CVE-2024-30172

@@ -566,7 +566,12 @@ private static boolean implVerify(byte[] sig, int sigOff, byte[] pk, int pkOff,
 
         int[] v0 = new int[4];
         int[] v1 = new int[4];
-        Scalar25519.reduceBasisVar(nA, v0, v1);
+
+        if (!Scalar25519.reduceBasisVar(nA, v0, v1))
+        {
+            throw new IllegalStateException();
+        }
+
         Scalar25519.multiply128Var(nS, v1, nS);
 
         PointAccum pZ = new PointAccum();
@@ -628,7 +633,12 @@ private static boolean implVerify(byte[] sig, int sigOff, PublicPoint publicPoin
 
         int[] v0 = new int[4];
         int[] v1 = new int[4];
-        Scalar25519.reduceBasisVar(nA, v0, v1);
+
+        if (!Scalar25519.reduceBasisVar(nA, v0, v1))
+        {
+            throw new IllegalStateException();
+        }
+
         Scalar25519.multiply128Var(nS, v1, nS);
 
         PointAccum pZ = new PointAccum();

@@ -510,7 +510,12 @@ private static boolean implVerify(byte[] sig, int sigOff, byte[] pk, int pkOff,
 
         int[] v0 = new int[8];
         int[] v1 = new int[8];
-        Scalar448.reduceBasisVar(nA, v0, v1);
+
+        if (!Scalar448.reduceBasisVar(nA, v0, v1))
+        {
+            throw new IllegalStateException();
+        }
+
         Scalar448.multiply225Var(nS, v1, nS);
 
         PointProjective pZ = new PointProjective();
@@ -569,7 +574,12 @@ private static boolean implVerify(byte[] sig, int sigOff, PublicPoint publicPoin
 
         int[] v0 = new int[8];
         int[] v1 = new int[8];
-        Scalar448.reduceBasisVar(nA, v0, v1);
+
+        if (!Scalar448.reduceBasisVar(nA, v0, v1))
+        {
+            throw new IllegalStateException();
+        }
+
         Scalar448.multiply225Var(nS, v1, nS);
 
         PointProjective pZ = new PointProjective();

@@ -295,7 +295,7 @@ static byte[] reduce512(byte[] n)
         return r;
     }
 
-    static void reduceBasisVar(int[] k, int[] z0, int[] z1)
+    static boolean reduceBasisVar(int[] k, int[] z0, int[] z1)
     {
         /*
          * Split scalar k into two half-size scalars z0 and z1, such that z1 * k == z0 mod L.
@@ -312,11 +312,18 @@ static void reduceBasisVar(int[] k, int[] z0, int[] z1)
         int[] v0 = new int[4];      System.arraycopy(k, 0, v0, 0, 4);
         int[] v1 = new int[4];      v1[0] = 1;
 
+        // Conservative upper bound on the number of loop iterations needed
+        int iterations = TARGET_LENGTH * 4;
         int last = 15;
         int len_Nv = ScalarUtil.getBitLengthPositive(last, Nv);
 
         while (len_Nv > TARGET_LENGTH)
         {
+            if (--iterations < 0)
+            {
+                return false;
+            }
+
             int len_p = ScalarUtil.getBitLength(last, p);
             int s = len_p - len_Nv;
             s &= ~(s >> 31);
@@ -346,6 +353,7 @@ static void reduceBasisVar(int[] k, int[] z0, int[] z1)
         // v1 * k == v0 mod L
         System.arraycopy(v0, 0, z0, 0, 4);
         System.arraycopy(v1, 0, z1, 0, 4);
+        return true;
     }
 
     static void toSignedDigits(int bits, int[] z)

@@ -560,7 +560,7 @@ static byte[] reduce912(byte[] n)
         return r;
     }
 
-    static void reduceBasisVar(int[] k, int[] z0, int[] z1)
+    static boolean reduceBasisVar(int[] k, int[] z0, int[] z1)
     {
         /*
          * Split scalar k into two half-size scalars z0 and z1, such that z1 * k == z0 mod L.
@@ -577,11 +577,18 @@ static void reduceBasisVar(int[] k, int[] z0, int[] z1)
         int[] v0 = new int[8];      System.arraycopy(k, 0, v0, 0, 8);
         int[] v1 = new int[8];      v1[0] = 1;
 
+        // Conservative upper bound on the number of loop iterations needed
+        int iterations = TARGET_LENGTH * 4;
         int last = 27;
         int len_Nv = ScalarUtil.getBitLengthPositive(last, Nv);
 
         while (len_Nv > TARGET_LENGTH)
         {
+            if (--iterations < 0)
+            {
+                return false;
+            }
+
             int len_p = ScalarUtil.getBitLength(last, p);
             int s = len_p - len_Nv;
             s &= ~(s >> 31);
@@ -614,6 +621,7 @@ static void reduceBasisVar(int[] k, int[] z0, int[] z1)
         // v1 * k == v0 mod L
         System.arraycopy(v0, 0, z0, 0, 8);
         System.arraycopy(v1, 0, z1, 0, 8);
+        return true;
     }
 
     static void toSignedDigits(int bits, int[] x, int[] z)

@@ -22,11 +22,11 @@ static void addShifted_NP(int last, int s, int[] Nu, int[] Nv, int[] p, int[] t)
 
                 cc_p += p_i & M;
                 cc_p += Nv[i] & M;
-                p_i    = (int)cc_p; cc_p >>= 32;
-                p[i]   = p_i;
+                p_i   = (int)cc_p; cc_p >>>= 32;
+                p[i]  = p_i;
 
                 cc_Nu += p_i & M;
-                Nu[i]  = (int)cc_Nu; cc_Nu >>= 32;
+                Nu[i]  = (int)cc_Nu; cc_Nu >>>= 32;
             }
         }
         else if (s < 32)
@@ -50,20 +50,20 @@ else if (s < 32)
 
                 cc_p += p_i & M;
                 cc_p += v_s & M;
-                p_i   = (int)cc_p; cc_p >>= 32;
+                p_i   = (int)cc_p; cc_p >>>= 32;
                 p[i]  = p_i;
 
                 int q_s = (p_i << s) | (prev_q >>> -s);
-                prev_q =p_i;
+                prev_q = p_i;
 
                 cc_Nu += q_s & M;
-                Nu[i]  = (int)cc_Nu; cc_Nu >>= 32;
+                Nu[i]  = (int)cc_Nu; cc_Nu >>>= 32;
             }
         }
         else
         {
-            // Keep the original value of p in t.
-            System.arraycopy(p, 0, t, 0, p.length);
+            // Copy the low limbs of the original p
+            System.arraycopy(p, 0, t, 0, last);
 
             int sWords = s >>> 5; int sBits = s & 31;
             if (sBits == 0)
@@ -75,10 +75,10 @@ else if (s < 32)
 
                     cc_p += p[i] & M;
                     cc_p += Nv[i - sWords] & M;
-                    p[i]  = (int)cc_p; cc_p >>= 32;
+                    p[i]  = (int)cc_p; cc_p >>>= 32;
 
                     cc_Nu += p[i - sWords] & M;
-                    Nu[i]  = (int)cc_Nu; cc_Nu >>= 32;
+                    Nu[i]  = (int)cc_Nu; cc_Nu >>>= 32;
                 }
             }
             else
@@ -102,14 +102,14 @@ else if (s < 32)
 
                     cc_p += p[i] & M;
                     cc_p += v_s & M;
-                    p[i]  = (int)cc_p; cc_p >>= 32;
+                    p[i]  = (int)cc_p; cc_p >>>= 32;
 
                     int next_q = p[i - sWords];
                     int q_s = (next_q << sBits) | (prev_q >>> -sBits);
                     prev_q = next_q;
 
                     cc_Nu += q_s & M;
-                    Nu[i]  = (int)cc_Nu; cc_Nu >>= 32;
+                    Nu[i]  = (int)cc_Nu; cc_Nu >>>= 32;
                 }
             }
         }
@@ -251,8 +251,8 @@ else if (s < 32)
         }
         else
         {
-            // Keep the original value of p in t.
-            System.arraycopy(p, 0, t, 0, p.length);
+            // Copy the low limbs of the original p
+            System.arraycopy(p, 0, t, 0, last);
 
             int sWords = s >>> 5; int sBits = s & 31;
             if (sBits == 0)

@@ -306,6 +306,7 @@ static void reduceBasisVar(int[] k, int[] z0, int[] z1)
         int[] Nu = new int[16];     System.arraycopy(LSq, 0, Nu, 0, 16);
         int[] Nv = new int[16];     Nat256.square(k, Nv); ++Nv[0];
         int[] p  = new int[16];     Nat256.mul(L, k, p);
+        int[] t  = new int[16];     // temp array
         int[] u0 = new int[4];      System.arraycopy(L, 0, u0, 0, 4);
         int[] u1 = new int[4];
         int[] v0 = new int[4];      System.arraycopy(k, 0, v0, 0, 4);
@@ -322,12 +323,12 @@ static void reduceBasisVar(int[] k, int[] z0, int[] z1)
 
             if (p[last] < 0)
             {
-                ScalarUtil.addShifted_NP(last, s, Nu, Nv, p);
+                ScalarUtil.addShifted_NP(last, s, Nu, Nv, p, t);
                 ScalarUtil.addShifted_UV(3, s, u0, u1, v0, v1);
             }
             else
             {
-                ScalarUtil.subShifted_NP(last, s, Nu, Nv, p);
+                ScalarUtil.subShifted_NP(last, s, Nu, Nv, p, t);
                 ScalarUtil.subShifted_UV(3, s, u0, u1, v0, v1);
             }
 

@@ -571,6 +571,7 @@ static void reduceBasisVar(int[] k, int[] z0, int[] z1)
         int[] Nu = new int[28];     System.arraycopy(LSq, 0, Nu, 0, 28);
         int[] Nv = new int[28];     Nat448.square(k, Nv); ++Nv[0];
         int[] p  = new int[28];     Nat448.mul(L, k, p);
+        int[] t  = new int[28];     // temp array
         int[] u0 = new int[8];      System.arraycopy(L, 0, u0, 0, 8);
         int[] u1 = new int[8];
         int[] v0 = new int[8];      System.arraycopy(k, 0, v0, 0, 8);
@@ -587,12 +588,12 @@ static void reduceBasisVar(int[] k, int[] z0, int[] z1)
 
             if (p[last] < 0)
             {
-                ScalarUtil.addShifted_NP(last, s, Nu, Nv, p);
+                ScalarUtil.addShifted_NP(last, s, Nu, Nv, p, t);
                 ScalarUtil.addShifted_UV(7, s, u0, u1, v0, v1);
             }
             else
             {
-                ScalarUtil.subShifted_NP(last, s, Nu, Nv, p);
+                ScalarUtil.subShifted_NP(last, s, Nu, Nv, p, t);
                 ScalarUtil.subShifted_UV(7, s, u0, u1, v0, v1);
             }
 

@@ -6,57 +6,111 @@ abstract class ScalarUtil
 {
     private static final long M = 0xFFFFFFFFL;
 
-    static void addShifted_NP(int last, int s, int[] Nu, int[] Nv, int[] _p)
+    static void addShifted_NP(int last, int s, int[] Nu, int[] Nv, int[] p, int[] t)
     {
-        int sWords = s >>> 5, sBits = s & 31;
-
-        long cc__p = 0L;
+        long cc_p = 0L;
         long cc_Nu = 0L;
 
-        if (sBits == 0)
+        if (s == 0)
         {
-            for (int i = sWords; i <= last; ++i)
+            for (int i = 0; i <= last; ++i)
             {
+                int p_i = p[i];
+
                 cc_Nu += Nu[i] & M;
-                cc_Nu += _p[i - sWords] & M;
+                cc_Nu += p_i & M;
 
-                cc__p += _p[i] & M;
-                cc__p += Nv[i - sWords] & M;
-                _p[i]  = (int)cc__p; cc__p >>>= 32;
+                cc_p += p_i & M;
+                cc_p += Nv[i] & M;
+                p_i    = (int)cc_p; cc_p >>= 32;
+                p[i]   = p_i;
 
-                cc_Nu += _p[i - sWords] & M;
-                Nu[i]  = (int)cc_Nu; cc_Nu >>>= 32;
+                cc_Nu += p_i & M;
+                Nu[i]  = (int)cc_Nu; cc_Nu >>= 32;
             }
         }
-        else
+        else if (s < 32)
         {
             int prev_p = 0;
             int prev_q = 0;
             int prev_v = 0;
 
-            for (int i = sWords; i <= last; ++i)
+            for (int i = 0; i <= last; ++i)
             {
-                int next_p = _p[i - sWords];
-                int p_s = (next_p << sBits) | (prev_p >>> -sBits);
-                prev_p = next_p;
+                int p_i = p[i];
+                int p_s = (p_i << s) | (prev_p >>> -s);
+                prev_p = p_i;
 
                 cc_Nu += Nu[i] & M;
                 cc_Nu += p_s & M;
 
-                int next_v = Nv[i - sWords];
-                int v_s = (next_v << sBits) | (prev_v >>> -sBits);
+                int next_v = Nv[i];
+                int v_s = (next_v << s) | (prev_v >>> -s);
                 prev_v = next_v;
 
-                cc__p += _p[i] & M;
-                cc__p += v_s & M;
-                _p[i]  = (int)cc__p; cc__p >>>= 32;
+                cc_p += p_i & M;
+                cc_p += v_s & M;
+                p_i   = (int)cc_p; cc_p >>= 32;
+                p[i]  = p_i;
 
-                int next_q = _p[i - sWords];
-                int q_s = (next_q << sBits) | (prev_q >>> -sBits);
-                prev_q = next_q;
+                int q_s = (p_i << s) | (prev_q >>> -s);
+                prev_q =p_i;
 
                 cc_Nu += q_s & M;
-                Nu[i]  = (int)cc_Nu; cc_Nu >>>= 32;
+                Nu[i]  = (int)cc_Nu; cc_Nu >>= 32;
+            }
+        }
+        else
+        {
+            // Keep the original value of p in t.
+            System.arraycopy(p, 0, t, 0, p.length);
+
+            int sWords = s >>> 5; int sBits = s & 31;
+            if (sBits == 0)
+            {
+                for (int i = sWords; i <= last; ++i)
+                {
+                    cc_Nu += Nu[i] & M;
+                    cc_Nu += t[i - sWords] & M;
+
+                    cc_p += p[i] & M;
+                    cc_p += Nv[i - sWords] & M;
+                    p[i]  = (int)cc_p; cc_p >>= 32;
+
+                    cc_Nu += p[i - sWords] & M;
+                    Nu[i]  = (int)cc_Nu; cc_Nu >>= 32;
+                }
+            }
+            else
+            {
+                int prev_t = 0;
+                int prev_q = 0;
+                int prev_v = 0;
+
+                for (int i = sWords; i <= last; ++i)
+                {
+                    int next_t = t[i - sWords];
+                    int t_s = (next_t << sBits) | (prev_t >>> -sBits);
+                    prev_t = next_t;
+
+                    cc_Nu += Nu[i] & M;
+                    cc_Nu += t_s & M;
+
+                    int next_v = Nv[i - sWords];
+                    int v_s = (next_v << sBits) | (prev_v >>> -sBits);
+                    prev_v = next_v;
+
+                    cc_p += p[i] & M;
+                    cc_p += v_s & M;
+                    p[i]  = (int)cc_p; cc_p >>= 32;
+
+                    int next_q = p[i - sWords];
+                    int q_s = (next_q << sBits) | (prev_q >>> -sBits);
+                    prev_q = next_q;
+
+                    cc_Nu += q_s & M;
+                    Nu[i]  = (int)cc_Nu; cc_Nu >>= 32;
+                }
             }
         }
     }
@@ -141,59 +195,113 @@ static boolean lessThan(int last, int[] x, int[] y)
         return false;
     }
 
