        {
+            Array.Copy(n, nOff, r, 0, ScalarBytes);
+
+            r[0] &= 0xF8;
+            r[ScalarBytes - 1] &= 0x7F;
+            r[ScalarBytes - 1] |= 0x40;
+        }
+
+        private static byte[] ReduceScalar(byte[] n)
+        {
+            long x00 = Decode32(n,  0) & M32L;          // x00:32/--
+            long x01 = (Decode24(n, 4) << 4) & M32L;    // x01:28/--
+            long x02 = Decode32(n,  7) & M32L;          // x02:32/--
+            long x03 = (Decode24(n, 11) << 4) & M32L;   // x03:28/--
+            long x04 = Decode32(n, 14) & M32L;          // x04:32/--
+            long x05 = (Decode24(n, 18) << 4) & M32L;   // x05:28/--
+            long x06 = Decode32(n, 21) & M32L;          // x06:32/--
+            long x07 = (Decode24(n, 25) << 4) & M32L;   // x07:28/--
+            long x08 = Decode32(n, 28) & M32L;          // x08:32/--
+            long x09 = (Decode24(n, 32) << 4) & M32L;   // x09:28/--
+            long x10 = Decode32(n, 35) & M32L;          // x10:32/--
+            long x11 = (Decode24(n, 39) << 4) & M32L;   // x11:28/--
+            long x12 = Decode32(n, 42) & M32L;          // x12:32/--
+            long x13 = (Decode24(n, 46) << 4) & M32L;   // x13:28/--
+            long x14 = Decode32(n, 49) & M32L;          // x14:32/--
+            long x15 = (Decode24(n, 53) << 4) & M32L;   // x15:28/--
+            long x16 = Decode32(n, 56) & M32L;          // x16:32/--
+            long x17 = (Decode24(n, 60) << 4) & M32L;   // x17:28/--
+            long x18 = n[63] & 0xFFL;                   // x18:08/--
+            long t;
+
+            //x18 += (x17 >> 28); x17 &= M28L;
+            x09 -= x18 * L0;                            // x09:34/28
+            x10 -= x18 * L1;                            // x10:33/30
+            x11 -= x18 * L2;                            // x11:35/28
+            x12 -= x18 * L3;                            // x12:32/31
+            x13 -= x18 * L4;                            // x13:28/21
+
+            x17 += (x16 >> 28); x16 &= M28L;            // x17:28/--, x16:28/--
+            x08 -= x17 * L0;                            // x08:54/32
+            x09 -= x17 * L1;                            // x09:52/51
+            x10 -= x17 * L2;                            // x10:55/34
+            x11 -= x17 * L3;                            // x11:51/36
+            x12 -= x17 * L4;                            // x12:41/--
+
+            //x16 += (x15 >> 28); x15 &= M28L;
+            x07 -= x16 * L0;                            // x07:54/28
+            x08 -= x16 * L1;                            // x08:54/53
+            x09 -= x16 * L2;                            // x09:55/53
+            x10 -= x16 * L3;                            // x10:55/52
+            x11 -= x16 * L4;                            // x11:51/41
+
+            x15 += (x14 >> 28); x14 &= M28L;            // x15:28/--, x14:28/--
+            x06 -= x15 * L0;                            // x06:54/32
+            x07 -= x15 * L1;                            // x07:54/53
+            x08 -= x15 * L2;                            // x08:56/--
+            x09 -= x15 * L3;                            // x09:55/54
+            x10 -= x15 * L4;                            // x10:55/53
+
+            //x14 += (x13 >> 28); x13 &= M28L;
+            x05 -= x14 * L0;                            // x05:54/28
+            x06 -= x14 * L1;                            // x06:54/53
+            x07 -= x14 * L2;                            // x07:56/--
+            x08 -= x14 * L3;                            // x08:56/51
+            x09 -= x14 * L4;                            // x09:56/--
+
+            x13 += (x12 >> 28); x12 &= M28L;            // x13:28/22, x12:28/--
+            x04 -= x13 * L0;                            // x04:54/49
+            x05 -= x13 * L1;                            // x05:54/53
+            x06 -= x13 * L2;                            // x06:56/--
+            x07 -= x13 * L3;                            // x07:56/52
+            x08 -= x13 * L4;                            // x08:56/52
+
+            x12 += (x11 >> 28); x11 &= M28L;            // x12:28/24, x11:28/--
+            x03 -= x12 * L0;                            // x03:54/49
+            x04 -= x12 * L1;                            // x04:54/51
+            x05 -= x12 * L2;                            // x05:56/--
+            x06 -= x12 * L3;                            // x06:56/52
+            x07 -= x12 * L4;                            // x07:56/53
+
+            x11 += (x10 >> 28); x10 &= M28L;            // x11:29/--, x10:28/--
+            x02 -= x11 * L0;                            // x02:55/32
+            x03 -= x11 * L1;                            // x03:55/--
+            x04 -= x11 * L2;                            // x04:56/55
+            x05 -= x11 * L3;                            // x05:56/52
+            x06 -= x11 * L4;                            // x06:56/53
+
+            x10 += (x09 >> 28); x09 &= M28L;            // x10:29/--, x09:28/--
+            x01 -= x10 * L0;                            // x01:55/28
+            x02 -= x10 * L1;                            // x02:55/54
+            x03 -= x10 * L2;                            // x03:56/55
+            x04 -= x10 * L3;                            // x04:57/--
+            x05 -= x10 * L4;                            // x05:56/53
+
+            x08 += (x07 >> 28); x07 &= M28L;            // x08:56/53, x07:28/--
+            x09 += (x08 >> 28); x08 &= M28L;            // x09:29/25, x08:28/--
+
+            t    = (x08 >> 27) & 1L;
+            x09 += t;                                   // x09:29/26
+
+            x00 -= x09 * L0;                            // x00:55/53
+            x01 -= x09 * L1;                            // x01:55/54
+            x02 -= x09 * L2;                            // x02:57/--
+            x03 -= x09 * L3;                            // x03:57/--
+            x04 -= x09 * L4;                            // x04:57/42
+
+            x01 += (x00 >> 28); x00 &= M28L;
+            x02 += (x01 >> 28); x01 &= M28L;
+            x03 += (x02 >> 28); x02 &= M28L;
+            x04 += (x03 >> 28); x03 &= M28L;
+            x05 += (x04 >> 28); x04 &= M28L;
+            x06 += (x05 >> 28); x05 &= M28L;
+            x07 += (x06 >> 28); x06 &= M28L;
+            x08 += (x07 >> 28); x07 &= M28L;
+            x09  = (x08 >> 28); x08 &= M28L;
+
+            x09 -= t;
+
+            Debug.Assert(x09 == 0L || x09 == -1L);
+
+            x00 += x09 & L0;
+            x01 += x09 & L1;
+            x02 += x09 & L2;
+            x03 += x09 & L3;
+            x04 += x09 & L4;
+
+            x01 += (x00 >> 28); x00 &= M28L;
+            x02 += (x01 >> 28); x01 &= M28L;
+            x03 += (x02 >> 28); x02 &= M28L;
+            x04 += (x03 >> 28); x03 &= M28L;
+            x05 += (x04 >> 28); x04 &= M28L;
+            x06 += (x05 >> 28); x05 &= M28L;
+            x07 += (x06 >> 28); x06 &= M28L;
+            x08 += (x07 >> 28); x07 &= M28L;
+
+            byte[] r = new byte[ScalarBytes];
+            Encode56((ulong)(x00 | (x01 << 28)), r, 0);
+            Encode56((ulong)(x02 | (x03 << 28)), r, 7);
+            Encode56((ulong)(x04 | (x05 << 28)), r, 14);
+            Encode56((ulong)(x06 | (x07 << 28)), r, 21);
+            Encode32((uint)x08, r, 28);
+            return r;
+        }
+
+        private static void ScalarMultBase(byte[] k, PointAccum r)
+        {
+            Precompute();
+
+            PointSetNeutral(r);
+
+            uint[] n = new uint[ScalarUints];
+            DecodeScalar(k, 0, n);
+
+            // Recode the scalar into signed-digit form, then group comb bits in each block
+            {
+                uint c1 = Nat.CAdd(ScalarUints, ~(int)n[0] & 1, n, L, n);   Debug.Assert(c1 == 0);
+                uint c2 = Nat.ShiftDownBit(ScalarUints, n, 1U);             Debug.Assert(c2 == (1U << 31));