-    static void subShifted_NP(int last, int s, int[] Nu, int[] Nv, int[] _p)
+    static void subShifted_NP(int last, int s, int[] Nu, int[] Nv, int[] p, int[] t)
     {
-        int sWords = s >>> 5, sBits = s & 31;
-
-        long cc__p = 0L;
+        long cc_p = 0L;
         long cc_Nu = 0L;
 
-        if (sBits == 0)
+        if (s == 0)
         {
-            for (int i = sWords; i <= last; ++i)
+            for (int i = 0; i <= last; ++i)
             {
+                int p_i = p[i];
+
                 cc_Nu += Nu[i] & M;
-                cc_Nu -= _p[i - sWords] & M;
+                cc_Nu -= p_i & M;
 
-                cc__p += _p[i] & M;
-                cc__p -= Nv[i - sWords] & M;
-                _p[i]  = (int)cc__p; cc__p >>= 32;
+                cc_p += p_i & M;
+                cc_p -= Nv[i] & M;
+                p_i   = (int)cc_p; cc_p >>= 32;
+                p[i]  = p_i;
 
-                cc_Nu -= _p[i - sWords] & M;
+                cc_Nu -= p_i & M;
                 Nu[i]  = (int)cc_Nu; cc_Nu >>= 32;
             }
         }
-        else
+        else if (s < 32)
         {
             int prev_p = 0;
             int prev_q = 0;
             int prev_v = 0;
 
-            for (int i = sWords; i <= last; ++i)
+            for (int i = 0; i <= last; ++i)
             {
-                int next_p = _p[i - sWords];
-                int p_s = (next_p << sBits) | (prev_p >>> -sBits);
-                prev_p = next_p;
+                int p_i = p[i];
+                int p_s = (p_i << s) | (prev_p >>> -s);
+                prev_p = p_i;
 
                 cc_Nu += Nu[i] & M;
                 cc_Nu -= p_s & M;
 
-                int next_v = Nv[i - sWords];
-                int v_s = (next_v << sBits) | (prev_v >>> -sBits);
+                int next_v = Nv[i];
+                int v_s = (next_v << s) | (prev_v >>> -s);
                 prev_v = next_v;
 
-                cc__p += _p[i] & M;
-                cc__p -= v_s & M;
-                _p[i]  = (int)cc__p; cc__p >>= 32;
+                cc_p += p_i & M;
+                cc_p -= v_s & M;
+                p_i   = (int)cc_p; cc_p >>= 32;
+                p[i]  = p_i;
 
-                int next_q = _p[i - sWords];
-                int q_s = (next_q << sBits) | (prev_q >>> -sBits);
-                prev_q = next_q;
+                int q_s = (p_i << s) | (prev_q >>> -s);
+                prev_q = p_i;
 
                 cc_Nu -= q_s & M;
                 Nu[i]  = (int)cc_Nu; cc_Nu >>= 32;
             }
         }
+        else
+        {
+            // Keep the original value of p in t.
+            System.arraycopy(p, 0, t, 0, p.length);
+
+            int sWords = s >>> 5; int sBits = s & 31;
+            if (sBits == 0)
+            {
+                for (int i = sWords; i <= last; ++i)
+                {
+                    cc_Nu += Nu[i] & M;
+                    cc_Nu -= t[i - sWords] & M;
+
+                    cc_p += p[i] & M;
+                    cc_p -= Nv[i - sWords] & M;
+                    p[i]  = (int)cc_p; cc_p >>= 32;
+
+                    cc_Nu -= p[i - sWords] & M;
+                    Nu[i]  = (int)cc_Nu; cc_Nu >>= 32;
+                }
+            }
+            else
+            {
+                int prev_t = 0;
+                int prev_q = 0;
+                int prev_v = 0;
+
+                for (int i = sWords; i <= last; ++i)
+                {
+                    int next_t = t[i - sWords];
+                    int t_s = (next_t << sBits) | (prev_t >>> -sBits);
+                    prev_t = next_t;
+
+                    cc_Nu += Nu[i] & M;
+                    cc_Nu -= t_s & M;
+
+                    int next_v = Nv[i - sWords];
+                    int v_s = (next_v << sBits) | (prev_v >>> -sBits);
+                    prev_v = next_v;
+
+                    cc_p += p[i] & M;
+                    cc_p -= v_s & M;
+                    p[i]  = (int)cc_p; cc_p >>= 32;
+
+                    int next_q = p[i - sWords];
+                    int q_s = (next_q << sBits) | (prev_q >>> -sBits);
+                    prev_q = next_q;
+
+                    cc_Nu -= q_s & M;
+                    Nu[i]  = (int)cc_Nu; cc_Nu >>= 32;
+                }
+            }
+        }
     }
 
     static void subShifted_UV(int last, int s, int[] u0, int[] u1, int[] v0, int[] v1)

@@ -64,9 +64,7 @@ public Ed25519PublicKeyParameters generatePublicKey()
         {
             if (null == cachedPublicKey)
             {
-                byte[] publicKey = new byte[Ed25519.PUBLIC_KEY_SIZE];
-                Ed25519.generatePublicKey(data, 0, publicKey, 0);
-                cachedPublicKey = new Ed25519PublicKeyParameters(publicKey, 0);
+                cachedPublicKey = new Ed25519PublicKeyParameters(Ed25519.generatePublicKey(data, 0));
             }
 
             return cachedPublicKey;

@@ -5,15 +5,14 @@
 import java.io.InputStream;
 
 import org.bouncycastle.math.ec.rfc8032.Ed25519;
-import org.bouncycastle.util.Arrays;
 import org.bouncycastle.util.io.Streams;
 
 public final class Ed25519PublicKeyParameters
     extends AsymmetricKeyParameter
 {
     public static final int KEY_SIZE = Ed25519.PUBLIC_KEY_SIZE;
 
-    private final byte[] data = new byte[KEY_SIZE];
+    private final Ed25519.PublicPoint publicPoint;
 
     public Ed25519PublicKeyParameters(byte[] buf)
     {
@@ -24,27 +23,45 @@ public Ed25519PublicKeyParameters(byte[] buf, int off)
     {
         super(false);
 
-        System.arraycopy(buf, off, data, 0, KEY_SIZE);
+        this.publicPoint = parse(buf, off);
     }
 
     public Ed25519PublicKeyParameters(InputStream input) throws IOException
     {
         super(false);
 
+        byte[] data = new byte[KEY_SIZE];
+
         if (KEY_SIZE != Streams.readFully(input, data))
         {
             throw new EOFException("EOF encountered in middle of Ed25519 public key");
         }
+
+        this.publicPoint = parse(data, 0);
+    }
+
+    public Ed25519PublicKeyParameters(Ed25519.PublicPoint publicPoint)
+    {
+        super(false);
+
+        if (publicPoint == null)
+        {
+            throw new NullPointerException("'publicPoint' cannot be null");
+        }
+
+        this.publicPoint = publicPoint;
     }
 
     public void encode(byte[] buf, int off)
     {
-        System.arraycopy(data, 0, buf, off, KEY_SIZE);
+        Ed25519.encodePublicPoint(publicPoint, buf, off);
     }
 
     public byte[] getEncoded()
     {
-        return Arrays.clone(data);
+        byte[] data = new byte[KEY_SIZE];
+        encode(data, 0);
+        return data;
     }
 
     public boolean verify(int algorithm, byte[] ctx, byte[] msg, int msgOff, int msgLen, byte[] sig, int sigOff)
@@ -58,7 +75,7 @@ public boolean verify(int algorithm, byte[] ctx, byte[] msg, int msgOff, int msg
                 throw new IllegalArgumentException("ctx");
             }
 
-            return Ed25519.verify(sig, sigOff, data, 0, msg, msgOff, msgLen);
+            return Ed25519.verify(sig, sigOff, publicPoint, msg, msgOff, msgLen);
         }
         case Ed25519.Algorithm.Ed25519ctx:
         {
@@ -71,7 +88,7 @@ public boolean verify(int algorithm, byte[] ctx, byte[] msg, int msgOff, int msg
                 throw new IllegalArgumentException("ctx");
             }
 
-            return Ed25519.verify(sig, sigOff, data, 0, ctx, msg, msgOff, msgLen);
+            return Ed25519.verify(sig, sigOff, publicPoint, ctx, msg, msgOff, msgLen);
         }
         case Ed25519.Algorithm.Ed25519ph:
         {
@@ -88,7 +105,7 @@ public boolean verify(int algorithm, byte[] ctx, byte[] msg, int msgOff, int msg
                 throw new IllegalArgumentException("msgLen");
             }
 
-            return Ed25519.verifyPrehash(sig, sigOff, data, 0, ctx, msg, msgOff);
+            return Ed25519.verifyPrehash(sig, sigOff, publicPoint, ctx, msg, msgOff);
         }
         default:
         {
@@ -97,6 +114,16 @@ public boolean verify(int algorithm, byte[] ctx, byte[] msg, int msgOff, int msg
         }
     }
 
+    private static Ed25519.PublicPoint parse(byte[] buf, int off)
+    {
+        Ed25519.PublicPoint publicPoint = Ed25519.validatePublicKeyPartialExport(buf, off);
+        if (publicPoint == null)
+        {
+            throw new IllegalArgumentException("invalid public key");
+        }
+        return publicPoint;
+    }
+
     private static byte[] validate(byte[] buf)
     {
         if (buf.length != KEY_SIZE)

@@ -64,9 +64,7 @@ public Ed448PublicKeyParameters generatePublicKey()
         {
             if (null == cachedPublicKey)
             {
-                byte[] publicKey = new byte[Ed448.PUBLIC_KEY_SIZE];
-                Ed448.generatePublicKey(data, 0, publicKey, 0);
-                cachedPublicKey = new Ed448PublicKeyParameters(publicKey, 0);
+                cachedPublicKey = new Ed448PublicKeyParameters(Ed448.generatePublicKey(data, 0));
             }
 
             return cachedPublicKey;

@@ -5,15 +5,14 @@
 import java.io.InputStream;
 
 import org.bouncycastle.math.ec.rfc8032.Ed448;
-import org.bouncycastle.util.Arrays;
 import org.bouncycastle.util.io.Streams;
 
 public final class Ed448PublicKeyParameters
     extends AsymmetricKeyParameter
 {
     public static final int KEY_SIZE = Ed448.PUBLIC_KEY_SIZE;
 
-    private final byte[] data = new byte[KEY_SIZE];
+    private final Ed448.PublicPoint publicPoint;
 
     public Ed448PublicKeyParameters(byte[] buf)
     {
@@ -24,27 +23,45 @@ public Ed448PublicKeyParameters(byte[] buf, int off)
     {
         super(false);
 
-        System.arraycopy(buf, off, data, 0, KEY_SIZE);
+        this.publicPoint = parse(buf, off);
     }
 
     public Ed448PublicKeyParameters(InputStream input) throws IOException
     {
         super(false);
 
+        byte[] data = new byte[KEY_SIZE];
+
         if (KEY_SIZE != Streams.readFully(input, data))
         {
             throw new EOFException("EOF encountered in middle of Ed448 public key");
         }
+
+        this.publicPoint = parse(data, 0);
+    }
+
+    public Ed448PublicKeyParameters(Ed448.PublicPoint publicPoint)
+    {
+        super(false);
+
+        if (publicPoint == null)
+        {
+            throw new NullPointerException("'publicPoint' cannot be null");
+        }
+
+        this.publicPoint = publicPoint;
     }
 
     public void encode(byte[] buf, int off)
     {
-        System.arraycopy(data, 0, buf, off, KEY_SIZE);
+        Ed448.encodePublicPoint(publicPoint, buf, off);
     }
 
     public byte[] getEncoded()
     {
-        return Arrays.clone(data);
+        byte[] data = new byte[KEY_SIZE];
+        encode(data, 0);
+        return data;
     }
 
     public boolean verify(int algorithm, byte[] ctx, byte[] msg, int msgOff, int msgLen, byte[] sig, int sigOff)
@@ -62,7 +79,7 @@ public boolean verify(int algorithm, byte[] ctx, byte[] msg, int msgOff, int msg
                 throw new IllegalArgumentException("ctx");
             }
 
-            return Ed448.verify(sig, sigOff, data, 0, ctx, msg, msgOff, msgLen);
+            return Ed448.verify(sig, sigOff, publicPoint, ctx, msg, msgOff, msgLen);
         }
         case Ed448.Algorithm.Ed448ph:
         {
@@ -79,7 +96,7 @@ public boolean verify(int algorithm, byte[] ctx, byte[] msg, int msgOff, int msg
                 throw new IllegalArgumentException("msgLen");
             }
 
-            return Ed448.verifyPrehash(sig, sigOff, data, 0, ctx, msg, msgOff);
+            return Ed448.verifyPrehash(sig, sigOff, publicPoint, ctx, msg, msgOff);
         }
         default:
         {
@@ -88,6 +105,16 @@ public boolean verify(int algorithm, byte[] ctx, byte[] msg, int msgOff, int msg
         }
     }
 
+    private static Ed448.PublicPoint parse(byte[] buf, int off)
+    {
+        Ed448.PublicPoint publicPoint = Ed448.validatePublicKeyPartialExport(buf, off);
+        if (publicPoint == null)
+        {
+            throw new IllegalArgumentException("invalid public key");
+        }
+        return publicPoint;
+    }
+
     private static byte[] validate(byte[] buf)
     {
         if (buf.length != KEY_SIZE)

@@ -152,13 +152,27 @@ public static void decode(int[] x, int xOff, int[] z)
         z[9] &= M24;
     }
 
+    public static void decode(byte[] x, int[] z)
+    {
+        decode128(x, 0, z, 0);
+        decode128(x, 16, z, 5);
+        z[9] &= M24;
+    }
+
     public static void decode(byte[] x, int xOff, int[] z)
     {
         decode128(x, xOff, z, 0);
         decode128(x, xOff + 16, z, 5);
         z[9] &= M24;
     }
 
+    public static void decode(byte[] x, int xOff, int[] z, int zOff)
+    {
+        decode128(x, xOff, z, zOff);
+        decode128(x, xOff + 16, z, zOff + 5);
+        z[zOff + 9] &= M24;
+    }
+
     private static void decode128(int[] is, int off, int[] z, int zOff)
     {
         int t0 = is[off + 0], t1 = is[off + 1], t2 = is[off + 2], t3 = is[off + 3];
@@ -199,12 +213,24 @@ public static void encode(int[] x, int[] z, int zOff)
         encode128(x, 5, z, zOff + 4);
     }
 
+    public static void encode(int[] x, byte[] z)
+    {
+        encode128(x, 0, z, 0);
+        encode128(x, 5, z, 16);
+    }
+
     public static void encode(int[] x, byte[] z, int zOff)
     {
         encode128(x, 0, z, zOff);
         encode128(x, 5, z, zOff + 16);
     }
 
+    public static void encode(int[] x, int xOff, byte[] z, int zOff)
+    {
+        encode128(x, xOff, z, zOff);
+        encode128(x, xOff + 5, z, zOff + 16);
+    }
+
     private static void encode128(int[] x, int xOff, int[] is, int off)
     {
         int x0 = x[xOff + 0], x1 = x[xOff + 1], x2 = x[xOff + 2], x3 = x[xOff + 3], x4 = x[xOff + 4];