+
+                for (int i = 0; i < ScalarUints; ++i)
+                {
+                    n[i] = Interleave.Shuffle2(n[i]);
+                }
+            }
+
+            PointPrecomp p = new PointPrecomp();
+
+            int cOff = (PrecompSpacing - 1) * PrecompTeeth;
+            for (; ; )
+            {
+                for (int b = 0; b < PrecompBlocks; ++b)
+                {
+                    uint w = n[b] >> cOff;
+                    int sign = (int)(w >> (PrecompTeeth - 1)) & 1;
+                    int abs = ((int)w ^ -sign) & PrecompMask;
+
+                    Debug.Assert(sign == 0 || sign == 1);
+                    Debug.Assert(0 <= abs && abs < PrecompPoints);
+
+                    PointLookup(b, abs, p);
+
+                    X25519Field.CSwap(sign, p.ypx_h, p.ymx_h);
+                    X25519Field.CNegate(sign, p.xyd);
+
+                    PointAddPrecomp(p, r);
+                }
+
+                if ((cOff -= PrecompTeeth) < 0)
+                {
+                    break;
+                }
+
+                PointDouble(r);
+            }
+        }
+
+        private static void ScalarMultBaseEncoded(byte[] k, byte[] r, int rOff)
+        {
+            PointAccum p = new PointAccum();
+            ScalarMultBase(k, p);
+            EncodePoint(p, r, rOff);
+        }
+
+        private static void ScalarMultStraussVar(uint[] nb, uint[] np, PointExt p, PointAccum r)
+        {
+            Precompute();
+
+            int width = 5;
+
+            sbyte[] ws_b = GetWnaf(nb, WnafWidthBase);
+            sbyte[] ws_p = GetWnaf(np, width);
+
+            PointExt[] tp = PointPrecompVar(p, 1 << (width - 2));
+
+            PointSetNeutral(r);
+
+            int bit = 255;
+            while (bit > 0 && (ws_b[bit] | ws_p[bit]) == 0)
+            {
+                --bit;
+            }
+
+            for (; ; )
+            {
+                int wb = ws_b[bit];
+                if (wb != 0)
+                {
+                    int sign = wb >> 31;
+                    int index = (wb ^ sign) >> 1;
+
+                    PointAddVar((sign != 0), precompBaseTable[index], r);
+                }
+
+                int wp = ws_p[bit];
+                if (wp != 0)
+                {
+                    int sign = wp >> 31;
+                    int index = (wp ^ sign) >> 1;
+
+                    PointAddVar((sign != 0), tp[index], r);
+                }
+
+                if (--bit < 0)
+                {
+                    break;
+                }
+
+                PointDouble(r);
+            }
+        }
+
+        public static void Sign(byte[] sk, int skOff, byte[] m, int mOff, int mLen, byte[] sig, int sigOff)
+        {
+            Sha512Digest d = new Sha512Digest();
+            byte[] h = new byte[d.GetDigestSize()];
+
+            d.BlockUpdate(sk, skOff, SecretKeySize);
+            d.DoFinal(h, 0);
+
+            byte[] s = new byte[ScalarBytes];
+            PruneScalar(h, 0, s);
+
+            byte[] pk = new byte[PointBytes];
+            ScalarMultBaseEncoded(s, pk, 0);
+
+            ImplSign(d, h, s, pk, 0, m, mOff, mLen, sig, sigOff);
+        }
+
+        public static void Sign(byte[] sk, int skOff, byte[] pk, int pkOff, byte[] m, int mOff, int mLen, byte[] sig, int sigOff)
+        {
+            Sha512Digest d = new Sha512Digest();
+            byte[] h = new byte[d.GetDigestSize()];
+
+            d.BlockUpdate(sk, skOff, SecretKeySize);
+            d.DoFinal(h, 0);
+
+            byte[] s = new byte[ScalarBytes];
+            PruneScalar(h, 0, s);
+
+            ImplSign(d, h, s, pk, pkOff, m, mOff, mLen, sig, sigOff);
+        }
+
+        public static bool Verify(byte[] sig, int sigOff, byte[] pk, int pkOff, byte[] m, int mOff, int mLen)
+        {
+            byte[] R = Arrays.CopyOfRange(sig, sigOff, sigOff + PointBytes);
+            byte[] S = Arrays.CopyOfRange(sig, sigOff + PointBytes, sigOff + SignatureSize);
+
+            if (!CheckPointVar(R))
+            {
+                return false;
+            }
+            if (!CheckScalarVar(S))
+            {
+                return false;
+            }
+
+            PointExt pA = new PointExt();
+            if (!DecodePointVar(pk, pkOff, true, pA))
+            {
+                return false;
+            }
+
+            Sha512Digest d = new Sha512Digest();
+            byte[] h = new byte[d.GetDigestSize()];
+
+            d.BlockUpdate(R, 0, PointBytes);
+            d.BlockUpdate(pk, pkOff, PointBytes);
+            d.BlockUpdate(m, mOff, mLen);
+            d.DoFinal(h, 0);
+
+            byte[] k = ReduceScalar(h);
+
+            uint[] nS = new uint[ScalarUints];
+            DecodeScalar(S, 0, nS);
+
+            uint[] nA = new uint[ScalarUints];
+            DecodeScalar(k, 0, nA);
+
+            PointAccum pR = new PointAccum();
+            ScalarMultStraussVar(nS, nA, pA, pR);
+
+            byte[] check = new byte[PointBytes];
+            EncodePoint(pR, check, 0);
+
+            return Arrays.AreEqual(check, R);
+        }
+    }
+}
diff --git a/crypto/src/math/ec/rfc8032/Ed448.cs b/crypto/src/math/ec/rfc8032/Ed448.cs
new file mode 100644
index 000000000..52c215160
--- /dev/null
+++ b/crypto/src/math/ec/rfc8032/Ed448.cs
@@ -0,0 +1,1067 @@
+using System;
+using System.Diagnostics;
+using System.Runtime.CompilerServices;
+
+using Org.BouncyCastle.Crypto.Digests;
+using Org.BouncyCastle.Math.EC.Rfc7748;
+using Org.BouncyCastle.Math.Raw;
+using Org.BouncyCastle.Utilities;
+
+namespace Org.BouncyCastle.Math.EC.Rfc8032
+{
+    public abstract class Ed448
+    {
+        private const ulong M26UL = 0x03FFFFFFUL;
+        private const ulong M28UL = 0x0FFFFFFFUL;
+
+        private const int PointBytes = 57;
+        private const int ScalarUints = 14;
+        private const int ScalarBytes = ScalarUints * 4 + 1;
+
+        public static readonly int PublicKeySize = PointBytes;
+        public static readonly int SecretKeySize = 57;
+        public static readonly int SignatureSize = PointBytes + ScalarBytes;
+
+        private static readonly byte[] Dom4Prefix = Strings.ToByteArray("SigEd448");
+
+        private static readonly uint[] P = { 0xFFFFFFFFU, 0xFFFFFFFFU, 0xFFFFFFFFU, 0xFFFFFFFFU, 0xFFFFFFFFU, 0xFFFFFFFFU, 0xFFFFFFFFU,
+            0xFFFFFFFEU, 0xFFFFFFFFU, 0xFFFFFFFFU, 0xFFFFFFFFU, 0xFFFFFFFFU, 0xFFFFFFFFU, 0xFFFFFFFFU };
+        private static readonly uint[] L = { 0xAB5844F3U, 0x2378C292U, 0x8DC58F55U, 0x216CC272U, 0xAED63690U, 0xC44EDB49U, 0x7CCA23E9U,
+            0xFFFFFFFFU, 0xFFFFFFFFU, 0xFFFFFFFFU, 0xFFFFFFFFU, 0xFFFFFFFFU, 0xFFFFFFFFU, 0x3FFFFFFFU };
+        private static readonly BigInteger N = Nat.ToBigInteger(L.Length, L);
+
+        private const int L_0 = 0x04A7BB0D;     // L_0:26/24
+        private const int L_1 = 0x0873D6D5;     // L_1:27/23
+        private const int L_2 = 0x0A70AADC;     // L_2:27/26
+        private const int L_3 = 0x03D8D723;     // L_3:26/--
+        private const int L_4 = 0x096FDE93;     // L_4:27/25
+        private const int L_5 = 0x0B65129C;     // L_5:27/26
+        private const int L_6 = 0x063BB124;     // L_6:27/--
+        private const int L_7 = 0x08335DC1;     // L_7:27/22
+
+        private const int L4_0 = 0x029EEC34;    // L4_0:25/24
+        private const int L4_1 = 0x01CF5B55;    // L4_1:25/--
+        private const int L4_2 = 0x09C2AB72;    // L4_2:27/25
+        private const int L4_3 = 0x0F635C8E;    // L4_3:28/--
+        private const int L4_4 = 0x05BF7A4C;    // L4_4:26/25
+        private const int L4_5 = 0x0D944A72;    // L4_5:28/--
+        private const int L4_6 = 0x08EEC492;    // L4_6:27/24
+        private const int L4_7 = 0x20CD7705;    // L4_7:29/24
+
+        private static readonly uint[] B_x = { 0x070CC05EU, 0x026A82BCU, 0x00938E26U, 0x080E18B0U, 0x0511433BU, 0x0F72AB66U, 0x0412AE1AU,