@@ -156,6 +156,18 @@ public static void decode(int[] x, int xOff, int[] z)
         decode224(x, xOff + 7, z, 8);
     }
 
+    public static void decode(byte[] x, int[] z)
+    {
+        decode56(x, 0, z, 0);
+        decode56(x, 7, z, 2);
+        decode56(x, 14, z, 4);
+        decode56(x, 21, z, 6);
+        decode56(x, 28, z, 8);
+        decode56(x, 35, z, 10);
+        decode56(x, 42, z, 12);
+        decode56(x, 49, z, 14);
+    }
+
     public static void decode(byte[] x, int xOff, int[] z)
     {
         decode56(x, xOff, z, 0);
@@ -168,6 +180,18 @@ public static void decode(byte[] x, int xOff, int[] z)
         decode56(x, xOff + 49, z, 14);
     }
 
+    public static void decode(byte[] x, int xOff, int[] z, int zOff)
+    {
+        decode56(x, xOff, z, zOff);
+        decode56(x, xOff + 7, z, zOff + 2);
+        decode56(x, xOff + 14, z, zOff + 4);
+        decode56(x, xOff + 21, z, zOff + 6);
+        decode56(x, xOff + 28, z, zOff + 8);
+        decode56(x, xOff + 35, z, zOff + 10);
+        decode56(x, xOff + 42, z, zOff + 12);
+        decode56(x, xOff + 49, z, zOff + 14);
+    }
+
     private static void decode224(int[] x, int xOff, int[] z, int zOff)
     {
         int x0 = x[xOff + 0], x1 = x[xOff + 1], x2 = x[xOff + 2], x3 = x[xOff + 3];
@@ -214,7 +238,19 @@ public static void encode(int[] x, int[] z, int zOff)
         encode224(x, 8, z, zOff + 7);
     }
 
-    public static void encode(int[] x,  byte[] z , int zOff)
+    public static void encode(int[] x, byte[] z)
+    {
+        encode56(x, 0, z, 0);
+        encode56(x, 2, z, 7);
+        encode56(x, 4, z, 14);
+        encode56(x, 6, z, 21);
+        encode56(x, 8, z, 28);
+        encode56(x, 10, z, 35);
+        encode56(x, 12, z, 42);
+        encode56(x, 14, z, 49);
+    }
+
+    public static void encode(int[] x, byte[] z, int zOff)
     {
         encode56(x, 0, z, zOff);
         encode56(x, 2, z, zOff + 7);
@@ -226,6 +262,18 @@ public static void encode(int[] x,  byte[] z , int zOff)
         encode56(x, 14, z, zOff + 49);
     }
 
+    public static void encode(int[] x, int xOff, byte[] z, int zOff)
+    {
+        encode56(x, xOff, z, zOff);
+        encode56(x, xOff + 2, z, zOff + 7);
+        encode56(x, xOff + 4, z, zOff + 14);
+        encode56(x, xOff + 6, z, zOff + 21);
+        encode56(x, xOff + 8, z, zOff + 28);
+        encode56(x, xOff + 10, z, zOff + 35);
+        encode56(x, xOff + 12, z, zOff + 42);
+        encode56(x, xOff + 14, z, zOff + 49);
+    }
+
     private static void encode224(int[] x, int xOff, int[] is, int off)
     {
         int x0 = x[xOff + 0], x1 = x[xOff + 1], x2 = x[xOff + 2], x3 = x[xOff + 3];

@@ -0,0 +1,65 @@
+package org.bouncycastle.math.ec.rfc8032;
+
+abstract class Codec
+{
+    static int decode16(byte[] bs, int off)
+    {
+        int n = bs[off] & 0xFF;
+        n |= (bs[++off] & 0xFF) << 8;
+        return n;
+    }
+
+    static int decode24(byte[] bs, int off)
+    {
+        int n = bs[  off] & 0xFF;
+        n |= (bs[++off] & 0xFF) << 8;
+        n |= (bs[++off] & 0xFF) << 16;
+        return n;
+    }
+
+    static int decode32(byte[] bs, int off)
+    {
+        int n = bs[off] & 0xFF;
+        n |= (bs[++off] & 0xFF) << 8;
+        n |= (bs[++off] & 0xFF) << 16;
+        n |=  bs[++off]         << 24;
+        return n;
+    }
+
+    static void decode32(byte[] bs, int bsOff, int[] n, int nOff, int nLen)
+    {
+        for (int i = 0; i < nLen; ++i)
+        {
+            n[nOff + i] = decode32(bs, bsOff + i * 4);
+        }
+    }
+
+    static void encode24(int n, byte[] bs, int off)
+    {
+        bs[  off] = (byte)(n       );
+        bs[++off] = (byte)(n >>>  8);
+        bs[++off] = (byte)(n >>> 16);
+    }
+
+    static void encode32(int n, byte[] bs, int off)
+    {
+        bs[  off] = (byte)(n       );
+        bs[++off] = (byte)(n >>>  8);
+        bs[++off] = (byte)(n >>> 16);
+        bs[++off] = (byte)(n >>> 24);
+    }
+
+    static void encode32(int[] n, int nOff, int nLen, byte[] bs, int bsOff)
+    {
+        for (int i = 0; i < nLen; ++i)
+        {
+            encode32(n[nOff + i], bs, bsOff + i * 4);
+        }
+    }
+
+    static void encode56(long n, byte[] bs, int off)
+    {
+        encode32((int)n, bs, off);
+        encode24((int)(n >>> 32), bs, off + 4);
+    }
+}

@@ -7,9 +7,7 @@
 import org.bouncycastle.math.ec.rfc7748.X25519;
 import org.bouncycastle.math.ec.rfc7748.X25519Field;
 import org.bouncycastle.math.raw.Interleave;
-import org.bouncycastle.math.raw.Nat;
 import org.bouncycastle.math.raw.Nat256;
-import org.bouncycastle.util.Arrays;
 
 /**
  * A low-level implementation of the Ed25519, Ed25519ctx, and Ed25519ph instantiations of the Edwards-Curve
@@ -33,11 +31,17 @@ public static final class Algorithm
         public static final int Ed25519ph = 2;
     }
 
-    private static class F extends X25519Field {};
+    public static final class PublicPoint
+    {
+        final int[] data;
 
-    private static final long M08L = 0x000000FFL;
-    private static final long M28L = 0x0FFFFFFFL;
-    private static final long M32L = 0xFFFFFFFFL;
+        PublicPoint(int[] data)
+        {
+            this.data = data;
+        }
+    }
+
+    private static class F extends X25519Field {};
 
     private static final int COORD_INTS = 8;
     private static final int POINT_BYTES = COORD_INTS * 4;
@@ -56,20 +60,23 @@ private static class F extends X25519Field {};
 
     private static final int[] P = new int[]{ 0xFFFFFFED, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF,
         0xFFFFFFFF, 0x7FFFFFFF };
-    private static final int[] L = new int[]{ 0x5CF5D3ED, 0x5812631A, 0xA2F79CD6, 0x14DEF9DE, 0x00000000, 0x00000000,
-        0x00000000, 0x10000000 };
 
-    private static final int L0 = -0x030A2C13;      // L0:26/--
-    private static final int L1 =  0x012631A6;      // L1:24/22
-    private static final int L2 =  0x079CD658;      // L2:27/--
-    private static final int L3 = -0x006215D1;      // L3:23/--
-    private static final int L4 =  0x000014DF;      // L4:12/11
+    private static final int[] ORDER8_y1 = new int[]{ 0x706A17C7, 0x4FD84D3D, 0x760B3CBA, 0x0F67100D, 0xFA53202A,
+        0xC6CC392C, 0x77FDC74E, 0x7A03AC92 };
+    private static final int[] ORDER8_y2 = new int[]{ 0x8F95E826, 0xB027B2C2, 0x89F4C345, 0xF098EFF2, 0x05ACDFD5,
+        0x3933C6D3, 0x880238B1, 0x05FC536D };
 
     private static final int[] B_x = new int[]{ 0x0325D51A, 0x018B5823, 0x007B2C95, 0x0304A92D, 0x00D2598E, 0x01D6DC5C,
         0x01388C7F, 0x013FEC0A, 0x029E6B72, 0x0042D26D };
     private static final int[] B_y = new int[]{ 0x02666658, 0x01999999, 0x00666666, 0x03333333, 0x00CCCCCC, 0x02666666,
         0x01999999, 0x00666666, 0x03333333, 0x00CCCCCC, };
 
+    // 2^128 * B
+    private static final int[] B128_x = new int[]{ 0x00B7E824, 0x0011EB98, 0x003E5FC8, 0x024E1739, 0x0131CD0B,
+        0x014E29A0, 0x034E6138, 0x0132C952, 0x03F9E22F, 0x00984F5F };
+    private static final int[] B128_y = new int[]{ 0x03F5A66B, 0x02AF4452, 0x0049E5BB, 0x00F28D26, 0x0121A17C,
+        0x02C29C3A, 0x0047AD89, 0x0087D95F, 0x0332936E, 0x00BE5933 };
+
     // Note that d == -121665/121666
     private static final int[] C_d = new int[]{ 0x035978A3, 0x02D37284, 0x018AB75E, 0x026A0A0E, 0x0000E014, 0x0379E898,
         0x01D01E5D, 0x01E738CC, 0x03715B7F, 0x00A406D9 };
@@ -78,19 +85,21 @@ private static class F extends X25519Field {};
     private static final int[] C_d4 = new int[]{ 0x0165E2B2, 0x034DCA13, 0x002ADD7A, 0x01A8283B, 0x00038052, 0x01E7A260,
         0x03407977, 0x019CE331, 0x01C56DFF, 0x00901B67 };
 
-    private static final int WNAF_WIDTH = 5;
-    private static final int WNAF_WIDTH_BASE = 7;
+//    private static final int WNAF_WIDTH = 5;
+    private static final int WNAF_WIDTH_128 = 4;
+    private static final int WNAF_WIDTH_BASE = 6;
 
     // scalarMultBase is hard-coded for these values of blocks, teeth, spacing so they can't be freely changed
     private static final int PRECOMP_BLOCKS = 8;
     private static final int PRECOMP_TEETH = 4;
     private static final int PRECOMP_SPACING = 8;
-//    private static final int PRECOMP_RANGE = PRECOMP_BLOCKS * PRECOMP_TEETH * PRECOMP_SPACING; // range == 256
+    private static final int PRECOMP_RANGE = PRECOMP_BLOCKS * PRECOMP_TEETH * PRECOMP_SPACING; // range == 256
     private static final int PRECOMP_POINTS = 1 << (PRECOMP_TEETH - 1);
     private static final int PRECOMP_MASK = PRECOMP_POINTS - 1;
 
     private static final Object PRECOMP_LOCK = new Object();
     private static PointPrecomp[] PRECOMP_BASE_WNAF = null;
+    private static PointPrecomp[] PRECOMP_BASE128_WNAF = null;    
     private static int[] PRECOMP_BASE_COMB = null;
 
     private static class PointAccum
@@ -140,18 +149,15 @@ private static class PointTemp
 
     private static byte[] calculateS(byte[] r, byte[] k, byte[] s)
     {
-        int[] t = new int[SCALAR_INTS * 2];     decodeScalar(r, 0, t);
-        int[] u = new int[SCALAR_INTS];         decodeScalar(k, 0, u);
-        int[] v = new int[SCALAR_INTS];         decodeScalar(s, 0, v);
+        int[] t = new int[SCALAR_INTS * 2];     Scalar25519.decode(r, t);
+        int[] u = new int[SCALAR_INTS];         Scalar25519.decode(k, u);
+        int[] v = new int[SCALAR_INTS];         Scalar25519.decode(s, v);
 
         Nat256.mulAddTo(u, v, t);
 
         byte[] result = new byte[SCALAR_BYTES * 2];
-        for (int i = 0; i < t.length; ++i)
-        {
-            encode32(t[i], result, i * 4);
-        }
-        return reduceScalar(result);
+        Codec.encode32(t, 0, t.length, result, 0);
+        return Scalar25519.reduce(result);
     }
 
     private static boolean checkContextVar(byte[] ctx , byte phflag)
@@ -160,14 +166,14 @@ private static boolean checkContextVar(byte[] ctx , byte phflag)
             || ctx != null && ctx.length < 256;
     }
 
-    private static int checkPoint(int[] x, int[] y)
+    private static int checkPoint(PointAffine p)
     {
         int[] t = F.create();
         int[] u = F.create();
         int[] v = F.create();
 
-        F.sqr(x, u);
-        F.sqr(y, v);
+        F.sqr(p.x, u);
+        F.sqr(p.y, v);
         F.mul(u, v, t);
         F.sub(v, u, v);
         F.mul(t, C_d, t);
@@ -178,16 +184,16 @@ private static int checkPoint(int[] x, int[] y)
         return F.isZero(t);
     }
 
-    private static int checkPoint(int[] x, int[] y, int[] z)
+    private static int checkPoint(PointAccum p)
     {
         int[] t = F.create();
         int[] u = F.create();
         int[] v = F.create();
         int[] w = F.create();
 
-        F.sqr(x, u);
-        F.sqr(y, v);
-        F.sqr(z, w);
+        F.sqr(p.x, u);
+        F.sqr(p.y, v);
+        F.sqr(p.z, w);
         F.mul(u, v, t);
         F.sub(v, u, v);
         F.mul(v, w, v);
@@ -200,25 +206,62 @@ private static int checkPoint(int[] x, int[] y, int[] z)
         return F.isZero(t);
     }
 
+    private static boolean checkPointFullVar(byte[] p)
+    {
+        int y7 = Codec.decode32(p, 28) & 0x7FFFFFFF;
+
+        int t0 = y7;
+        int t1 = y7 ^ P[7];
+        int t2 = y7 ^ ORDER8_y1[7];
+        int t3 = y7 ^ ORDER8_y2[7];
+
+        for (int i = COORD_INTS - 2; i > 0; --i)
+        {
+            int yi = Codec.decode32(p, i * 4);
+
+            t0 |= yi;
+            t1 |= yi ^ P[i];
+            t2 |= yi ^ ORDER8_y1[i];
+            t3 |= yi ^ ORDER8_y2[i];
+        }
+
+        int y0 = Codec.decode32(p, 0);
+
+        // Reject 0 and 1
+        if (t0 == 0 && (y0 + Integer.MIN_VALUE) <= (1 + Integer.MIN_VALUE))
+            return false;
+
+        // Reject P - 1 and non-canonical encodings (i.e. >= P)
+        if (t1 == 0 && (y0 + Integer.MIN_VALUE) >= (P[0] - 1 + Integer.MIN_VALUE))
+            return false;
+
+        t2 |= y0 ^ ORDER8_y1[0];
+        t3 |= y0 ^ ORDER8_y2[0];
+
+        // Reject order 8 points
+        return (t2 != 0) & (t3 != 0);
+    }
+
+    private static boolean checkPointOrderVar(PointAffine p)
+    {
+        PointAccum r = new PointAccum();
+        scalarMultOrderVar(p, r);
+        return normalizeToNeutralElementVar(r);
+    }
+
     private static boolean checkPointVar(byte[] p)
     {
-        if ((decode32(p, 28) & 0x7FFFFFFF) < P[7])
+        if ((Codec.decode32(p, 28) & 0x7FFFFFFF) < P[7])
         {
             return true;
         }
 
         int[] t = new int[COORD_INTS];
-        decode32(p, 0, t, 0, COORD_INTS);
+        Codec.decode32(p, 0, t, 0, COORD_INTS);
         t[COORD_INTS - 1] &= 0x7FFFFFFF;
         return !Nat256.gte(t, P);
     }
 