+            0x0A3D3A46U, 0x0A6DE324U, 0x00F1767EU, 0x04657047U, 0x036DA9E1U, 0x05A622BFU, 0x0ED221D1U, 0x066BED0DU, 0x04F1970CU };
+        private static readonly uint[] B_y = { 0x0230FA14U, 0x008795BFU, 0x07C8AD98U, 0x0132C4EDU, 0x09C4FDBDU, 0x01CE67C3U, 0x073AD3FFU,
+            0x005A0C2DU, 0x07789C1EU, 0x0A398408U, 0x0A73736CU, 0x0C7624BEU, 0x003756C9U, 0x02488762U, 0x016EB6BCU, 0x0693F467U };
+        private const int C_d = -39081;
+
+        private const int WnafWidthBase = 7;
+
+        private const int PrecompBlocks = 5;
+        private const int PrecompTeeth = 5;
+        private const int PrecompSpacing = 18;
+        private const int PrecompPoints = 1 << (PrecompTeeth - 1);
+        private const int PrecompMask = PrecompPoints - 1;
+
+        // TODO[ed448] Convert to PointPrecomp
+        private static PointExt[] precompBaseTable = null;
+        private static uint[] precompBase = null;
+
+        private class PointExt
+        {
+            internal uint[] x = X448Field.Create();
+            internal uint[] y = X448Field.Create();
+            internal uint[] z = X448Field.Create();
+        }
+
+        private class PointPrecomp
+        {
+            internal uint[] x = X448Field.Create();
+            internal uint[] y = X448Field.Create();
+        }
+
+        private static byte[] CalculateS(byte[] r, byte[] k, byte[] s)
+        {
+            uint[] t = new uint[ScalarUints * 2];   DecodeScalar(r, 0, t);
+            uint[] u = new uint[ScalarUints];       DecodeScalar(k, 0, u);
+            uint[] v = new uint[ScalarUints];       DecodeScalar(s, 0, v);
+
+            Nat.MulAddTo(14, u, v, t);
+
+            byte[] result = new byte[ScalarBytes * 2];
+            for (int i = 0; i < t.Length; ++i)
+            {
+                Encode32(t[i], result, i * 4);
+            }
+            return ReduceScalar(result);
+        }
+
+        private static bool CheckContextVar(byte[] ctx)
+        {
+            return ctx != null && ctx.Length < 256;
+        }
+
+        private static bool CheckPointVar(byte[] p)
+        {
+            if ((p[PointBytes - 1] & 0x7F) != 0x00)
+            {
+                return false;
+            }
+
+            uint[] t = new uint[14];
+            Decode32(p, 0, t, 0, 14);
+            return !Nat.Gte(14, t, P);
+        }
+
+        private static bool CheckScalarVar(byte[] s)
+        {
+            if (s[ScalarBytes - 1] != 0x00)
+            {
+                return false;
+            }
+
+            uint[] n = new uint[ScalarUints];
+            DecodeScalar(s, 0, n);
+            return !Nat.Gte(ScalarUints, n, L);
+        }
+
+        private static uint Decode16(byte[] bs, int off)
+        {
+            uint n = bs[off];
+            n |= (uint)bs[++off] << 8;
+            return n;
+        }
+
+        private static uint Decode24(byte[] bs, int off)
+        {
+            uint n = bs[off];
+            n |= (uint)bs[++off] << 8;
+            n |= (uint)bs[++off] << 16;
+            return n;
+        }
+
+        private static uint Decode32(byte[] bs, int off)
+        {
+            uint n = bs[off];
+            n |= (uint)bs[++off] << 8;
+            n |= (uint)bs[++off] << 16;
+            n |= (uint)bs[++off] << 24;
+            return n;
+        }
+
+        private static void Decode32(byte[] bs, int bsOff, uint[] n, int nOff, int nLen)
+        {
+            for (int i = 0; i < nLen; ++i)
+            {
+                n[nOff + i] = Decode32(bs, bsOff + i * 4);
+            }
+        }
+
+        private static bool DecodePointVar(byte[] p, int pOff, bool negate, PointExt r)
+        {
+            byte[] py = Arrays.CopyOfRange(p, pOff, pOff + PointBytes);
+            if (!CheckPointVar(py))
+            {
+                return false;
+            }
+
+            int x_0 = (py[PointBytes - 1] & 0x80) >> 7;
+            py[PointBytes - 1] &= 0x7F;
+
+            X448Field.Decode(py, 0, r.y);
+
+            uint[] u = X448Field.Create();
+            uint[] v = X448Field.Create();
+
+            X448Field.Sqr(r.y, u);
+            X448Field.Mul(u, (uint)-C_d, v);
+            X448Field.Negate(u, u);
+            X448Field.AddOne(u);
+            X448Field.AddOne(v);
+
+            if (!X448Field.SqrtRatioVar(u, v, r.x))
+            {
+                return false;
+            }
+
+            X448Field.Normalize(r.x);
+            if (x_0 == 1 && X448Field.IsZeroVar(r.x))
+            {
+                return false;
+            }
+
+            if (negate ^ (x_0 != (r.x[0] & 1)))
+            {
+                X448Field.Negate(r.x, r.x);
+            }
+
+            PointExtendXY(r);
+            return true;
+        }
+
+        private static void DecodeScalar(byte[] k, int kOff, uint[] n)
+        {
+            Debug.Assert(k[kOff + ScalarBytes - 1] == 0x00);
+
+            Decode32(k, kOff, n, 0, ScalarUints);
+        }
+
+        private static void Dom4(ShakeDigest d, byte x, byte[] y)
+        {
+            d.BlockUpdate(Dom4Prefix, 0, Dom4Prefix.Length);
+            d.Update(x);
+            d.Update((byte)y.Length);
+            d.BlockUpdate(y, 0, y.Length);
+        }
+
+        private static void Encode24(uint n, byte[] bs, int off)
+        {
+            bs[off] = (byte)(n);
+            bs[++off] = (byte)(n >> 8);
+            bs[++off] = (byte)(n >> 16);
+        }
+
+        private static void Encode32(uint n, byte[] bs, int off)
+        {
+            bs[off] = (byte)(n);
+            bs[++off] = (byte)(n >> 8);
+            bs[++off] = (byte)(n >> 16);
+            bs[++off] = (byte)(n >> 24);
+        }
+
+        private static void Encode56(ulong n, byte[] bs, int off)
+        {
+            Encode32((uint)n, bs, off);
+            Encode24((uint)(n >> 32), bs, off + 4);
+        }
+
+        private static void EncodePoint(PointExt p, byte[] r, int rOff)
+        {
+            uint[] x = X448Field.Create();
+            uint[] y = X448Field.Create();
+
+            X448Field.Inv(p.z, y);
+            X448Field.Mul(p.x, y, x);
+            X448Field.Mul(p.y, y, y);
+            X448Field.Normalize(x);
+            X448Field.Normalize(y);
+
+            X448Field.Encode(y, r, rOff);
+            r[rOff + PointBytes - 1] = (byte)((x[0] & 1) << 7);
+        }
+
+        public static void GeneratePublicKey(byte[] sk, int skOff, byte[] pk, int pkOff)
+        {
+            ShakeDigest d = new ShakeDigest(256);
+            byte[] h = new byte[ScalarBytes * 2];
+
+            d.BlockUpdate(sk, skOff, SecretKeySize);
+            d.DoFinal(h, 0, h.Length);
+
+            byte[] s = new byte[ScalarBytes];
+            PruneScalar(h, 0, s);
+
+            ScalarMultBaseEncoded(s, pk, pkOff);
+        }
+
+        private static sbyte[] GetWnaf(uint[] n, int width)
+        {
+            Debug.Assert(n[ScalarUints - 1] >> 31 == 0U);
+
+            uint[] t = new uint[ScalarUints * 2];
+            {
+                uint c = 0;
+                int tPos = t.Length, i = ScalarUints;
+                while (--i >= 0)
+                {
+                    uint next = n[i];
+                    t[--tPos] = (next >> 16) | (c << 16);
+                    t[--tPos] = c = next;
+                }
+            }
+
+            sbyte[] ws = new sbyte[448];
+
+            uint pow2 = 1U << width;
+            uint mask = pow2 - 1U;
+            uint sign = pow2 >> 1;
+
+            uint carry = 0U;
+            int j = 0;
+            for (int i = 0; i < t.Length; ++i, j -= 16)
+            {
+                uint word = t[i];
+                while (j < 16)
+                {
+                    uint word16 = word >> j;
+                    uint bit = word16 & 1U;
+
+                    if (bit == carry)
+                    {
+                        ++j;
+                        continue;
+                    }
+
+                    uint digit = (word16 & mask) + carry;
+                    carry = digit & sign;
+                    digit -= (carry << 1);
+                    carry >>= (width - 1);
+
+                    ws[(i << 4) + j] = (sbyte)digit;
+
+                    j += width;
+                }
+            }
+
+            Debug.Assert(carry == 0);
+
+            return ws;
+        }
+
+        private static void ImplSign(ShakeDigest d, byte[] h, byte[] s, byte[] pk, int pkOff, byte[] ctx, byte[] m, int mOff, int mLen, byte[] sig, int sigOff)
+        {
+            byte phflag = 0x00;
+
+            Dom4(d, phflag, ctx);
+            d.BlockUpdate(h, ScalarBytes, ScalarBytes);
+            d.BlockUpdate(m, mOff, mLen);
+            d.DoFinal(h, 0, h.Length);
+
+            byte[] r = ReduceScalar(h);
+            byte[] R = new byte[PointBytes];
+            ScalarMultBaseEncoded(r, R, 0);
+
+            Dom4(d, phflag, ctx);
+            d.BlockUpdate(R, 0, PointBytes);
+            d.BlockUpdate(pk, pkOff, PointBytes);
+            d.BlockUpdate(m, mOff, mLen);
+            d.DoFinal(h, 0, h.Length);
+
+            byte[] k = ReduceScalar(h);
+            byte[] S = CalculateS(r, k, s);
+
+            Array.Copy(R, 0, sig, sigOff, PointBytes);
+            Array.Copy(S, 0, sig, sigOff + PointBytes, ScalarBytes);
+        }
+
+        private static void PointAddVar(bool negate, PointExt p, PointExt r)
+        {
+            uint[] A = X448Field.Create();
+            uint[] B = X448Field.Create();
+            uint[] C = X448Field.Create();
+            uint[] D = X448Field.Create();
+            uint[] E = X448Field.Create();
+            uint[] F = X448Field.Create();
+            uint[] G = X448Field.Create();
+            uint[] H = X448Field.Create();
+
+            uint[] b, e, f, g;
+            if (negate)
+            {
+                b = E; e = B; f = G; g = F;
+                X448Field.Sub(p.y, p.x, H);
+            }
+            else
+            {
+                b = B; e = E; f = F; g = G;
+                X448Field.Add(p.y, p.x, H);
+            }
+
+            X448Field.Mul(p.z, r.z, A);
+            X448Field.Sqr(A, B);
+            X448Field.Mul(p.x, r.x, C);
+            X448Field.Mul(p.y, r.y, D);
+            X448Field.Mul(C, D, E);
+            X448Field.Mul(E, -C_d, E);
+    //        X448Field.Apm(B, E, F, G);
+            X448Field.Add(B, E, f);
+            X448Field.Sub(B, E, g);
+            X448Field.Add(r.x, r.y, E);
+            X448Field.Mul(H, E, H);
+    //        X448Field.Apm(D, C, B, E);
+            X448Field.Add(D, C, b);
+            X448Field.Sub(D, C, e);
+            X448Field.Carry(b);
+            X448Field.Sub(H, B, H);
+            X448Field.Mul(H, A, H);
+            X448Field.Mul(E, A, E);
+            X448Field.Mul(F, H, r.x);
+            X448Field.Mul(E, G, r.y);
+            X448Field.Mul(F, G, r.z);
+        }
+
+        private static void PointAddPrecomp(PointPrecomp p, PointExt r)
+        {
+            uint[] B = X448Field.Create();
+            uint[] C = X448Field.Create();
+            uint[] D = X448Field.Create();
+            uint[] E = X448Field.Create();
+            uint[] F = X448Field.Create();
+            uint[] G = X448Field.Create();
+            uint[] H = X448Field.Create();
+
+            X448Field.Sqr(r.z, B);
+            X448Field.Mul(p.x, r.x, C);
+            X448Field.Mul(p.y, r.y, D);
+            X448Field.Mul(C, D, E);
+            X448Field.Mul(E, -C_d, E);
+    //        X448Field.Apm(B, E, F, G);
+            X448Field.Add(B, E, F);
+            X448Field.Sub(B, E, G);
+            X448Field.Add(p.x, p.y, B);
+            X448Field.Add(r.x, r.y, E);
+            X448Field.Mul(B, E, H);
+    //        X448Field.Apm(D, C, B, E);
+            X448Field.Add(D, C, B);
+            X448Field.Sub(D, C, E);
+            X448Field.Carry(B);
+            X448Field.Sub(H, B, H);
+            X448Field.Mul(H, r.z, H);
+            X448Field.Mul(E, r.z, E);
+            X448Field.Mul(F, H, r.x);
+            X448Field.Mul(E, G, r.y);
+            X448Field.Mul(F, G, r.z);
+        }
+
+        private static PointExt PointCopy(PointExt p)
+        {
+            PointExt r = new PointExt();
+            X448Field.Copy(p.x, 0, r.x, 0);
+            X448Field.Copy(p.y, 0, r.y, 0);
+            X448Field.Copy(p.z, 0, r.z, 0);
+            return r;
+        }
+
+        private static void PointDouble(PointExt r)
+        {
+            uint[] B = X448Field.Create();
+            uint[] C = X448Field.Create();
+            uint[] D = X448Field.Create();
+            uint[] E = X448Field.Create();
+            uint[] H = X448Field.Create();
+            uint[] J = X448Field.Create();
+
+            X448Field.Add(r.x, r.y, B);
+            X448Field.Sqr(B, B);
+            X448Field.Sqr(r.x, C);
+            X448Field.Sqr(r.y, D);
+            X448Field.Add(C, D, E);
+            X448Field.Carry(E);
+            X448Field.Sqr(r.z, H);
+            X448Field.Add(H, H, H);
+            X448Field.Carry(H);
+            X448Field.Sub(E, H, J);
+            X448Field.Sub(B, E, B);
+            X448Field.Sub(C, D, C);
+            X448Field.Mul(B, J, r.x);
+            X448Field.Mul(E, C, r.y);
+            X448Field.Mul(E, J, r.z);
+        }
+
+        private static void PointExtendXY(PointExt p)
+        {
+            X448Field.One(p.z);
+        }
+
+        private static void PointLookup(int block, int index, PointPrecomp p)
+        {
+            Debug.Assert(0 <= block && block < PrecompBlocks);
+            Debug.Assert(0 <= index && index < PrecompPoints);
+
+            int off = block * PrecompPoints * 2 * X448Field.Size;
+
+            for (int i = 0; i < PrecompPoints; ++i)
+            {
+                int mask = ((i ^ index) - 1) >> 31;
+                Nat.CMov(X448Field.Size, mask, precompBase, off, p.x, 0);   off += X448Field.Size;
+                Nat.CMov(X448Field.Size, mask, precompBase, off, p.y, 0);   off += X448Field.Size;
+            }
+        }
+
+        private static PointExt[] PointPrecompVar(PointExt p, int count)
+        {
+            Debug.Assert(count > 0);
+
+            PointExt d = PointCopy(p);
+            PointDouble(d);
+
+            PointExt[] table = new PointExt[count];
+            table[0] = PointCopy(p);
+            for (int i = 1; i < count; ++i)
+            {
+                table[i] = PointCopy(table[i - 1]);
+                PointAddVar(false, d, table[i]);
+            }
+            return table;
+        }
+
+        private static void PointSetNeutral(PointExt p)
+        {
+            X448Field.Zero(p.x);
+            X448Field.One(p.y);
+            X448Field.One(p.z);
+        }
+
+        [MethodImpl(MethodImplOptions.Synchronized)]
+        public static void Precompute()
+        {
+            if (precompBase != null)
+            {
+                return;
+            }
+
+            PointExt p = new PointExt();
+            X448Field.Copy(B_x, 0, p.x, 0);
+            X448Field.Copy(B_y, 0, p.y, 0);
+            PointExtendXY(p);
+
+            precompBaseTable = PointPrecompVar(p, 1 << (WnafWidthBase - 2));
+
+            precompBase = new uint[PrecompBlocks * PrecompPoints * 2 * X448Field.Size];
+
+            int off = 0;
+            for (int b = 0; b < PrecompBlocks; ++b)
+            {
+                PointExt[] ds = new PointExt[PrecompTeeth];
+
+                PointExt sum = new PointExt();
+                PointSetNeutral(sum);
+
+                for (int t = 0; t < PrecompTeeth; ++t)
+                {
+                    PointAddVar(true, p, sum);
+                    PointDouble(p);
+
+                    ds[t] = PointCopy(p);
+
+                    for (int s = 1; s < PrecompSpacing; ++s)
+                    {
+                        PointDouble(p);
+                    }
+                }
+
+                PointExt[] points = new PointExt[PrecompPoints];
+                int k = 0;