-    private static boolean checkScalarVar(byte[] s, int[] n)
-    {
-        decodeScalar(s, 0, n);
-        return !Nat256.gte(n, L);
-    }
-
     private static byte[] copy(byte[] buf, int off, int len)
     {
         byte[] result = new byte[len];
@@ -241,43 +284,11 @@ public static Digest createPrehash()
         return createDigest();
     }
 
-    private static int decode24(byte[] bs, int off)
+    private static boolean decodePointVar(byte[] p, boolean negate, PointAffine r)
     {
-        int n = bs[  off] & 0xFF;
-        n |= (bs[++off] & 0xFF) << 8;
-        n |= (bs[++off] & 0xFF) << 16;
-        return n;
-    }
+        int x_0 = (p[POINT_BYTES - 1] & 0x80) >>> 7;
 
-    private static int decode32(byte[] bs, int off)
-    {
-        int n = bs[off] & 0xFF;
-        n |= (bs[++off] & 0xFF) << 8;
-        n |= (bs[++off] & 0xFF) << 16;
-        n |=  bs[++off]         << 24;
-        return n;
-    }
-
-    private static void decode32(byte[] bs, int bsOff, int[] n, int nOff, int nLen)
-    {
-        for (int i = 0; i < nLen; ++i)
-        {
-            n[nOff + i] = decode32(bs, bsOff + i * 4);
-        }
-    }
-
-    private static boolean decodePointVar(byte[] p, int pOff, boolean negate, PointAffine r)
-    {
-        byte[] py = copy(p, pOff, POINT_BYTES);
-        if (!checkPointVar(py))
-        {
-            return false;
-        }
-
-        int x_0 = (py[POINT_BYTES - 1] & 0x80) >>> 7;
-        py[POINT_BYTES - 1] &= 0x7F;
-
-        F.decode(py, 0, r.y);
+        F.decode(p, r.y);
 
         int[] u = F.create();
         int[] v = F.create();
@@ -301,71 +312,59 @@ private static boolean decodePointVar(byte[] p, int pOff, boolean negate, PointA
         if (negate ^ (x_0 != (r.x[0] & 1)))
         {
             F.negate(r.x, r.x);
+            F.normalize(r.x);
         }
 
         return true;
     }
 
-    private static void decodeScalar(byte[] k, int kOff, int[] n)
-    {
-        decode32(k, kOff, n, 0, SCALAR_INTS);
-    }
-
     private static void dom2(Digest d, byte phflag, byte[] ctx)
     {
-        if (ctx != null)
-        {
-            int n = DOM2_PREFIX.length;
-            byte[] t = new byte[n + 2 + ctx.length];
-            System.arraycopy(DOM2_PREFIX, 0, t, 0, n);
-            t[n] = phflag;
-            t[n + 1] = (byte)ctx.length;
-            System.arraycopy(ctx, 0, t, n + 2, ctx.length);
-
-            d.update(t, 0, t.length);
-        }
-    }
+//        assert ctx != null;
 
-    private static void encode24(int n, byte[] bs, int off)
-    {
-        bs[  off] = (byte)(n       );
-        bs[++off] = (byte)(n >>>  8);
-        bs[++off] = (byte)(n >>> 16);
+        int n = DOM2_PREFIX.length;
+        byte[] t = new byte[n + 2 + ctx.length];
+        System.arraycopy(DOM2_PREFIX, 0, t, 0, n);
+        t[n] = phflag;
+        t[n + 1] = (byte)ctx.length;
+        System.arraycopy(ctx, 0, t, n + 2, ctx.length);
+
+        d.update(t, 0, t.length);
     }
 
-    private static void encode32(int n, byte[] bs, int off)
+    private static void encodePoint(PointAffine p, byte[] r, int rOff)
     {
-        bs[  off] = (byte)(n       );
-        bs[++off] = (byte)(n >>>  8);
-        bs[++off] = (byte)(n >>> 16);
-        bs[++off] = (byte)(n >>> 24);
+        F.encode(p.y, r, rOff);
+        r[rOff + POINT_BYTES - 1] |= (p.x[0] & 1) << 7;
     }
 
-    private static void encode56(long n, byte[] bs, int off)
+    public static void encodePublicPoint(PublicPoint publicPoint, byte[] pk, int pkOff)
     {
-        encode32((int)n, bs, off);
-        encode24((int)(n >>> 32), bs, off + 4);
+        F.encode(publicPoint.data, F.SIZE, pk, pkOff);
+        pk[pkOff + POINT_BYTES - 1] |= (publicPoint.data[0] & 1) << 7;
     }
 
-    private static int encodePoint(PointAccum p, byte[] r, int rOff)
+    private static int encodeResult(PointAccum p, byte[] r, int rOff)
     {
-        int[] x = F.create();
-        int[] y = F.create();
+        PointAffine q = new PointAffine();
+        normalizeToAffine(p, q);
 
-        F.inv(p.z, y);
-        F.mul(p.x, y, x);
-        F.mul(p.y, y, y);
-        F.normalize(x);
-        F.normalize(y);
+        int result = checkPoint(q);
 
-        int result = checkPoint(x, y);
-
-        F.encode(y, r, rOff);
-        r[rOff + POINT_BYTES - 1] |= ((x[0] & 1) << 7);
+        encodePoint(q, r, rOff);
 
         return result;
     }
 
+    private static PublicPoint exportPoint(PointAffine p)
+    {
+        int[] data = new int[F.SIZE * 2];
+        F.copy(p.x, 0, data, 0);
+        F.copy(p.y, 0, data, F.SIZE);
+
+        return new PublicPoint(data);
+    }
+
     public static void generatePrivateKey(SecureRandom random, byte[] k)
     {
         if (k.length != SECRET_KEY_SIZE)
@@ -390,81 +389,74 @@ public static void generatePublicKey(byte[] sk, int skOff, byte[] pk, int pkOff)
         scalarMultBaseEncoded(s, pk, pkOff);
     }
 
-    private static int getWindow4(int[] x, int n)
+    public static PublicPoint generatePublicKey(byte[] sk, int skOff)
     {
-        int w = n >>> 3, b = (n & 7) << 2;
-        return (x[w] >>> b) & 15;
-    }
+        Digest d = createDigest();
+        byte[] h = new byte[64];
 
-    private static byte[] getWnafVar(int[] n, int width)
-    {
-//        assert 0 <= n[SCALAR_INTS - 1] && n[SCALAR_INTS - 1] <= L[SCALAR_INTS - 1];
-//        assert 2 <= width && width <= 8;
+        d.update(sk, skOff, SECRET_KEY_SIZE);
+        d.doFinal(h, 0);
 
-        int[] t = new int[SCALAR_INTS * 2];
-        {
-            int tPos = t.length, c = 0;
-            int i = SCALAR_INTS;
-            while (--i >= 0)
-            {
-                int next = n[i];
-                t[--tPos] = (next >>> 16) | (c << 16);
-                t[--tPos] = c = next;
-            }
-        }
+        byte[] s = new byte[SCALAR_BYTES];
+        pruneScalar(h, 0, s);
 
-        byte[] ws = new byte[253];
+        PointAccum p = new PointAccum();
+        scalarMultBase(s, p);
 
-        final int lead = 32 - width;
+        PointAffine q = new PointAffine();
+        normalizeToAffine(p, q);
 
-        int j = 0, carry = 0;
-        for (int i = 0; i < t.length; ++i, j -= 16)
+        if (0 == checkPoint(q))
         {
-            int word = t[i];
-            while (j < 16)
-            {
-                int word16 = word >>> j;
-                int bit = word16 & 1;
-
-                if (bit == carry)
-                {
-                    ++j;
-                    continue;
-                }
+            throw new IllegalStateException();
+        }
 
-                int digit = (word16 | 1) << lead;
-                carry = digit >>> 31;
+        return exportPoint(q);
+    }
 
-                ws[(i << 4) + j] = (byte)(digit >> lead);
+    private static int getWindow4(int[] x, int n)
+    {
+        int w = n >>> 3, b = (n & 7) << 2;
+        return (x[w] >>> b) & 15;
+    }
 
-                j += width;
-            }
+    private static void groupCombBits(int[] n)
+    {
+        /*
+         * Because we are using 4 teeth and 8 spacing, each limb of n corresponds to one of the 8 blocks.
+         * Therefore we can efficiently group the bits for each comb position using a (double) shuffle. 
+         */
+        for (int i = 0; i < n.length; ++i)
+        {
+            n[i] = Interleave.shuffle2(n[i]);
         }
-
-//        assert carry == 0;
-
-        return ws;
     }
 
     private static void implSign(Digest d, byte[] h, byte[] s, byte[] pk, int pkOff, byte[] ctx, byte phflag, byte[] m,
         int mOff, int mLen, byte[] sig, int sigOff)
     {
-        dom2(d, phflag, ctx);
+        if (ctx != null)
+        {
+            dom2(d, phflag, ctx);
+        }
         d.update(h, SCALAR_BYTES, SCALAR_BYTES);
         d.update(m, mOff, mLen);
         d.doFinal(h, 0);
 
-        byte[] r = reduceScalar(h);
+        byte[] r = Scalar25519.reduce(h);
         byte[] R = new byte[POINT_BYTES];
         scalarMultBaseEncoded(r, R, 0);
 
-        dom2(d, phflag, ctx);
+        if (ctx != null)
+        {
+            dom2(d, phflag, ctx);
+        }
         d.update(R, 0, POINT_BYTES);
         d.update(pk, pkOff, POINT_BYTES);
         d.update(m, mOff, mLen);
         d.doFinal(h, 0);
 
-        byte[] k = reduceScalar(h);
+        byte[] k = Scalar25519.reduce(h);
         byte[] S = calculateS(r, k, s);
 
         System.arraycopy(R, 0, sig, sigOff, POINT_BYTES);
@@ -524,43 +516,121 @@ private static boolean implVerify(byte[] sig, int sigOff, byte[] pk, int pkOff,
 
         byte[] R = copy(sig, sigOff, POINT_BYTES);
         byte[] S = copy(sig, sigOff + POINT_BYTES, SCALAR_BYTES);
+        byte[] A = copy(pk, pkOff, PUBLIC_KEY_SIZE);
 
         if (!checkPointVar(R))
         {
             return false;
         }
 
         int[] nS = new int[SCALAR_INTS];
-        if (!checkScalarVar(S, nS))
+        if (!Scalar25519.checkVar(S, nS))
+        {
+            return false;
+        }
+
+        if (!checkPointFullVar(A))
+            return false;
+
+        PointAffine pR = new PointAffine();
+        if (!decodePointVar(R, true, pR))
         {
             return false;
         }
 
         PointAffine pA = new PointAffine();
-        if (!decodePointVar(pk, pkOff, true, pA))
+        if (!decodePointVar(A, true, pA))
         {
             return false;
         }
 
         Digest d = createDigest();
         byte[] h = new byte[64];
 
-        dom2(d, phflag, ctx);
+        if (ctx != null)
+        {
+            dom2(d, phflag, ctx);
+        }
         d.update(R, 0, POINT_BYTES);
-        d.update(pk, pkOff, POINT_BYTES);
+        d.update(A, 0, POINT_BYTES);
         d.update(m, mOff, mLen);
         d.doFinal(h, 0);
 
-        byte[] k = reduceScalar(h);
+        byte[] k = Scalar25519.reduce(h);
 
         int[] nA = new int[SCALAR_INTS];
-        decodeScalar(k, 0, nA);
+        Scalar25519.decode(k, nA);
 
-        PointAccum pR = new PointAccum();
-        scalarMultStrausVar(nS, nA, pA, pR);
+        int[] v0 = new int[4];
+        int[] v1 = new int[4];
+        Scalar25519.reduceBasisVar(nA, v0, v1);
+        Scalar25519.multiply128Var(nS, v1, nS);
 
-        byte[] check = new byte[POINT_BYTES];
-        return 0 != encodePoint(pR, check, 0) && Arrays.areEqual(check, R);
+        PointAccum pZ = new PointAccum();
+        scalarMultStraus128Var(nS, v0, pA, v1, pR, pZ);
+        return normalizeToNeutralElementVar(pZ);
+    }
+
+    private static boolean implVerify(byte[] sig, int sigOff, PublicPoint publicPoint, byte[] ctx, byte phflag,
+        byte[] m, int mOff, int mLen)
+    {
+        if (!checkContextVar(ctx, phflag))
+        {
+            throw new IllegalArgumentException("ctx");
+        }
+
+        byte[] R = copy(sig, sigOff, POINT_BYTES);
+        byte[] S = copy(sig, sigOff + POINT_BYTES, SCALAR_BYTES);
+
+        if (!checkPointVar(R))
+        {
+            return false;
+        }
+
+        int[] nS = new int[SCALAR_INTS];
+        if (!Scalar25519.checkVar(S, nS))
+        {
+            return false;
+        }
+
+        PointAffine pR = new PointAffine();
+        if (!decodePointVar(R, true, pR))
+        {
+            return false;
+        }
+
+        PointAffine pA = new PointAffine();
+        F.negate(publicPoint.data, pA.x);
+        F.copy(publicPoint.data, F.SIZE, pA.y, 0);
+
+        byte[] A = new byte[PUBLIC_KEY_SIZE];
+        encodePublicPoint(publicPoint, A, 0);
+
+        Digest d = createDigest();
+        byte[] h = new byte[64];
+
+        if (ctx != null)
+        {
+            dom2(d, phflag, ctx);
+        }
+        d.update(R, 0, POINT_BYTES);
+        d.update(A, 0, POINT_BYTES);
+        d.update(m, mOff, mLen);
+        d.doFinal(h, 0);
+
+        byte[] k = Scalar25519.reduce(h);
+
+        int[] nA = new int[SCALAR_INTS];
+        Scalar25519.decode(k, nA);
+
+        int[] v0 = new int[4];
+        int[] v1 = new int[4];
+        Scalar25519.reduceBasisVar(nA, v0, v1);
+        Scalar25519.multiply128Var(nS, v1, nS);
+
+        PointAccum pZ = new PointAccum();
+        scalarMultStraus128Var(nS, v0, pA, v1, pR, pZ);
+        return normalizeToNeutralElementVar(pZ);
     }
 
     private static void invertDoubleZs(PointExtended[] points)
@@ -597,16 +667,34 @@ private static void invertDoubleZs(PointExtended[] points)
         F.copy(u, 0, points[0].z, 0);
     }
 
-    private static boolean isNeutralElementVar(int[] x, int[] y)
-    {
-        return F.isZeroVar(x) && F.isOneVar(y);
-    }
+//    private static boolean isNeutralElementVar(int[] x, int[] y)
+//    {
+//        return F.isZeroVar(x) && F.isOneVar(y);
+//    }
 
     private static boolean isNeutralElementVar(int[] x, int[] y, int[] z)
     {
         return F.isZeroVar(x) && F.areEqualVar(y, z);
     }
 
+    private static void normalizeToAffine(PointAccum p, PointAffine r)
+    {
+        F.inv(p.z, r.y);
+        F.mul(r.y, p.x, r.x);
+        F.mul(r.y, p.y, r.y);
+        F.normalize(r.x);
+        F.normalize(r.y);
+    }
+
+    private static boolean normalizeToNeutralElementVar(PointAccum p)
+    {
+        F.normalize(p.x);
+        F.normalize(p.y);
+        F.normalize(p.z);
+
+        return isNeutralElementVar(p.x, p.y, p.z);
+    }
+
     private static void pointAdd(PointExtended p, PointExtended q, PointExtended r, PointTemp t)
     {
         // p may ref the same point as r (or q), but q may not ref the same point as r.
@@ -841,18 +929,19 @@ private static void pointLookupZ(int[] x, int n, int[] table, PointPrecompZ r)
         F.cnegate(sign, r.xyd);
     }
 
-    private static void pointPrecompute(PointAffine p, PointExtended[] points, int count, PointTemp t)
+    private static void pointPrecompute(PointAffine p, PointExtended[] points, int pointsOff, int pointsLen,
+        PointTemp t)
     {
-//        assert count > 0;
+//        assert pointsLen > 0;
 
-        pointCopy(p, points[0] = new PointExtended());
+        pointCopy(p, points[pointsOff] = new PointExtended());
 
         PointExtended d = new PointExtended();
-        pointAdd(points[0], points[0], d, t);
+        pointAdd(points[pointsOff], points[pointsOff], d, t);
 
-        for (int i = 1; i < count; ++i)
+        for (int i = 1; i < pointsLen; ++i)
         {
-            pointAdd(points[i - 1], d, points[i] = new PointExtended(), t);
+            pointAdd(points[pointsOff + i - 1], d, points[pointsOff + i] = new PointExtended(), t);
         }
     }
 
@@ -929,23 +1018,29 @@ public static void precompute()
     {
         synchronized (PRECOMP_LOCK)
         {
-            if (PRECOMP_BASE_WNAF != null && PRECOMP_BASE_COMB != null)
+            if (PRECOMP_BASE_COMB != null)
             {
                 return;
             }
 
             int wnafPoints = 1 << (WNAF_WIDTH_BASE - 2);
             int combPoints = PRECOMP_BLOCKS * PRECOMP_POINTS;
-            int totalPoints = wnafPoints + combPoints;
+            int totalPoints = wnafPoints * 2 + combPoints;
 
             PointExtended[] points = new PointExtended[totalPoints];
             PointTemp t = new PointTemp();
 
-            PointAffine b = new PointAffine();
-            F.copy(B_x, 0, b.x, 0);
-            F.copy(B_y, 0, b.y, 0);
+            PointAffine B = new PointAffine();
+            F.copy(B_x, 0, B.x, 0);
+            F.copy(B_y, 0, B.y, 0);
+
+            pointPrecompute(B, points, 0, wnafPoints, t);
 
-            pointPrecompute(b, points, wnafPoints, t);
+            PointAffine B128 = new PointAffine();
+            F.copy(B128_x, 0, B128.x, 0);
+            F.copy(B128_y, 0, B128.y, 0);
+
+            pointPrecompute(B128, points, wnafPoints, wnafPoints, t);
 
             PointAccum p = new PointAccum();
             F.copy(B_x, 0, p.x, 0);
@@ -954,12 +1049,13 @@ public static void precompute()
             F.copy(p.x, 0, p.u, 0);
             F.copy(p.y, 0, p.v, 0);
 
-            int pointsIndex = wnafPoints;
+            int pointsIndex = wnafPoints * 2;
             PointExtended[] toothPowers = new PointExtended[PRECOMP_TEETH];
             for (int tooth = 0; tooth < PRECOMP_TEETH; ++tooth)
             {
                 toothPowers[tooth] = new PointExtended();
             }
+
             PointExtended u = new PointExtended();
             for (int block = 0; block < PRECOMP_BLOCKS; ++block)
             {
@@ -1029,10 +1125,32 @@ public static void precompute()
                 F.normalize(r.xyd);
             }
 
+            PRECOMP_BASE128_WNAF = new PointPrecomp[wnafPoints];
+            for (int i = 0; i < wnafPoints; ++i)
+            {
+                PointExtended q = points[wnafPoints + i];
+                PointPrecomp r = PRECOMP_BASE128_WNAF[i] = new PointPrecomp();
+
+                // Calculate x/2 and y/2 (because the z value holds half the inverse; see above).
+                F.mul(q.x, q.z, q.x);
+                F.mul(q.y, q.z, q.y);
+
+                // y/2 +/- x/2
+                F.apm(q.y, q.x, r.ypx_h, r.ymx_h);
+
+                // x/2 * y/2 * (4.d) == x.y.d
+                F.mul(q.x, q.y, r.xyd);
+                F.mul(r.xyd, C_d4, r.xyd);
+
+                F.normalize(r.ymx_h);
+                F.normalize(r.ypx_h);
+                F.normalize(r.xyd);
+            }
+
             PRECOMP_BASE_COMB = F.createTable(combPoints * 3);
             PointPrecomp s = new PointPrecomp();
             int off = 0;
-            for (int i = wnafPoints; i < totalPoints; ++i)
+            for (int i = wnafPoints * 2; i < totalPoints; ++i)
             {
                 PointExtended q = points[i];
 
@@ -1055,7 +1173,7 @@ public static void precompute()
                 F.copy(s.ypx_h, 0, PRECOMP_BASE_COMB, off);       off += F.SIZE;
                 F.copy(s.xyd  , 0, PRECOMP_BASE_COMB, off);       off += F.SIZE;
             }
-//            assert off == precompBaseComb.length;
+//            assert off == PRECOMP_BASE_COMB.length;
         }
     }
 
@@ -1068,154 +1186,11 @@ private static void pruneScalar(byte[] n, int nOff, byte[] r)
         r[SCALAR_BYTES - 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]                 & M08L;   // 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;
-        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;
-
-//        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[SCALAR_BYTES];
-        encode56(x00 | (x01 << 28), r,  0);
-        encode56(x02 | (x03 << 28), r,  7);
-        encode56(x04 | (x05 << 28), r, 14);
-        encode56(x06 | (x07 << 28), r, 21);
-        encode32((int)x08,          r, 28);
-        return r;
-    }
-
     private static void scalarMult(byte[] k, PointAffine p, PointAccum r)
     {
         int[] n = new int[SCALAR_INTS];
-        decodeScalar(k, 0, n);
-
-        // Recode the scalar into signed-digit form
-        {
-            //int c1 =
-            Nat.cadd(SCALAR_INTS, ~n[0] & 1, n, L, n);      //assert c1 == 0;
-            //int c2 =
-            Nat.shiftDownBit(SCALAR_INTS, n, 1);            //assert c2 == (1 << 31);
-        }
+        Scalar25519.decode(k, n);
+        Scalar25519.toSignedDigits(256, n, n);
 
         PointPrecompZ q = new PointPrecompZ();
         PointTemp t = new PointTemp();
@@ -1252,24 +1227,9 @@ private static void scalarMultBase(byte[] k, PointAccum r)
         precompute();
 
         int[] n = new int[SCALAR_INTS];
-        decodeScalar(k, 0, n);
-
-        // Recode the scalar into signed-digit form, then group comb bits in each block
-        {
-            //int c1 =
-            Nat.cadd(SCALAR_INTS, ~n[0] & 1, n, L, n);      //assert c1 == 0;
-            //int c2 =
-            Nat.shiftDownBit(SCALAR_INTS, n, 1);            //assert c2 == (1 << 31);
-
-            /*
-             * Because we are using 4 teeth and 8 spacing, each limb of n corresponds to one of the 8 blocks.
-             * Therefore we can efficiently group the bits for each comb position using a (double) shuffle. 
-             */
-            for (int i = 0; i < SCALAR_INTS; ++i)
-            {
-                n[i] = Interleave.shuffle2(n[i]);
-            }
-        }
+        Scalar25519.decode(k, n);
+        Scalar25519.toSignedDigits(PRECOMP_RANGE, n, n);
+        groupCombBits(n);
 
         PointPrecomp p = new PointPrecomp();
         PointTemp t = new PointTemp();
@@ -1280,16 +1240,16 @@ private static void scalarMultBase(byte[] k, PointAccum r)
         int cOff = (PRECOMP_SPACING - 1) * PRECOMP_TEETH;
         for (;;)
         {
-            for (int b = 0; b < PRECOMP_BLOCKS; ++b)
+            for (int block = 0; block < PRECOMP_BLOCKS; ++block)
             {
-                int w = n[b] >>> cOff;
+                int w = n[block] >>> cOff;
                 int sign = (w >>> (PRECOMP_TEETH - 1)) & 1;
                 int abs = (w ^ -sign) & PRECOMP_MASK;
 
 //                assert sign == 0 || sign == 1;
 //                assert 0 <= abs && abs < PRECOMP_POINTS;
 
-                pointLookup(b, abs, p);
+                pointLookup(block, abs, p);
 
                 F.cnegate(resultSign ^ sign, r.x);
                 F.cnegate(resultSign ^ sign, r.u);
@@ -1314,7 +1274,7 @@ private static void scalarMultBaseEncoded(byte[] k, byte[] r, int rOff)
     {
         PointAccum p = new PointAccum();
         scalarMultBase(k, p);
-        if (0 == encodePoint(p, r, rOff))
+        if (0 == encodeResult(p, r, rOff))
         {
             throw new IllegalStateException();
         }
@@ -1335,19 +1295,23 @@ public static void scalarMultBaseYZ(X25519.Friend friend, byte[] k, int kOff, in
 
         PointAccum p = new PointAccum();
         scalarMultBase(n, p);
-        if (0 == checkPoint(p.x, p.y, p.z))
+        if (0 == checkPoint(p))
         {
             throw new IllegalStateException();
         }
+
         F.copy(p.y, 0, y, 0);
         F.copy(p.z, 0, z, 0);
     }
 
     private static void scalarMultOrderVar(PointAffine p, PointAccum r)
     {
-        byte[] ws_p = getWnafVar(L, WNAF_WIDTH);
+        byte[] ws_p = new byte[253];
 
-        int count = 1 << (WNAF_WIDTH - 2);
+        // NOTE: WNAF_WIDTH_128 because of the special structure of the order
+        Scalar25519.getOrderWnafVar(WNAF_WIDTH_128, ws_p);
+
+        int count = 1 << (WNAF_WIDTH_128 - 2);
         PointPrecompZ[] tp = new PointPrecompZ[count];
         PointTemp t = new PointTemp();
         pointPrecomputeZ(p, tp, count, t);
@@ -1359,10 +1323,8 @@ private static void scalarMultOrderVar(PointAffine p, PointAccum r)
             int wp = ws_p[bit];
             if (wp != 0)
             {
-                int sign = wp >> 31;
-                int index = (wp ^ sign) >>> 1;
-
-                pointAddVar((sign != 0), tp[index], r, t);
+                int index = (wp >> 1) ^ (wp >> 31);
+                pointAddVar(wp < 0, tp[index], r, t);
             }
 
             if (--bit < 0)
@@ -1374,47 +1336,69 @@ private static void scalarMultOrderVar(PointAffine p, PointAccum r)
         }
     }
 
-    private static void scalarMultStrausVar(int[] nb, int[] np, PointAffine p, PointAccum r)
+    private static void scalarMultStraus128Var(int[] nb, int[] np, PointAffine p, int[] nq, PointAffine q, PointAccum r)
     {
+//        assert nb.length == SCALAR_INTS;
+//        assert nb[SCALAR_INTS - 1] >>> 29 == 0;
+//        assert np.length == 4;
+//        assert nq.length == 4;
+
         precompute();
 
-        byte[] ws_b = getWnafVar(nb, WNAF_WIDTH_BASE);
-        byte[] ws_p = getWnafVar(np, WNAF_WIDTH);
+        byte[] ws_b = new byte[256];
+        byte[] ws_p = new byte[128];
+        byte[] ws_q = new byte[128];
+
+        Wnaf.getSignedVar(nb, WNAF_WIDTH_BASE, ws_b);
+        Wnaf.getSignedVar(np, WNAF_WIDTH_128, ws_p);
+        Wnaf.getSignedVar(nq, WNAF_WIDTH_128, ws_q);
 
-        int count = 1 << (WNAF_WIDTH - 2);
+        int count = 1 << (WNAF_WIDTH_128 - 2);
         PointPrecompZ[] tp = new PointPrecompZ[count];
+        PointPrecompZ[] tq = new PointPrecompZ[count];
         PointTemp t = new PointTemp();
         pointPrecomputeZ(p, tp, count, t);
+        pointPrecomputeZ(q, tq, count, t);
 
         pointSetNeutral(r);
 
-        for (int bit = 252;;)
+        int bit = 128;
+        while (--bit >= 0)
         {
             int wb = ws_b[bit];
             if (wb != 0)
             {
-                int sign = wb >> 31;
-                int index = (wb ^ sign) >>> 1;
+                int index = (wb >> 1) ^ (wb >> 31);
+                pointAddVar(wb < 0, PRECOMP_BASE_WNAF[index], r, t);
+            }
 
-                pointAddVar(sign != 0, PRECOMP_BASE_WNAF[index], r, t);
+            int wb128 = ws_b[128 + bit];
+            if (wb128 != 0)
+            {
+                int index = (wb128 >> 1) ^ (wb128 >> 31);
+                pointAddVar(wb128 < 0, PRECOMP_BASE128_WNAF[index], r, t);
             }
 
             int wp = ws_p[bit];
             if (wp != 0)
             {
-                int sign = wp >> 31;
-                int index = (wp ^ sign) >>> 1;
-
-                pointAddVar(sign != 0, tp[index], r, t);
+                int index = (wp >> 1) ^ (wp >> 31);
+                pointAddVar(wp < 0, tp[index], r, t);
             }
 
-            if (--bit < 0)
+            int wq = ws_q[bit];
+            if (wq != 0)
             {
-                break;
+                int index = (wq >> 1) ^ (wq >> 31);
+                pointAddVar(wq < 0, tq[index], r, t);
             }
 
             pointDouble(r);
         }
+
+        // NOTE: Together with the final pointDouble of the loop, this clears the cofactor of 8
+        pointDouble(r);
+        pointDouble(r);
     }
 
     public static void sign(byte[] sk, int skOff, byte[] m, int mOff, int mLen, byte[] sig, int sigOff)
@@ -1425,7 +1409,8 @@ public static void sign(byte[] sk, int skOff, byte[] m, int mOff, int mLen, byte
         implSign(sk, skOff, ctx, phflag, 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)
+    public static void sign(byte[] sk, int skOff, byte[] pk, int pkOff, byte[] m, int mOff, int mLen, byte[] sig,
+        int sigOff)
     {
         byte[] ctx = null;
         byte phflag = 0x00;
@@ -1440,7 +1425,8 @@ public static void sign(byte[] sk, int skOff, byte[] ctx, byte[] m, int mOff, in
         implSign(sk, skOff, ctx, phflag, 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)
+    public static void sign(byte[] sk, int skOff, byte[] pk, int pkOff, byte[] ctx, byte[] m, int mOff, int mLen,
+        byte[] sig, int sigOff)
     {
         byte phflag = 0x00;
 
@@ -1454,7 +1440,8 @@ public static void signPrehash(byte[] sk, int skOff, byte[] ctx, byte[] ph, int
         implSign(sk, skOff, ctx, phflag, ph, phOff, PREHASH_SIZE, sig, sigOff);
     }
 