+                points[k++] = sum;
+
+                for (int t = 0; t < (PrecompTeeth - 1); ++t)
+                {
+                    int size = 1 << t;
+                    for (int j = 0; j < size; ++j, ++k)
+                    {
+                        points[k] = PointCopy(points[k - size]);
+                        PointAddVar(false, ds[t], points[k]);
+                    }
+                }
+
+                Debug.Assert(k == PrecompPoints);
+
+                for (int i = 0; i < PrecompPoints; ++i)
+                {
+                    PointExt q = points[i];
+                    // TODO[ed448] Batch inversion
+                    X448Field.Inv(q.z, q.z);
+                    X448Field.Mul(q.x, q.z, q.x);
+                    X448Field.Mul(q.y, q.z, q.y);
+
+    //                X448Field.Normalize(q.x);
+    //                X448Field.Normalize(q.y);
+
+                    X448Field.Copy(q.x, 0, precompBase, off);   off += X448Field.Size;
+                    X448Field.Copy(q.y, 0, precompBase, off);   off += X448Field.Size;
+                }
+            }
+
+            Debug.Assert(off == precompBase.Length);
+        }
+
+        private static void PruneScalar(byte[] n, int nOff, byte[] r)
+        {
+            Array.Copy(n, nOff, r, 0, ScalarBytes);
+
+            r[0] &= 0xFC;
+            r[ScalarBytes - 2] |= 0x80;
+            r[ScalarBytes - 1] &= 0x00;
+        }
+
+        private static byte[] ReduceScalar(byte[] n)
+        {
+            ulong x00 =  Decode32(n,   0);          // x00:32/--
+            ulong x01 = (Decode24(n,   4) << 4);    // x01:28/--
+            ulong x02 =  Decode32(n,   7);          // x02:32/--
+            ulong x03 = (Decode24(n,  11) << 4);    // x03:28/--
+            ulong x04 =  Decode32(n,  14);          // x04:32/--
+            ulong x05 = (Decode24(n,  18) << 4);    // x05:28/--
+            ulong x06 =  Decode32(n,  21);          // x06:32/--
+            ulong x07 = (Decode24(n,  25) << 4);    // x07:28/--
+            ulong x08 =  Decode32(n,  28);          // x08:32/--
+            ulong x09 = (Decode24(n,  32) << 4);    // x09:28/--
+            ulong x10 =  Decode32(n,  35);          // x10:32/--
+            ulong x11 = (Decode24(n,  39) << 4);    // x11:28/--
+            ulong x12 =  Decode32(n,  42);          // x12:32/--
+            ulong x13 = (Decode24(n,  46) << 4);    // x13:28/--
+            ulong x14 =  Decode32(n,  49);          // x14:32/--
+            ulong x15 = (Decode24(n,  53) << 4);    // x15:28/--
+            ulong x16 =  Decode32(n,  56);          // x16:32/--
+            ulong x17 = (Decode24(n,  60) << 4);    // x17:28/--
+            ulong x18 =  Decode32(n,  63);          // x18:32/--
+            ulong x19 = (Decode24(n,  67) << 4);    // x19:28/--
+            ulong x20 =  Decode32(n,  70);          // x20:32/--
+            ulong x21 = (Decode24(n,  74) << 4);    // x21:28/--
+            ulong x22 =  Decode32(n,  77);          // x22:32/--
+            ulong x23 = (Decode24(n,  81) << 4);    // x23:28/--
+            ulong x24 =  Decode32(n,  84);          // x24:32/--
+            ulong x25 = (Decode24(n,  88) << 4);    // x25:28/--
+            ulong x26 =  Decode32(n,  91);          // x26:32/--
+            ulong x27 = (Decode24(n,  95) << 4);    // x27:28/--
+            ulong x28 =  Decode32(n,  98);          // x28:32/--
+            ulong x29 = (Decode24(n, 102) << 4);    // x29:28/--
+            ulong x30 =  Decode32(n, 105);          // x30:32/--
+            ulong x31 = (Decode24(n, 109) << 4);    // x31:28/--
+            ulong x32 =  Decode16(n, 112);          // x32:16/--
+
+    //        x32 += (x31 >> 28); x31 &= M28UL;
+            x16 += x32 * L4_0;                          // x16:42/--
+            x17 += x32 * L4_1;                          // x17:41/28
+            x18 += x32 * L4_2;                          // x18:43/42
+            x19 += x32 * L4_3;                          // x19:44/28
+            x20 += x32 * L4_4;                          // x20:43/--
+            x21 += x32 * L4_5;                          // x21:44/28
+            x22 += x32 * L4_6;                          // x22:43/41
+            x23 += x32 * L4_7;                          // x23:45/41
+
+            x31 += (x30 >> 28); x30 &= M28UL;           // x31:28/--, x30:28/--
+            x15 += x31 * L4_0;                          // x15:54/--
+            x16 += x31 * L4_1;                          // x16:53/42
+            x17 += x31 * L4_2;                          // x17:55/54
+            x18 += x31 * L4_3;                          // x18:56/44
+            x19 += x31 * L4_4;                          // x19:55/--
+            x20 += x31 * L4_5;                          // x20:56/43
+            x21 += x31 * L4_6;                          // x21:55/53
+            x22 += x31 * L4_7;                          // x22:57/53
+
+    //        x30 += (x29 >> 28); x29 &= M28UL;
+            x14 += x30 * L4_0;                          // x14:54/--
+            x15 += x30 * L4_1;                          // x15:54/53
+            x16 += x30 * L4_2;                          // x16:56/--
+            x17 += x30 * L4_3;                          // x17:57/--
+            x18 += x30 * L4_4;                          // x18:56/55
+            x19 += x30 * L4_5;                          // x19:56/55
+            x20 += x30 * L4_6;                          // x20:57/--
+            x21 += x30 * L4_7;                          // x21:57/56
+
+            x29 += (x28 >> 28); x28 &= M28UL;           // x29:28/--, x28:28/--
+            x13 += x29 * L4_0;                          // x13:54/--
+            x14 += x29 * L4_1;                          // x14:54/53
+            x15 += x29 * L4_2;                          // x15:56/--
+            x16 += x29 * L4_3;                          // x16:57/--
+            x17 += x29 * L4_4;                          // x17:57/55
+            x18 += x29 * L4_5;                          // x18:57/55
+            x19 += x29 * L4_6;                          // x19:57/52
+            x20 += x29 * L4_7;                          // x20:58/52
+
+    //        x28 += (x27 >> 28); x27 &= M28UL;
+            x12 += x28 * L4_0;                          // x12:54/--
+            x13 += x28 * L4_1;                          // x13:54/53
+            x14 += x28 * L4_2;                          // x14:56/--
+            x15 += x28 * L4_3;                          // x15:57/--
+            x16 += x28 * L4_4;                          // x16:57/55
+            x17 += x28 * L4_5;                          // x17:58/--
+            x18 += x28 * L4_6;                          // x18:58/--
+            x19 += x28 * L4_7;                          // x19:58/53
+
+            x27 += (x26 >> 28); x26 &= M28UL;           // x27:28/--, x26:28/--
+            x11 += x27 * L4_0;                          // x11:54/--
+            x12 += x27 * L4_1;                          // x12:54/53
+            x13 += x27 * L4_2;                          // x13:56/--
+            x14 += x27 * L4_3;                          // x14:57/--
+            x15 += x27 * L4_4;                          // x15:57/55
+            x16 += x27 * L4_5;                          // x16:58/--
+            x17 += x27 * L4_6;                          // x17:58/56
+            x18 += x27 * L4_7;                          // x18:59/--
+
+    //        x26 += (x25 >> 28); x25 &= M28UL;
+            x10 += x26 * L4_0;                          // x10:54/--
+            x11 += x26 * L4_1;                          // x11:54/53
+            x12 += x26 * L4_2;                          // x12:56/--
+            x13 += x26 * L4_3;                          // x13:57/--
+            x14 += x26 * L4_4;                          // x14:57/55
+            x15 += x26 * L4_5;                          // x15:58/--
+            x16 += x26 * L4_6;                          // x16:58/56
+            x17 += x26 * L4_7;                          // x17:59/--
+
+            x25 += (x24 >> 28); x24 &= M28UL;           // x25:28/--, x24:28/--
+            x09 += x25 * L4_0;                          // x09:54/--
+            x10 += x25 * L4_1;                          // x10:54/53
+            x11 += x25 * L4_2;                          // x11:56/--
+            x12 += x25 * L4_3;                          // x12:57/--
+            x13 += x25 * L4_4;                          // x13:57/55
+            x14 += x25 * L4_5;                          // x14:58/--
+            x15 += x25 * L4_6;                          // x15:58/56
+            x16 += x25 * L4_7;                          // x16:59/--
+
+            x21 += (x20 >> 28); x20 &= M28UL;           // x21:58/--, x20:28/--
+            x22 += (x21 >> 28); x21 &= M28UL;           // x22:57/54, x21:28/--
+            x23 += (x22 >> 28); x22 &= M28UL;           // x23:45/42, x22:28/--
+            x24 += (x23 >> 28); x23 &= M28UL;           // x24:28/18, x23:28/--
+
+            x08 += x24 * L4_0;                          // x08:54/--
+            x09 += x24 * L4_1;                          // x09:55/--
+            x10 += x24 * L4_2;                          // x10:56/46
+            x11 += x24 * L4_3;                          // x11:57/46
+            x12 += x24 * L4_4;                          // x12:57/55
+            x13 += x24 * L4_5;                          // x13:58/--
+            x14 += x24 * L4_6;                          // x14:58/56
+            x15 += x24 * L4_7;                          // x15:59/--
+
+            x07 += x23 * L4_0;                          // x07:54/--
+            x08 += x23 * L4_1;                          // x08:54/53
+            x09 += x23 * L4_2;                          // x09:56/53
+            x10 += x23 * L4_3;                          // x10:57/46
+            x11 += x23 * L4_4;                          // x11:57/55
+            x12 += x23 * L4_5;                          // x12:58/--
+            x13 += x23 * L4_6;                          // x13:58/56
+            x14 += x23 * L4_7;                          // x14:59/--
+
+            x06 += x22 * L4_0;                          // x06:54/--
+            x07 += x22 * L4_1;                          // x07:54/53
+            x08 += x22 * L4_2;                          // x08:56/--
+            x09 += x22 * L4_3;                          // x09:57/53
+            x10 += x22 * L4_4;                          // x10:57/55
+            x11 += x22 * L4_5;                          // x11:58/--
+            x12 += x22 * L4_6;                          // x12:58/56
+            x13 += x22 * L4_7;                          // x13:59/--
+
+            x18 += (x17 >> 28); x17 &= M28UL;           // x18:59/31, x17:28/--
+            x19 += (x18 >> 28); x18 &= M28UL;           // x19:58/54, x18:28/--
+            x20 += (x19 >> 28); x19 &= M28UL;           // x20:30/29, x19:28/--
+            x21 += (x20 >> 28); x20 &= M28UL;           // x21:28/03, x20:28/--
+
+            x05 += x21 * L4_0;                          // x05:54/--
+            x06 += x21 * L4_1;                          // x06:55/--
+            x07 += x21 * L4_2;                          // x07:56/31
+            x08 += x21 * L4_3;                          // x08:57/31
+            x09 += x21 * L4_4;                          // x09:57/56
+            x10 += x21 * L4_5;                          // x10:58/--
+            x11 += x21 * L4_6;                          // x11:58/56
+            x12 += x21 * L4_7;                          // x12:59/--
+
+            x04 += x20 * L4_0;                          // x04:54/--
+            x05 += x20 * L4_1;                          // x05:54/53
+            x06 += x20 * L4_2;                          // x06:56/53
+            x07 += x20 * L4_3;                          // x07:57/31
+            x08 += x20 * L4_4;                          // x08:57/55
+            x09 += x20 * L4_5;                          // x09:58/--
+            x10 += x20 * L4_6;                          // x10:58/56
+            x11 += x20 * L4_7;                          // x11:59/--
+
+            x03 += x19 * L4_0;                          // x03:54/--
+            x04 += x19 * L4_1;                          // x04:54/53
+            x05 += x19 * L4_2;                          // x05:56/--
+            x06 += x19 * L4_3;                          // x06:57/53
+            x07 += x19 * L4_4;                          // x07:57/55
+            x08 += x19 * L4_5;                          // x08:58/--
+            x09 += x19 * L4_6;                          // x09:58/56
+            x10 += x19 * L4_7;                          // x10:59/--
+
+            x15 += (x14 >> 28); x14 &= M28UL;           // x15:59/31, x14:28/--
+            x16 += (x15 >> 28); x15 &= M28UL;           // x16:59/32, x15:28/--
+            x17 += (x16 >> 28); x16 &= M28UL;           // x17:31/29, x16:28/--
+            x18 += (x17 >> 28); x17 &= M28UL;           // x18:28/04, x17:28/--
+
+            x02 += x18 * L4_0;                          // x02:54/--
+            x03 += x18 * L4_1;                          // x03:55/--
+            x04 += x18 * L4_2;                          // x04:56/32
+            x05 += x18 * L4_3;                          // x05:57/32
+            x06 += x18 * L4_4;                          // x06:57/56
+            x07 += x18 * L4_5;                          // x07:58/--
+            x08 += x18 * L4_6;                          // x08:58/56
+            x09 += x18 * L4_7;                          // x09:59/--
+
+            x01 += x17 * L4_0;                          // x01:54/--
+            x02 += x17 * L4_1;                          // x02:54/53
+            x03 += x17 * L4_2;                          // x03:56/53
+            x04 += x17 * L4_3;                          // x04:57/32
+            x05 += x17 * L4_4;                          // x05:57/55
+            x06 += x17 * L4_5;                          // x06:58/--
+            x07 += x17 * L4_6;                          // x07:58/56
+            x08 += x17 * L4_7;                          // x08:59/--
+
+            x16 *= 4;
+            x16 += (x15 >> 26); x15 &= M26UL;
+            x16 += 1;                                   // x16:30/01
+
+            x00 += x16 * L_0;
+            x01 += x16 * L_1;
+            x02 += x16 * L_2;
+            x03 += x16 * L_3;
+            x04 += x16 * L_4;
+            x05 += x16 * L_5;
+            x06 += x16 * L_6;
+            x07 += x16 * L_7;
+
+            x01 += (x00 >> 28); x00 &= M28UL;
+            x02 += (x01 >> 28); x01 &= M28UL;
+            x03 += (x02 >> 28); x02 &= M28UL;
+            x04 += (x03 >> 28); x03 &= M28UL;
+            x05 += (x04 >> 28); x04 &= M28UL;
+            x06 += (x05 >> 28); x05 &= M28UL;
+            x07 += (x06 >> 28); x06 &= M28UL;
+            x08 += (x07 >> 28); x07 &= M28UL;
+            x09 += (x08 >> 28); x08 &= M28UL;
+            x10 += (x09 >> 28); x09 &= M28UL;
+            x11 += (x10 >> 28); x10 &= M28UL;
+            x12 += (x11 >> 28); x11 &= M28UL;
+            x13 += (x12 >> 28); x12 &= M28UL;
+            x14 += (x13 >> 28); x13 &= M28UL;
+            x15 += (x14 >> 28); x14 &= M28UL;
+            x16  = (x15 >> 26); x15 &= M26UL;
+
+            x16 -= 1;
+
+            Debug.Assert(x16 == 0UL || x16 == ulong.MaxValue);
+
+            x00 -= x16 & L_0;
+            x01 -= x16 & L_1;
+            x02 -= x16 & L_2;
+            x03 -= x16 & L_3;
+            x04 -= x16 & L_4;
+            x05 -= x16 & L_5;
+            x06 -= x16 & L_6;
+            x07 -= x16 & L_7;
+
+            x01 += (ulong)((long)x00 >> 28); x00 &= M28UL;
+            x02 += (ulong)((long)x01 >> 28); x01 &= M28UL;
+            x03 += (ulong)((long)x02 >> 28); x02 &= M28UL;