-    public static void signPrehash(byte[] sk, int skOff, byte[] pk, int pkOff, byte[] ctx, byte[] ph, int phOff, byte[] sig, int sigOff)
+    public static void signPrehash(byte[] sk, int skOff, byte[] pk, int pkOff, byte[] ctx, byte[] ph, int phOff,
+        byte[] sig, int sigOff)
     {
         byte phflag = 0x01;
 
@@ -1474,7 +1461,8 @@ public static void signPrehash(byte[] sk, int skOff, byte[] ctx, Digest ph, byte
         implSign(sk, skOff, ctx, phflag, m, 0, m.length, sig, sigOff);
     }
 
-    public static void signPrehash(byte[] sk, int skOff, byte[] pk, int pkOff, byte[] ctx, Digest ph, byte[] sig, int sigOff)
+    public static void signPrehash(byte[] sk, int skOff, byte[] pk, int pkOff, byte[] ctx, Digest ph, byte[] sig,
+        int sigOff)
     {
         byte[] m = new byte[PREHASH_SIZE];
         if (PREHASH_SIZE != ph.doFinal(m, 0))
@@ -1489,34 +1477,74 @@ public static void signPrehash(byte[] sk, int skOff, byte[] pk, int pkOff, byte[
 
     public static boolean validatePublicKeyFull(byte[] pk, int pkOff)
     {
-        PointAffine p = new PointAffine();
-        if (!decodePointVar(pk, pkOff, false, p))
+        byte[] A = copy(pk, pkOff, PUBLIC_KEY_SIZE);
+
+        if (!checkPointFullVar(A))
         {
             return false;
         }
 
-        F.normalize(p.x);
-        F.normalize(p.y);
-
-        if (isNeutralElementVar(p.x, p.y))
+        PointAffine pA = new PointAffine();
+        if (!decodePointVar(A, false, pA))
         {
             return false;
         }
 
-        PointAccum r = new PointAccum();
-        scalarMultOrderVar(p, r);
+        return checkPointOrderVar(pA);
+    }
 
-        F.normalize(r.x);
-        F.normalize(r.y);
-        F.normalize(r.z);
+    public static PublicPoint validatePublicKeyFullExport(byte[] pk, int pkOff)
+    {
+        byte[] A = copy(pk, pkOff, PUBLIC_KEY_SIZE);
 
-        return isNeutralElementVar(r.x, r.y, r.z);
+        if (!checkPointFullVar(A))
+        {
+            return null;
+        }
+
+        PointAffine pA = new PointAffine();
+        if (!decodePointVar(A, false, pA))
+        {
+            return null;
+        }
+
+        if (!checkPointOrderVar(pA))
+        {
+            return null;
+        }
+
+        return exportPoint(pA);
     }
 
     public static boolean validatePublicKeyPartial(byte[] pk, int pkOff)
     {
-        PointAffine p = new PointAffine();
-        return decodePointVar(pk, pkOff, false, p);
+        byte[] A = copy(pk, pkOff, PUBLIC_KEY_SIZE);
+
+        if (!checkPointFullVar(A))
+        {
+            return false;
+        }
+
+        PointAffine pA = new PointAffine();
+        return decodePointVar(A, false, pA);
+    }
+
+    public static PublicPoint validatePublicKeyPartialExport(byte[] pk, int pkOff)
+    {
+        byte[] A = copy(pk, pkOff, PUBLIC_KEY_SIZE);
+
+        if (!checkPointFullVar(A))
+        {
+            return null;
+        }
+
+        PointAffine pA = new PointAffine();
+        if (!decodePointVar(A, false, pA))
+        {
+            return null;
+        }
+
+        return exportPoint(pA);
     }
 
     public static boolean verify(byte[] sig, int sigOff, byte[] pk, int pkOff, byte[] m, int mOff, int mLen)
@@ -1527,20 +1555,44 @@ public static boolean verify(byte[] sig, int sigOff, byte[] pk, int pkOff, byte[
         return implVerify(sig, sigOff, pk, pkOff, ctx, phflag, m, mOff, mLen);
     }
 
+    public static boolean verify(byte[] sig, int sigOff, PublicPoint publicPoint, byte[] m, int mOff, int mLen)
+    {
+        byte[] ctx = null;
+        byte phflag = 0x00;
+
+        return implVerify(sig, sigOff, publicPoint, ctx, phflag, m, mOff, mLen);
+    }
+
     public static boolean verify(byte[] sig, int sigOff, byte[] pk, int pkOff, byte[] ctx, byte[] m, int mOff, int mLen)
     {
         byte phflag = 0x00;
 
         return implVerify(sig, sigOff, pk, pkOff, ctx, phflag, m, mOff, mLen);
     }
 
+    public static boolean verify(byte[] sig, int sigOff, PublicPoint publicPoint, byte[] ctx, byte[] m, int mOff,
+        int mLen)
+    {
+        byte phflag = 0x00;
+
+        return implVerify(sig, sigOff, publicPoint, ctx, phflag, m, mOff, mLen);
+    }
+
     public static boolean verifyPrehash(byte[] sig, int sigOff, byte[] pk, int pkOff, byte[] ctx, byte[] ph, int phOff)
     {
         byte phflag = 0x01;
 
         return implVerify(sig, sigOff, pk, pkOff, ctx, phflag, ph, phOff, PREHASH_SIZE);
     }
 
+    public static boolean verifyPrehash(byte[] sig, int sigOff, PublicPoint publicPoint, byte[] ctx, byte[] ph,
+        int phOff)
+    {
+        byte phflag = 0x01;
+
+        return implVerify(sig, sigOff, publicPoint, ctx, phflag, ph, phOff, PREHASH_SIZE);
+    }
+
     public static boolean verifyPrehash(byte[] sig, int sigOff, byte[] pk, int pkOff, byte[] ctx, Digest ph)
     {
         byte[] m = new byte[PREHASH_SIZE];
@@ -1553,4 +1605,17 @@ public static boolean verifyPrehash(byte[] sig, int sigOff, byte[] pk, int pkOff
 
         return implVerify(sig, sigOff, pk, pkOff, ctx, phflag, m, 0, m.length);
     }
+
+    public static boolean verifyPrehash(byte[] sig, int sigOff, PublicPoint publicPoint, byte[] ctx, Digest ph)
+    {
+        byte[] m = new byte[PREHASH_SIZE];
+        if (PREHASH_SIZE != ph.doFinal(m, 0))
+        {
+            throw new IllegalArgumentException("ph");
+        }
+
+        byte phflag = 0x01;
+
+        return implVerify(sig, sigOff, publicPoint, ctx, phflag, m, 0, m.length);
+    }
 }

@@ -7,7 +7,6 @@
 import org.bouncycastle.math.ec.rfc7748.X448;
 import org.bouncycastle.math.ec.rfc7748.X448Field;
 import org.bouncycastle.math.raw.Nat;
-import org.bouncycastle.util.Arrays;
 
 /**
  * A low-level implementation of the Ed448 and Ed448ph instantiations of the Edwards-Curve Digital Signature
@@ -28,11 +27,17 @@ public static final class Algorithm
         public static final int Ed448ph = 1;
     }
 
-    private static class F extends X448Field {};
+    public static final class PublicPoint
+    {
+        final int[] data;
 
-    private static final long M26L = 0x03FFFFFFL;
-    private static final long M28L = 0x0FFFFFFFL;
-    private static final long M32L = 0xFFFFFFFFL;
+        PublicPoint(int[] data)
+        {
+            this.data = data;
+        }
+    }
+
+    private static class F extends X448Field {};
 
     private static final int COORD_INTS = 14;
     private static final int POINT_BYTES = COORD_INTS * 4 + 1;
@@ -47,36 +52,28 @@ private static class F extends X448Field {};
     // "SigEd448"
     private static final byte[] DOM4_PREFIX = new byte[]{ 0x53, 0x69, 0x67, 0x45, 0x64, 0x34, 0x34, 0x38 };
 
-    private static final int[] P = new int[] { 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF,
-        0xFFFFFFFE, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF };
-    private static final int[] L = new int[] { 0xAB5844F3, 0x2378C292, 0x8DC58F55, 0x216CC272, 0xAED63690, 0xC44EDB49, 0x7CCA23E9,
-        0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0x3FFFFFFF };
-
-    private static final int L_0 = 0x04A7BB0D;      // L_0:26/24
-    private static final int L_1 = 0x0873D6D5;      // L_1:27/23
-    private static final int L_2 = 0x0A70AADC;      // L_2:27/26
-    private static final int L_3 = 0x03D8D723;      // L_3:26/--
-    private static final int L_4 = 0x096FDE93;      // L_4:27/25
-    private static final int L_5 = 0x0B65129C;      // L_5:27/26
-    private static final int L_6 = 0x063BB124;      // L_6:27/--
-    private static final int L_7 = 0x08335DC1;      // L_7:27/22
-
-    private static final int L4_0 = 0x029EEC34;     // L4_0:25/24
-    private static final int L4_1 = 0x01CF5B55;     // L4_1:25/--
-    private static final int L4_2 = 0x09C2AB72;     // L4_2:27/25
-    private static final int L4_3 = 0x0F635C8E;     // L4_3:28/--
-    private static final int L4_4 = 0x05BF7A4C;     // L4_4:26/25
-    private static final int L4_5 = 0x0D944A72;     // L4_5:28/--
-    private static final int L4_6 = 0x08EEC492;     // L4_6:27/24
-    private static final int L4_7 = 0x20CD7705;     // L4_7:29/24
-
-    private static final int[] B_x = new int[] { 0x070CC05E, 0x026A82BC, 0x00938E26, 0x080E18B0, 0x0511433B, 0x0F72AB66, 0x0412AE1A,
-        0x0A3D3A46, 0x0A6DE324, 0x00F1767E, 0x04657047, 0x036DA9E1, 0x05A622BF, 0x0ED221D1, 0x066BED0D, 0x04F1970C };
-    private static final int[] B_y = new int[] { 0x0230FA14, 0x008795BF, 0x07C8AD98, 0x0132C4ED, 0x09C4FDBD, 0x01CE67C3, 0x073AD3FF,
-        0x005A0C2D, 0x07789C1E, 0x0A398408, 0x0A73736C, 0x0C7624BE, 0x003756C9, 0x02488762, 0x016EB6BC, 0x0693F467 };
+    private static final int[] P = new int[] { 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF,
+        0xFFFFFFFF, 0xFFFFFFFE, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF };
+
+    private static final int[] B_x = new int[]{ 0x070CC05E, 0x026A82BC, 0x00938E26, 0x080E18B0, 0x0511433B, 0x0F72AB66,
+        0x0412AE1A, 0x0A3D3A46, 0x0A6DE324, 0x00F1767E, 0x04657047, 0x036DA9E1, 0x05A622BF, 0x0ED221D1, 0x066BED0D,
+        0x04F1970C };
+    private static final int[] B_y = new int[]{ 0x0230FA14, 0x008795BF, 0x07C8AD98, 0x0132C4ED, 0x09C4FDBD, 0x01CE67C3,
+        0x073AD3FF, 0x005A0C2D, 0x07789C1E, 0x0A398408, 0x0A73736C, 0x0C7624BE, 0x003756C9, 0x02488762, 0x016EB6BC,
+        0x0693F467 };
+
+    // 2^225 * B
+    private static final int[] B225_x = new int[]{ 0x06909EE2, 0x01D7605C, 0x0995EC8A, 0x0FC4D970, 0x0CF2B361,
+        0x02D82E9D, 0x01225F55, 0x007F0EF6, 0x0AEE9C55, 0x0A240C13, 0x05627B54, 0x0D449D1E, 0x03A44575, 0x007164A7,
+        0x0BD4BD71, 0x061A15FD };
+    private static final int[] B225_y = new int[]{ 0x0D3A9FE4, 0x030696B9, 0x07E7E326, 0x068308C7, 0x0CE0B8C8,
+        0x03AC222B, 0x0304DB8E, 0x083EE319, 0x05E5DB0B, 0x0ECA503B, 0x0B1C6539, 0x078A8DCE, 0x02D256BC, 0x04A8B05E,
+        0x0BD9FD57, 0x0A1C3CB8 };
+
     private static final int C_d = -39081;
 
-    private static final int WNAF_WIDTH = 5;
+//    private static final int WNAF_WIDTH = 6;
+    private static final int WNAF_WIDTH_225 = 5;
     private static final int WNAF_WIDTH_BASE = 7;
 
     // scalarMultBase supports varying blocks, teeth, spacing so long as their product is in range [449, 479]
@@ -89,6 +86,7 @@ private static class F extends X448Field {};
 
     private static final Object PRECOMP_LOCK = new Object();
     private static PointAffine[] PRECOMP_BASE_WNAF = null;
+    private static PointAffine[] PRECOMP_BASE225_WNAF = null;
     private static int[] PRECOMP_BASE_COMB = null;
 
     private static class PointAffine
@@ -104,35 +102,45 @@ private static class PointProjective
         int[] z = F.create();
     }
 
+    // Temp space to avoid allocations in point formulae.
+    private static class PointTemp
+    {
+        int[] r0 = F.create();
+        int[] r1 = F.create();;
+        int[] r2 = F.create();
+        int[] r3 = F.create();;
+        int[] r4 = F.create();
+        int[] r5 = F.create();;
+        int[] r6 = F.create();
+        int[] r7 = F.create();;
+    }
+
     private static byte[] calculateS(byte[] r, byte[] k, byte[] s)
     {
-        int[] t = new int[SCALAR_INTS * 2];     decodeScalar(r, 0, t);
-        int[] u = new int[SCALAR_INTS];         decodeScalar(k, 0, u);
-        int[] v = new int[SCALAR_INTS];         decodeScalar(s, 0, v);
+        int[] t = new int[SCALAR_INTS * 2];     Scalar448.decode(r, t);
+        int[] u = new int[SCALAR_INTS];         Scalar448.decode(k, u);
+        int[] v = new int[SCALAR_INTS];         Scalar448.decode(s, v);
 
         Nat.mulAddTo(SCALAR_INTS, u, v, t);
 
         byte[] result = new byte[SCALAR_BYTES * 2];
-        for (int i = 0; i < t.length; ++i)
-        {
-            encode32(t[i], result, i * 4);
-        }
-        return reduceScalar(result);
+        Codec.encode32(t, 0, t.length, result, 0);
+        return Scalar448.reduce(result);
     }
 
     private static boolean checkContextVar(byte[] ctx)
     {
         return ctx != null && ctx.length < 256;
     }
 
-    private static int checkPoint(int[] x, int[] y)
+    private static int checkPoint(PointAffine p)
     {
         int[] t = F.create();
         int[] u = F.create();
         int[] v = F.create();
 
-        F.sqr(x, u);
-        F.sqr(y, v);
+        F.sqr(p.x, u);
+        F.sqr(p.y, v);
         F.mul(u, v, t);
         F.add(u, v, u);
         F.mul(t, -C_d, t);
@@ -143,16 +151,16 @@ private static int checkPoint(int[] x, int[] y)
         return F.isZero(t);
     }
 
-    private static int checkPoint(int[] x, int[] y, int[] z)
+    private static int checkPoint(PointProjective p)
     {
         int[] t = F.create();
         int[] u = F.create();
         int[] v = F.create();
         int[] w = F.create();
 
-        F.sqr(x, u);
-        F.sqr(y, v);
-        F.sqr(z, w);
+        F.sqr(p.x, u);
+        F.sqr(p.y, v);
+        F.sqr(p.z, w);
         F.mul(u, v, t);
         F.add(u, v, u);
         F.mul(u, w, u);
@@ -165,31 +173,62 @@ private static int checkPoint(int[] x, int[] y, int[] z)
         return F.isZero(t);
     }
 