+            x04 += (ulong)((long)x03 >> 28); x03 &= M28UL;
+            x05 += (ulong)((long)x04 >> 28); x04 &= M28UL;
+            x06 += (ulong)((long)x05 >> 28); x05 &= M28UL;
+            x07 += (ulong)((long)x06 >> 28); x06 &= M28UL;
+            x08 += (ulong)((long)x07 >> 28); x07 &= M28UL;
+            x09 += (ulong)((long)x08 >> 28); x08 &= M28UL;
+            x10 += (ulong)((long)x09 >> 28); x09 &= M28UL;
+            x11 += (ulong)((long)x10 >> 28); x10 &= M28UL;
+            x12 += (ulong)((long)x11 >> 28); x11 &= M28UL;
+            x13 += (ulong)((long)x12 >> 28); x12 &= M28UL;
+            x14 += (ulong)((long)x13 >> 28); x13 &= M28UL;
+            x15 += (ulong)((long)x14 >> 28); x14 &= M28UL;
+
+            Debug.Assert(x15 >> 26 == 0UL);
+
+            byte[] r = new byte[ScalarBytes];
+            Encode56(x00 | (x01 << 28), r,  0);
+            Encode56(x02 | (x03 << 28), r,  7);
+            Encode56(x04 | (x05 << 28), r, 14);
+            Encode56(x06 | (x07 << 28), r, 21);
+            Encode56(x08 | (x09 << 28), r, 28);
+            Encode56(x10 | (x11 << 28), r, 35);
+            Encode56(x12 | (x13 << 28), r, 42);
+            Encode56(x14 | (x15 << 28), r, 49);
+    //        r[ScalarBytes - 1] = 0;
+            return r;
+        }
+
+        private static void ScalarMultBase(byte[] k, PointExt r)
+        {
+            Precompute();
+
+            PointSetNeutral(r);
+
+            uint[] n = new uint[ScalarUints + 1];
+            DecodeScalar(k, 0, n);
+
+            // Recode the scalar into signed-digit form
+            {
+                n[ScalarUints] = 4U + Nat.CAdd(ScalarUints, ~(int)n[0] & 1, n, L, n);
+                uint c = Nat.ShiftDownBit(n.Length, n, 0);
+                Debug.Assert(c == (1U << 31));
+            }
+
+            PointPrecomp p = new PointPrecomp();
+
+            int cOff = PrecompSpacing - 1;
+            for (;;)
+            {
+                int tPos = cOff;
+
+                for (int b = 0; b < PrecompBlocks; ++b)
+                {
+                    uint w = 0;
+                    for (int t = 0; t < PrecompTeeth; ++t)
+                    {
+                        uint tBit = (n[tPos >> 5] >> (tPos & 0x1F)) & 1U;
+                        w |= tBit << t;
+                        tPos += PrecompSpacing;
+                    }
+
+                    int sign = (int)(w >> (PrecompTeeth - 1)) & 1;
+                    int abs = ((int)w ^ -sign) & PrecompMask;
+
+                    Debug.Assert(sign == 0 || sign == 1);
+                    Debug.Assert(0 <= abs && abs < PrecompPoints);
+
+                    PointLookup(b, abs, p);
+
+                    X448Field.CNegate(sign, p.x);
+
+                    PointAddPrecomp(p, r);
+                }
+
+                if (--cOff < 0)
+                {
+                    break;
+                }
+
+                PointDouble(r);
+            }
+        }
+
+        private static void ScalarMultBaseEncoded(byte[] k, byte[] r, int rOff)
+        {
+            PointExt p = new PointExt();
+            ScalarMultBase(k, p);
+            EncodePoint(p, r, rOff);
+        }
+
+        private static void ScalarMultStraussVar(uint[] nb, uint[] np, PointExt p, PointExt r)
+        {
+            Precompute();
+
+            int width = 5;
+
+            sbyte[] ws_b = GetWnaf(nb, WnafWidthBase);
+            sbyte[] ws_p = GetWnaf(np, width);
+
+            PointExt[] tp = PointPrecompVar(p, 1 << (width - 2));
+
+            PointSetNeutral(r);
+
+            int bit = 447;
+            while (bit > 0 && (ws_b[bit] | ws_p[bit]) == 0)
+            {
+                --bit;
+            }
+
+            for (;;)
+            {
+                int wb = ws_b[bit];
+                if (wb != 0)
+                {
+                    int sign = wb >> 31;
+                    int index = (wb ^ sign) >> 1;
+
+                    PointAddVar((sign != 0), precompBaseTable[index], r);
+                }
+
+                int wp = ws_p[bit];
+                if (wp != 0)
+                {
+                    int sign = wp >> 31;
+                    int index = (wp ^ sign) >> 1;
+
+                    PointAddVar((sign != 0), tp[index], r);
+                }
+
+                if (--bit < 0)
+                {
+                    break;
+                }
+
+                PointDouble(r);
+            }
+        }
+
+        public static void Sign(byte[] sk, int skOff, byte[] ctx, byte[] m, int mOff, int mLen, byte[] sig, int sigOff)
+        {
+            if (!CheckContextVar(ctx))
+            {
+                throw new ArgumentException("ctx");
+            }
+
+            ShakeDigest d = new ShakeDigest(256);
+            byte[] h = new byte[ScalarBytes * 2];
+
+            d.BlockUpdate(sk, skOff, SecretKeySize);
+            d.DoFinal(h, 0, h.Length);
+
+            byte[] s = new byte[ScalarBytes];
+            PruneScalar(h, 0, s);
+
+            byte[] pk = new byte[PointBytes];
+            ScalarMultBaseEncoded(s, pk, 0);
+
+            ImplSign(d, h, s, pk, 0, ctx, m, mOff, mLen, sig, sigOff);
+        }
+
+        public static void Sign(byte[] sk, int skOff, byte[] pk, int pkOff, byte[] ctx, byte[] m, int mOff, int mLen, byte[] sig, int sigOff)
+        {
+            if (!CheckContextVar(ctx))
+            {
+                throw new ArgumentException("ctx");
+            }
+
+            ShakeDigest d = new ShakeDigest(256);
+            byte[] h = new byte[ScalarBytes * 2];
+
+            d.BlockUpdate(sk, skOff, SecretKeySize);
+            d.DoFinal(h, 0, h.Length);
+
+            byte[] s = new byte[ScalarBytes];
+            PruneScalar(h, 0, s);
+
+            ImplSign(d, h, s, pk, pkOff, ctx, m, mOff, mLen, sig, sigOff);
+        }
+
+        public static bool Verify(byte[] sig, int sigOff, byte[] pk, int pkOff, byte[] ctx, byte[] m, int mOff, int mLen)
+        {
+            if (!CheckContextVar(ctx))
+            {
+                throw new ArgumentException("ctx");
+            }
+
+            byte[] R = Arrays.CopyOfRange(sig, sigOff, sigOff + PointBytes);
+            byte[] S = Arrays.CopyOfRange(sig, sigOff + PointBytes, sigOff + SignatureSize);
+
+            if (!CheckPointVar(R))
+            {
+                return false;
+            }
+            if (!CheckScalarVar(S))
+            {
+                return false;
+            }
+
+            PointExt pA = new PointExt();
+            if (!DecodePointVar(pk, pkOff, true, pA))
+            {
+                return false;
+            }
+
+            byte phflag = 0x00;
+
+            ShakeDigest d = new ShakeDigest(256);
+            byte[] h = new byte[ScalarBytes * 2];
+
+            Dom4(d, phflag, ctx);
+            d.BlockUpdate(R, 0, PointBytes);
+            d.BlockUpdate(pk, pkOff, PointBytes);
+            d.BlockUpdate(m, mOff, mLen);
+            d.DoFinal(h, 0, h.Length);
+
+            byte[] k = ReduceScalar(h);
+
+            uint[] nS = new uint[ScalarUints];
+            DecodeScalar(S, 0, nS);
+
+            uint[] nA = new uint[ScalarUints];
+            DecodeScalar(k, 0, nA);
+
+            PointExt pR = new PointExt();
+            ScalarMultStraussVar(nS, nA, pA, pR);
+
+            byte[] check = new byte[PointBytes];
+            EncodePoint(pR, check, 0);
+
+            return Arrays.AreEqual(check, R);
+        }
+    }
+}
diff --git a/crypto/src/math/raw/Interleave.cs b/crypto/src/math/raw/Interleave.cs
index d21840644..591ba3f15 100644
--- a/crypto/src/math/raw/Interleave.cs
+++ b/crypto/src/math/raw/Interleave.cs
@@ -6,6 +6,7 @@ namespace Org.BouncyCastle.Math.Raw
     {
         private const ulong M32 = 0x55555555UL;
         private const ulong M64 = 0x5555555555555555UL;
+        private const ulong M64R = 0xAAAAAAAAAAAAAAAAUL;
 
         /*
          * This expands 8 bit indices into 16 bit contents (high bit 14), by inserting 0s between bits.