-    private static boolean checkPointVar(byte[] p)
+    private static boolean checkPointFullVar(byte[] p)
     {
         if ((p[POINT_BYTES - 1] & 0x7F) != 0x00)
-        {
             return false;
-        }
-        if (decode32(p, 52) != P[13])
+
+        int y13 = Codec.decode32(p, 52);
+
+        int t0 = y13;
+        int t1 = y13 ^ P[13];
+
+        for (int i = COORD_INTS - 2; i > 0; --i)
         {
-            return true;
+            int yi = Codec.decode32(p, i * 4);
+
+            // Reject non-canonical encodings (i.e. >= P)
+            if (t1 == 0 && (yi + Integer.MIN_VALUE) > (P[i] + Integer.MIN_VALUE))
+                return false;
+
+            t0 |= yi;
+            t1 |= yi ^ P[i];
         }
 
-        int[] t = new int[COORD_INTS];
-        decode32(p, 0, t, 0, COORD_INTS);
-        return !Nat.gte(COORD_INTS, t, P);
+        int y0 = Codec.decode32(p, 0);
+
+        // Reject 0 and 1
+        if (t0 == 0 && (y0 + Integer.MIN_VALUE) <= (1 + Integer.MIN_VALUE))
+            return false;
+
+        // Reject P - 1 and non-canonical encodings (i.e. >= P)
+        if (t1 == 0 && (y0 + Integer.MIN_VALUE) >= (P[0] - 1 + Integer.MIN_VALUE))
+            return false;
+
+        return true;
+    }
+
+    private static boolean checkPointOrderVar(PointAffine p)
+    {
+        PointProjective r = new PointProjective();
+        scalarMultOrderVar(p, r);
+        return normalizeToNeutralElementVar(r);
     }
 
-    private static boolean checkScalarVar(byte[] s, int[] n)
+    private static boolean checkPointVar(byte[] p)
     {
-        if (s[SCALAR_BYTES - 1] != 0x00)
+        if ((p[POINT_BYTES - 1] & 0x7F) != 0x00)
         {
             return false;
         }
+        if (Codec.decode32(p, 52) != P[13])
+        {
+            return true;
+        }
 
-        decodeScalar(s, 0, n);
-        return !Nat.gte(SCALAR_INTS, n, L);
+        int[] t = new int[COORD_INTS];
+        Codec.decode32(p, 0, t, 0, COORD_INTS);
+        return !Nat.gte(COORD_INTS, t, P);
     }
 
     private static byte[] copy(byte[] buf, int off, int len)
@@ -209,50 +248,11 @@ private static Xof createXof()
         return new SHAKEDigest(256);
     }
 
-    private static int decode16(byte[] bs, int off)
-    {
-        int n = bs[off] & 0xFF;
-        n |= (bs[++off] & 0xFF) << 8;
-        return n;
-    }
-
-    private static int decode24(byte[] bs, int off)
-    {
-        int n = bs[  off] & 0xFF;
-        n |= (bs[++off] & 0xFF) << 8;
-        n |= (bs[++off] & 0xFF) << 16;
-        return n;
-    }
-
-    private static int decode32(byte[] bs, int off)
-    {
-        int n = bs[off] & 0xFF;
-        n |= (bs[++off] & 0xFF) << 8;
-        n |= (bs[++off] & 0xFF) << 16;
-        n |=  bs[++off]         << 24;
-        return n;
-    }
-
-    private static void decode32(byte[] bs, int bsOff, int[] n, int nOff, int nLen)
+    private static boolean decodePointVar(byte[] p, boolean negate, PointAffine r)
     {
-        for (int i = 0; i < nLen; ++i)
-        {
-            n[nOff + i] = decode32(bs, bsOff + i * 4);
-        }
-    }
+        int x_0 = (p[POINT_BYTES - 1] & 0x80) >>> 7;
 
-    private static boolean decodePointVar(byte[] p, int pOff, boolean negate, PointProjective r)
-    {
-        byte[] py = copy(p, pOff, POINT_BYTES);
-        if (!checkPointVar(py))
-        {
-            return false;
-        }
-
-        int x_0 = (py[POINT_BYTES - 1] & 0x80) >>> 7;
-        py[POINT_BYTES - 1] &= 0x7F;
-
-        F.decode(py, 0, r.y);
+        F.decode(p, r.y);
 
         int[] u = F.create();
         int[] v = F.create();
@@ -277,21 +277,16 @@ private static boolean decodePointVar(byte[] p, int pOff, boolean negate, PointP
         if (negate ^ (x_0 != (r.x[0] & 1)))
         {
             F.negate(r.x, r.x);
+            F.normalize(r.x);
         }
 
-        F.one(r.z);
         return true;
     }
 
-    private static void decodeScalar(byte[] k, int kOff, int[] n)
-    {
-//        assert k[kOff + SCALAR_BYTES - 1] == 0x00;
-
-        decode32(k, kOff, n, 0, SCALAR_INTS);
-    }
-
     private static void dom4(Xof d, byte phflag, byte[] ctx)
     {
+//        assert ctx != null;
+
         int n = DOM4_PREFIX.length;
         byte[] t = new byte[n + 2 + ctx.length];
         System.arraycopy(DOM4_PREFIX, 0, t, 0, n);
@@ -302,44 +297,37 @@ private static void dom4(Xof d, byte phflag, byte[] ctx)
         d.update(t, 0, t.length);
     }
 
-    private static void encode24(int n, byte[] bs, int off)
+    private static void encodePoint(PointAffine p, byte[] r, int rOff)
     {
-        bs[  off] = (byte)(n       );
-        bs[++off] = (byte)(n >>>  8);
-        bs[++off] = (byte)(n >>> 16);
+        F.encode(p.y, r, rOff);
+        r[rOff + POINT_BYTES - 1] = (byte)((p.x[0] & 1) << 7);
     }
 
-    private static void encode32(int n, byte[] bs, int off)
+    public static void encodePublicPoint(PublicPoint publicPoint, byte[] pk, int pkOff)
     {
-        bs[  off] = (byte)(n       );
-        bs[++off] = (byte)(n >>>  8);
-        bs[++off] = (byte)(n >>> 16);
-        bs[++off] = (byte)(n >>> 24);
+        F.encode(publicPoint.data, F.SIZE, pk, pkOff);
+        pk[pkOff + POINT_BYTES - 1] = (byte)((publicPoint.data[0] & 1) << 7);
     }
 
-    private static void encode56(long n, byte[] bs, int off)
+    private static int encodeResult(PointProjective p, byte[] r, int rOff)
     {
-        encode32((int)n, bs, off);
-        encode24((int)(n >>> 32), bs, off + 4);
-    }
+        PointAffine q = new PointAffine();
+        normalizeToAffine(p, q);
 
-    private static int encodePoint(PointProjective p, byte[] r, int rOff)
-    {
-        int[] x = F.create();
-        int[] y = F.create();
+        int result = checkPoint(q);
 
-        F.inv(p.z, y);
-        F.mul(p.x, y, x);
-        F.mul(p.y, y, y);
-        F.normalize(x);
-        F.normalize(y);
+        encodePoint(q, r, rOff);
 
-        int result = checkPoint(x, y);
+        return result;
+    }
 
-        F.encode(y, r, rOff);
-        r[rOff + POINT_BYTES - 1] = (byte)((x[0] & 1) << 7);
+    private static PublicPoint exportPoint(PointAffine p)
+    {
+        int[] data = new int[F.SIZE * 2];
+        F.copy(p.x, 0, data, 0);
+        F.copy(p.y, 0, data, F.SIZE);
 
-        return result;
+        return new PublicPoint(data);
     }
 
     public static void generatePrivateKey(SecureRandom random, byte[] k)
@@ -366,60 +354,35 @@ public static void generatePublicKey(byte[] sk, int skOff, byte[] pk, int pkOff)
         scalarMultBaseEncoded(s, pk, pkOff);
     }
 
-    private static int getWindow4(int[] x, int n)
+    public static PublicPoint generatePublicKey(byte[] sk, int skOff)
     {
-        int w = n >>> 3, b = (n & 7) << 2;
-        return (x[w] >>> b) & 15;
-    }
+        Xof d = createXof();
+        byte[] h = new byte[SCALAR_BYTES * 2];
 
-    private static byte[] getWnafVar(int[] n, int width)
-    {
-//        assert 0 <= n[SCALAR_INTS - 1] && n[SCALAR_INTS - 1] <= L[SCALAR_INTS - 1];
-//        assert 2 <= width && width <= 8;
+        d.update(sk, skOff, SECRET_KEY_SIZE);
+        d.doFinal(h, 0, h.length);
 
-        int[] t = new int[SCALAR_INTS * 2];
-        {
-            int tPos = t.length, c = 0;
-            int i = SCALAR_INTS;
-            while (--i >= 0)
-            {
-                int next = n[i];
-                t[--tPos] = (next >>> 16) | (c << 16);
-                t[--tPos] = c = next;
-            }
-        }
+        byte[] s = new byte[SCALAR_BYTES];
+        pruneScalar(h, 0, s);
 
-        byte[] ws = new byte[447];
+        PointProjective p = new PointProjective();
+        scalarMultBase(s, p);
 
-        final int lead = 32 - width;
+        PointAffine q = new PointAffine();
+        normalizeToAffine(p, q);
 
-        int j = 0, carry = 0;
-        for (int i = 0; i < t.length; ++i, j -= 16)
+        if (0 == checkPoint(q))
         {
-            int word = t[i];
-            while (j < 16)
-            {
-                int word16 = word >>> j;
-                int bit = word16 & 1;
-
-                if (bit == carry)
-                {
-                    ++j;
-                    continue;
-                }
-
-                int digit = (word16 | 1) << lead;
-                carry = digit >>> 31;
-
-                ws[(i << 4) + j] = (byte)(digit >> lead);
-
-                j += width;
-            }
+            throw new IllegalStateException();
         }
 
-//        assert carry == 0;
+        return exportPoint(q);
+    }
 
-        return ws;
+    private static int getWindow4(int[] x, int n)
+    {
+        int w = n >>> 3, b = (n & 7) << 2;
+        return (x[w] >>> b) & 15;
     }
 
     private static void implSign(Xof d, byte[] h, byte[] s, byte[] pk, int pkOff, byte[] ctx, byte phflag,
@@ -430,7 +393,7 @@ private static void implSign(Xof d, byte[] h, byte[] s, byte[] pk, int pkOff, by
         d.update(m, mOff, mLen);
         d.doFinal(h, 0, h.length);
 
-        byte[] r = reduceScalar(h);
+        byte[] r = Scalar448.reduce(h);
         byte[] R = new byte[POINT_BYTES];
         scalarMultBaseEncoded(r, R, 0);
 
@@ -440,7 +403,7 @@ private static void implSign(Xof d, byte[] h, byte[] s, byte[] pk, int pkOff, by
         d.update(m, mOff, mLen);
         d.doFinal(h, 0, h.length);
 
-        byte[] k = reduceScalar(h);
+        byte[] k = Scalar448.reduce(h);
         byte[] S = calculateS(r, k, s);
 
         System.arraycopy(R, 0, sig, sigOff, POINT_BYTES);
@@ -500,20 +463,30 @@ private static boolean implVerify(byte[] sig, int sigOff, byte[] pk, int pkOff,
 
         byte[] R = copy(sig, sigOff, POINT_BYTES);
         byte[] S = copy(sig, sigOff + POINT_BYTES, SCALAR_BYTES);
+        byte[] A = copy(pk, pkOff, PUBLIC_KEY_SIZE);
 
         if (!checkPointVar(R))
         {
             return false;
         }
 
         int[] nS = new int[SCALAR_INTS];
-        if (!checkScalarVar(S, nS))
+        if (!Scalar448.checkVar(S, nS))
         {
             return false;
         }
 
-        PointProjective pA = new PointProjective();
-        if (!decodePointVar(pk, pkOff, true, pA))
+        if (!checkPointFullVar(A))
+            return false;
+
+        PointAffine pR = new PointAffine();
+        if (!decodePointVar(R, true, pR))
+        {
+            return false;
+        }
+
+        PointAffine pA = new PointAffine();
+        if (!decodePointVar(A, true, pA))
         {
             return false;
         }
@@ -523,20 +496,82 @@ private static boolean implVerify(byte[] sig, int sigOff, byte[] pk, int pkOff,
 
         dom4(d, phflag, ctx);
         d.update(R, 0, POINT_BYTES);
-        d.update(pk, pkOff, POINT_BYTES);
+        d.update(A, 0, POINT_BYTES);
         d.update(m, mOff, mLen);
         d.doFinal(h, 0, h.length);
 
-        byte[] k = reduceScalar(h);
+        byte[] k = Scalar448.reduce(h);
 
         int[] nA = new int[SCALAR_INTS];
-        decodeScalar(k, 0, nA);
+        Scalar448.decode(k, nA);
 
-        PointProjective pR = new PointProjective();
-        scalarMultStrausVar(nS, nA, pA, pR);
+        int[] v0 = new int[8];
+        int[] v1 = new int[8];
+        Scalar448.reduceBasisVar(nA, v0, v1);
+        Scalar448.multiply225Var(nS, v1, nS);
 
-        byte[] check = new byte[POINT_BYTES];
-        return 0 != encodePoint(pR, check, 0) && Arrays.areEqual(check, R);
+        PointProjective pZ = new PointProjective();
+        scalarMultStraus225Var(nS, v0, pA, v1, pR, pZ);
+        return normalizeToNeutralElementVar(pZ);
+    }
+
+    private static boolean implVerify(byte[] sig, int sigOff, PublicPoint publicPoint, byte[] ctx, byte phflag,
+        byte[] m, int mOff, int mLen)
+    {
+        if (!checkContextVar(ctx))
+        {
+            throw new IllegalArgumentException("ctx");
+        }
+
+        byte[] R = copy(sig, sigOff, POINT_BYTES);
+        byte[] S = copy(sig, sigOff + POINT_BYTES, SCALAR_BYTES);
+
+        if (!checkPointVar(R))
+        {
+            return false;
+        }
+
+        int[] nS = new int[SCALAR_INTS];
+        if (!Scalar448.checkVar(S, nS))
+        {
+            return false;
+        }
+
+        PointAffine pR = new PointAffine();
+        if (!decodePointVar(R, true, pR))
+        {
+            return false;
+        }
+
+        PointAffine pA = new PointAffine();
+        F.negate(publicPoint.data, pA.x);
+        F.copy(publicPoint.data, F.SIZE, pA.y, 0);
+
+        byte[] A = new byte[PUBLIC_KEY_SIZE];
+        encodePublicPoint(publicPoint, A, 0);
+
+        Xof d = createXof();
+        byte[] h = new byte[SCALAR_BYTES * 2];
+
+        dom4(d, phflag, ctx);
+        d.update(R, 0, POINT_BYTES);
+        d.update(A, 0, POINT_BYTES);
+        d.update(m, mOff, mLen);
+        d.doFinal(h, 0, h.length);
+
+        byte[] k = Scalar448.reduce(h);
+
+        int[] nA = new int[SCALAR_INTS];
+        Scalar448.decode(k, nA);
+
+        int[] v0 = new int[8];
+        int[] v1 = new int[8];
+        Scalar448.reduceBasisVar(nA, v0, v1);
+        Scalar448.multiply225Var(nS, v1, nS);
+
+        PointProjective pZ = new PointProjective();
+        scalarMultStraus225Var(nS, v0, pA, v1, pR, pZ);
+        return normalizeToNeutralElementVar(pZ);
     }
 
     private static void invertZs(PointProjective[] points)
@@ -572,20 +607,43 @@ private static void invertZs(PointProjective[] points)
         F.copy(u, 0, points[0].z, 0);
     }
 