@@ -92,6 +93,65 @@ namespace Org.BouncyCastle.Math.Raw
             z[zOff + 1] = (x >> 1) & M64;
         }
 
+        internal static void Expand64To128Rev(ulong x, ulong[] z, int zOff)
+        {
+            // "shuffle" low half to even bits and high half to odd bits
+            ulong t;
+            t = (x ^ (x >> 16)) & 0x00000000FFFF0000UL; x ^= (t ^ (t << 16));
+            t = (x ^ (x >>  8)) & 0x0000FF000000FF00UL; x ^= (t ^ (t <<  8));
+            t = (x ^ (x >>  4)) & 0x00F000F000F000F0UL; x ^= (t ^ (t <<  4));
+            t = (x ^ (x >>  2)) & 0x0C0C0C0C0C0C0C0CUL; x ^= (t ^ (t <<  2));
+            t = (x ^ (x >>  1)) & 0x2222222222222222UL; x ^= (t ^ (t <<  1));
+
+            z[zOff]     = (x     ) & M64R;
+            z[zOff + 1] = (x << 1) & M64R;
+        }
+
+        internal static uint Shuffle(uint x)
+        {
+            // "shuffle" low half to even bits and high half to odd bits
+            uint t;
+            t = (x ^ (x >> 8)) & 0x0000FF00U; x ^= (t ^ (t << 8));
+            t = (x ^ (x >> 4)) & 0x00F000F0U; x ^= (t ^ (t << 4));
+            t = (x ^ (x >> 2)) & 0x0C0C0C0CU; x ^= (t ^ (t << 2));
+            t = (x ^ (x >> 1)) & 0x22222222U; x ^= (t ^ (t << 1));
+            return x;
+        }
+
+        internal static ulong Shuffle(ulong x)
+        {
+            // "shuffle" low half to even bits and high half to odd bits
+            ulong t;
+            t = (x ^ (x >> 16)) & 0x00000000FFFF0000UL; x ^= (t ^ (t << 16));
+            t = (x ^ (x >>  8)) & 0x0000FF000000FF00UL; x ^= (t ^ (t <<  8));
+            t = (x ^ (x >>  4)) & 0x00F000F000F000F0UL; x ^= (t ^ (t <<  4));
+            t = (x ^ (x >>  2)) & 0x0C0C0C0C0C0C0C0CUL; x ^= (t ^ (t <<  2));
+            t = (x ^ (x >>  1)) & 0x2222222222222222UL; x ^= (t ^ (t <<  1));
+            return x;
+        }
+
+        internal static uint Shuffle2(uint x)
+        {
+            // "shuffle" (twice) low half to even bits and high half to odd bits
+            uint t;
+            t = (x ^ (x >>  7)) & 0x00AA00AAU; x ^= (t ^ (t <<  7));
+            t = (x ^ (x >> 14)) & 0x0000CCCCU; x ^= (t ^ (t << 14));
+            t = (x ^ (x >>  4)) & 0x00F000F0U; x ^= (t ^ (t <<  4));
+            t = (x ^ (x >>  8)) & 0x0000FF00U; x ^= (t ^ (t <<  8));
+            return x;
+        }
+
+        internal static uint Unshuffle(uint x)
+        {
+            // "unshuffle" even bits to low half and odd bits to high half
+            uint t;
+            t = (x ^ (x >> 1)) & 0x22222222U; x ^= (t ^ (t << 1));
+            t = (x ^ (x >> 2)) & 0x0C0C0C0CU; x ^= (t ^ (t << 2));
+            t = (x ^ (x >> 4)) & 0x00F000F0U; x ^= (t ^ (t << 4));
+            t = (x ^ (x >> 8)) & 0x0000FF00U; x ^= (t ^ (t << 8));
+            return x;
+        }
+
         internal static ulong Unshuffle(ulong x)
         {
             // "unshuffle" even bits to low half and odd bits to high half
@@ -103,5 +163,16 @@ namespace Org.BouncyCastle.Math.Raw
             t = (x ^ (x >> 16)) & 0x00000000FFFF0000UL; x ^= (t ^ (t << 16));
             return x;
         }
+
+        internal static uint Unshuffle2(uint x)
+        {
+            // "unshuffle" (twice) even bits to low half and odd bits to high half
+            uint t;
+            t = (x ^ (x >>  8)) & 0x0000FF00U; x ^= (t ^ (t <<  8));
+            t = (x ^ (x >>  4)) & 0x00F000F0U; x ^= (t ^ (t <<  4));
+            t = (x ^ (x >> 14)) & 0x0000CCCCU; x ^= (t ^ (t << 14));
+            t = (x ^ (x >>  7)) & 0x00AA00AAU; x ^= (t ^ (t <<  7));
+            return x;
+        }
     }
 }
diff --git a/crypto/src/math/raw/Nat.cs b/crypto/src/math/raw/Nat.cs
index cf6516c61..7ca60278a 100644
--- a/crypto/src/math/raw/Nat.cs
+++ b/crypto/src/math/raw/Nat.cs
@@ -195,6 +195,64 @@ namespace Org.BouncyCastle.Math.Raw
             return c == 0 ? 0 : IncAt(len, z, zOff, 1);
         }
 
+        public static uint CAdd(int len, int mask, uint[] x, uint[] y, uint[] z)
+        {
+            uint MASK = (uint)-(mask & 1);
+
+            ulong c = 0;
+            for (int i = 0; i < len; ++i)
+            {
+                c += (ulong)x[i] + (y[i] & MASK);
+                z[i] = (uint)c;
+                c >>= 32;
+            }
+            return (uint)c;
+        }
+
+        public static void CMov(int len, int mask, uint[] x, int xOff, uint[] z, int zOff)
+        {
+            uint MASK = (uint)-(mask & 1);
+
+            for (int i = 0; i < len; ++i)
+            {
+                uint z_i = z[zOff + i], diff = z_i ^ x[xOff + i];
+                z_i ^= (diff & MASK);
+                z[zOff + i] = z_i;
+            }
+
+            //uint half = 0x55555555U, rest = half << (-(int)MASK);
+
+            //for (int i = 0; i < len; ++i)
+            //{
+            //    uint z_i = z[zOff + i], diff = z_i ^ x[xOff + i];
+            //    z_i ^= (diff & half);
+            //    z_i ^= (diff & rest);
+            //    z[zOff + i] = z_i;
+            //}
+        }
+
+        public static void CMov(int len, int mask, int[] x, int xOff, int[] z, int zOff)
+        {
+            mask = -(mask & 1);
+
+            for (int i = 0; i < len; ++i)
+            {
+                int z_i = z[zOff + i], diff = z_i ^ x[xOff + i];
+                z_i ^= (diff & mask);
+                z[zOff + i] = z_i;
+            }
+
+            //int half = 0x55555555, rest = half << (-mask);
+
+            //for (int i = 0; i < len; ++i)
+            //{
+            //    int z_i = z[zOff + i], diff = z_i ^ x[xOff + i];
+            //    z_i ^= (diff & half);
+            //    z_i ^= (diff & rest);
+            //    z[zOff + i] = z_i;
+            //}
+        }
+
         public static void Copy(int len, uint[] x, uint[] z)
         {
             Array.Copy(x, 0, z, 0, len);
@@ -448,6 +506,33 @@ namespace Org.BouncyCastle.Math.Raw
             }
         }
 
+        public static uint MulAddTo(int len, uint[] x, uint[] y, uint[] zz)
+        {
+            ulong zc = 0;
+            for (int i = 0; i < len; ++i)
+            {
+                ulong c = MulWordAddTo(len, x[i], y, 0, zz, i) & M;
+                c += zc + (zz[i + len] & M);
+                zz[i + len] = (uint)c;
+                zc = c >> 32;
+            }
+            return (uint)zc;
+        }
+
+        public static uint MulAddTo(int len, uint[] x, int xOff, uint[] y, int yOff, uint[] zz, int zzOff)
+        {
+            ulong zc = 0;
+            for (int i = 0; i < len; ++i)
+            {
+                ulong c = MulWordAddTo(len, x[xOff + i], y, yOff, zz, zzOff) & M;
+                c += zc + (zz[zzOff + len] & M);
+                zz[zzOff + len] = (uint)c;
+                zc = c >> 32;
+                ++zzOff;
+            }
+            return (uint)zc;
+        }
+
         public static uint Mul31BothAdd(int len, uint a, uint[] x, uint b, uint[] y, uint[] z, int zOff)
         {
             ulong c = 0, aVal = (ulong)a, bVal = (ulong)b;