+//    private static boolean isNeutralElementVar(int[] x, int[] y)
+//    {
+//        return F.isZeroVar(x) && F.isOneVar(y);
+//    }
+
     private static boolean isNeutralElementVar(int[] x, int[] y, int[] z)
     {
         return F.isZeroVar(x) && F.areEqualVar(y, z);
     }
 
-    private static void pointAdd(PointAffine p, PointProjective r)
+    private static void normalizeToAffine(PointProjective p, PointAffine r)
     {
-        int[] b = F.create();
-        int[] c = F.create();
-        int[] d = F.create();
-        int[] e = F.create();
-        int[] f = F.create();
-        int[] g = F.create();
-        int[] h = F.create();
+        F.inv(p.z, r.y);
+        F.mul(r.y, p.x, r.x);
+        F.mul(r.y, p.y, r.y);
+        F.normalize(r.x);
+        F.normalize(r.y);
+    }
+
+    private static boolean normalizeToNeutralElementVar(PointProjective p)
+    {
+        F.normalize(p.x);
+        F.normalize(p.y);
+        F.normalize(p.z);
+
+        return isNeutralElementVar(p.x, p.y, p.z);
+    }
+
+    private static void pointAdd(PointAffine p, PointProjective r, PointTemp t)
+    {
+        int[] b = t.r1;
+        int[] c = t.r2;
+        int[] d = t.r3;
+        int[] e = t.r4;
+        int[] f = t.r5;
+        int[] g = t.r6;
+        int[] h = t.r7;
 
         F.sqr(r.z, b);
         F.mul(p.x, r.x, c);
@@ -610,16 +668,16 @@ private static void pointAdd(PointAffine p, PointProjective r)
         F.mul(f, g, r.z);
     }
 
-    private static void pointAdd(PointProjective p, PointProjective r)
+    private static void pointAdd(PointProjective p, PointProjective r, PointTemp t)
     {
-        int[] a = F.create();
-        int[] b = F.create();
-        int[] c = F.create();
-        int[] d = F.create();
-        int[] e = F.create();
-        int[] f = F.create();
-        int[] g = F.create();
-        int[] h = F.create();
+        int[] a = t.r0;
+        int[] b = t.r1;
+        int[] c = t.r2;
+        int[] d = t.r3;
+        int[] e = t.r4;
+        int[] f = t.r5;
+        int[] g = t.r6;
+        int[] h = t.r7;
 
         F.mul(p.z, r.z, a);
         F.sqr(a, b);
@@ -645,15 +703,15 @@ private static void pointAdd(PointProjective p, PointProjective r)
         F.mul(f, g, r.z);
     }
 
-    private static void pointAddVar(boolean negate, PointAffine p, PointProjective r)
+    private static void pointAddVar(boolean negate, PointAffine p, PointProjective r, PointTemp t)
     {
-        int[] b = F.create();
-        int[] c = F.create();
-        int[] d = F.create();
-        int[] e = F.create();
-        int[] f = F.create();
-        int[] g = F.create();
-        int[] h = F.create();
+        int[] b = t.r1;
+        int[] c = t.r2;
+        int[] d = t.r3;
+        int[] e = t.r4;
+        int[] f = t.r5;
+        int[] g = t.r6;
+        int[] h = t.r7;
 
         int[] nb, ne, nf, ng;
         if (negate)
@@ -689,16 +747,16 @@ private static void pointAddVar(boolean negate, PointAffine p, PointProjective r
         F.mul(f, g, r.z);
     }
 
-    private static void pointAddVar(boolean negate, PointProjective p, PointProjective r)
+    private static void pointAddVar(boolean negate, PointProjective p, PointProjective r, PointTemp t)
     {
-        int[] a = F.create();
-        int[] b = F.create();
-        int[] c = F.create();
-        int[] d = F.create();
-        int[] e = F.create();
-        int[] f = F.create();
-        int[] g = F.create();
-        int[] h = F.create();
+        int[] a = t.r0;
+        int[] b = t.r1;
+        int[] c = t.r2;
+        int[] d = t.r3;
+        int[] e = t.r4;
+        int[] f = t.r5;
+        int[] g = t.r6;
+        int[] h = t.r7;
 
         int[] nb, ne, nf, ng;
         if (negate)
@@ -735,21 +793,28 @@ private static void pointAddVar(boolean negate, PointProjective p, PointProjecti
         F.mul(f, g, r.z);
     }
 
+    private static void pointCopy(PointAffine p, PointProjective r)
+    {
+        F.copy(p.x, 0, r.x, 0);
+        F.copy(p.y, 0, r.y, 0);
+        F.one(r.z);
+    }
+
     private static void pointCopy(PointProjective p, PointProjective r)
     {
         F.copy(p.x, 0, r.x, 0);
         F.copy(p.y, 0, r.y, 0);
         F.copy(p.z, 0, r.z, 0);
     }
 
-    private static void pointDouble(PointProjective r)
+    private static void pointDouble(PointProjective r, PointTemp t)
     {
-        int[] b = F.create();
-        int[] c = F.create();
-        int[] d = F.create();
-        int[] e = F.create();
-        int[] h = F.create();
-        int[] j = F.create();
+        int[] b = t.r1;
+        int[] c = t.r2;
+        int[] d = t.r3;
+        int[] e = t.r4;
+        int[] h = t.r7;
+        int[] j = t.r0;
 
         F.add(r.x, r.y, b);
         F.sqr(b, b);
@@ -815,7 +880,7 @@ private static void pointLookup15(int[] table, PointProjective r)
         F.copy(table, off, r.z, 0);
     }
 
-    private static int[] pointPrecompute(PointProjective p, int count)
+    private static int[] pointPrecompute(PointProjective p, int count, PointTemp t)
     {
 //        assert count > 0;
 
@@ -824,7 +889,7 @@ private static int[] pointPrecompute(PointProjective p, int count)
 
         PointProjective d = new PointProjective();
         pointCopy(q, d);
-        pointDouble(d);
+        pointDouble(d, t);
 
         int[] table = F.createTable(count * 3);
         int off = 0;
@@ -841,27 +906,28 @@ private static int[] pointPrecompute(PointProjective p, int count)
                 break;
             }
 
-            pointAdd(d, q);
+            pointAdd(d, q, t);
         }
 
         return table;
     }
 
-    private static void pointPrecomputeVar(PointProjective p, PointProjective[] points, int count)
+    private static void pointPrecompute(PointAffine p, PointProjective[] points, int pointsOff, int pointsLen,
+        PointTemp t)
     {
-//        assert count > 0;
+//        assert pointsLen > 0;
 
         PointProjective d = new PointProjective();
         pointCopy(p, d);
-        pointDouble(d);
+        pointDouble(d, t);
 
-        points[0] = new PointProjective();
-        pointCopy(p, points[0]);
-        for (int i = 1; i < count; ++i)
+        points[pointsOff] = new PointProjective();
+        pointCopy(p, points[pointsOff]);
+        for (int i = 1; i < pointsLen; ++i)
         {
-            points[i] = new PointProjective();
-            pointCopy(points[i - 1], points[i]);
-            pointAdd(d, points[i]);
+            points[pointsOff + i] = new PointProjective();
+            pointCopy(points[pointsOff + i - 1], points[pointsOff + i]);
+            pointAdd(d, points[pointsOff + i], t);
         }
     }
 
@@ -876,7 +942,7 @@ public static void precompute()
     {
         synchronized (PRECOMP_LOCK)
         {
-            if (PRECOMP_BASE_WNAF != null && PRECOMP_BASE_COMB != null)
+            if (PRECOMP_BASE_COMB != null)
             {
                 return;
             }
@@ -886,23 +952,33 @@ public static void precompute()
 
             int wnafPoints = 1 << (WNAF_WIDTH_BASE - 2);
             int combPoints = PRECOMP_BLOCKS * PRECOMP_POINTS;
-            int totalPoints = wnafPoints + combPoints;
+            int totalPoints = wnafPoints * 2 + combPoints;
 
             PointProjective[] points = new PointProjective[totalPoints];
+            PointTemp t = new PointTemp();
 
-            PointProjective p = new PointProjective();
-            F.copy(B_x, 0, p.x, 0);
-            F.copy(B_y, 0, p.y, 0);
-            F.one(p.z);
+            PointAffine B = new PointAffine();
+            F.copy(B_x, 0, B.x, 0);
+            F.copy(B_y, 0, B.y, 0);
 
-            pointPrecomputeVar(p, points, wnafPoints);
+            pointPrecompute(B, points, 0, wnafPoints, t);
+
+            PointAffine B225 = new PointAffine();
+            F.copy(B225_x, 0, B225.x, 0);
+            F.copy(B225_y, 0, B225.y, 0);
+
+            pointPrecompute(B225, points, wnafPoints, wnafPoints, t);
+
+            PointProjective p = new PointProjective();
+            pointCopy(B, p);
 
-            int pointsIndex = wnafPoints;
+            int pointsIndex = wnafPoints * 2;
             PointProjective[] toothPowers = new PointProjective[PRECOMP_TEETH];
             for (int tooth = 0; tooth < PRECOMP_TEETH; ++tooth)
             {
                 toothPowers[tooth] = new PointProjective();
             }
+
             for (int block = 0; block < PRECOMP_BLOCKS; ++block)
             {
                 PointProjective sum = points[pointsIndex++] = new PointProjective();
@@ -915,17 +991,17 @@ public static void precompute()
                     }
                     else
                     {
-                        pointAdd(p, sum);
+                        pointAdd(p, sum, t);
                     }
 
-                    pointDouble(p);
+                    pointDouble(p, t);
                     pointCopy(p, toothPowers[tooth]);
 
                     if (block + tooth != PRECOMP_BLOCKS + PRECOMP_TEETH - 2)
                     {
                         for (int spacing = 1; spacing < PRECOMP_SPACING; ++spacing)
                         {
-                            pointDouble(p);
+                            pointDouble(p, t);
                         }
                     }
                 }
@@ -939,7 +1015,7 @@ public static void precompute()
                     {
                         points[pointsIndex] = new PointProjective();
                         pointCopy(points[pointsIndex - size], points[pointsIndex]);
-                        pointAdd(toothPowers[tooth], points[pointsIndex]);
+                        pointAdd(toothPowers[tooth], points[pointsIndex], t);
                     }
                 }
             }
@@ -957,9 +1033,19 @@ public static void precompute()
                 F.mul(q.y, q.z, r.y);       F.normalize(r.y);
             }
 
+            PRECOMP_BASE225_WNAF = new PointAffine[wnafPoints];
+            for (int i = 0; i < wnafPoints; ++i)
+            {
+                PointProjective q = points[wnafPoints + i];
+                PointAffine r = PRECOMP_BASE225_WNAF[i] = new PointAffine();
+
+                F.mul(q.x, q.z, r.x);       F.normalize(r.x);
+                F.mul(q.y, q.z, r.y);       F.normalize(r.y);
+            }
+
             PRECOMP_BASE_COMB = F.createTable(combPoints * 2);
             int off = 0;
-            for (int i = wnafPoints; i < totalPoints; ++i)
+            for (int i = wnafPoints * 2; i < totalPoints; ++i)
             {
                 PointProjective q = points[i];
 
@@ -982,309 +1068,28 @@ private static void pruneScalar(byte[] n, int nOff, byte[] r)
         r[SCALAR_BYTES - 1]  = 0x00;
     }
 
-    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 =  decode32(n,  63)       & M32L;  // x18:32/--
-        long x19 = (decode24(n,  67) << 4) & M32L;  // x19:28/--
-        long x20 =  decode32(n,  70)       & M32L;  // x20:32/--
-        long x21 = (decode24(n,  74) << 4) & M32L;  // x21:28/--
-        long x22 =  decode32(n,  77)       & M32L;  // x22:32/--
-        long x23 = (decode24(n,  81) << 4) & M32L;  // x23:28/--
-        long x24 =  decode32(n,  84)       & M32L;  // x24:32/--
-        long x25 = (decode24(n,  88) << 4) & M32L;  // x25:28/--
-        long x26 =  decode32(n,  91)       & M32L;  // x26:32/--
-        long x27 = (decode24(n,  95) << 4) & M32L;  // x27:28/--
-        long x28 =  decode32(n,  98)       & M32L;  // x28:32/--
-        long x29 = (decode24(n, 102) << 4) & M32L;  // x29:28/--
-        long x30 =  decode32(n, 105)       & M32L;  // x30:32/--
-        long x31 = (decode24(n, 109) << 4) & M32L;  // x31:28/--
-        long x32 =  decode16(n, 112)       & M32L;  // x32:16/--
-
-//        x32 += (x31 >>> 28); x31 &= M28L;
-        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 &= M28L;           // 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 &= M28L;
-        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 &= M28L;           // 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 &= M28L;
-        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 &= M28L;           // 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 &= M28L;
-        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 &= M28L;           // 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 &= M28L;           // x21:58/--, x20:28/--
-        x22 += (x21 >>> 28); x21 &= M28L;           // x22:57/54, x21:28/--
-        x23 += (x22 >>> 28); x22 &= M28L;           // x23:45/42, x22:28/--
-        x24 += (x23 >>> 28); x23 &= M28L;           // 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 &= M28L;           // x18:59/31, x17:28/--
-        x19 += (x18 >>> 28); x18 &= M28L;           // x19:58/54, x18:28/--
-        x20 += (x19 >>> 28); x19 &= M28L;           // x20:30/29, x19:28/--
-        x21 += (x20 >>> 28); x20 &= M28L;           // 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 &= M28L;           // x15:59/31, x14:28/--
-        x16 += (x15 >>> 28); x15 &= M28L;           // x16:59/32, x15:28/--
-        x17 += (x16 >>> 28); x16 &= M28L;           // x17:31/29, x16:28/--
-        x18 += (x17 >>> 28); x17 &= M28L;           // 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 &= M26L;
-        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 &= 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;
-        x10 += (x09 >>> 28); x09 &= M28L;
-        x11 += (x10 >>> 28); x10 &= M28L;
-        x12 += (x11 >>> 28); x11 &= M28L;
-        x13 += (x12 >>> 28); x12 &= M28L;
-        x14 += (x13 >>> 28); x13 &= M28L;
-        x15 += (x14 >>> 28); x14 &= M28L;
-        x16  = (x15 >>> 26); x15 &= M26L;
-
-        x16 -= 1;
-
-//        assert x16 == 0L || x16 == -1L;
-
-        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 &= 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;
-        x10 += (x09 >> 28); x09 &= M28L;
-        x11 += (x10 >> 28); x10 &= M28L;
-        x12 += (x11 >> 28); x11 &= M28L;
-        x13 += (x12 >> 28); x12 &= M28L;
-        x14 += (x13 >> 28); x13 &= M28L;
-        x15 += (x14 >> 28); x14 &= M28L;
-
-//        assert x15 >>> 26 == 0L;
-
-        byte[] r = new byte[SCALAR_BYTES];
-        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[SCALAR_BYTES - 1] = 0;
-        return r;
-    }
-
     private static void scalarMult(byte[] k, PointProjective p, PointProjective r)
     {
-        int[] n = new int[SCALAR_INTS];
-        decodeScalar(k, 0, n);
-
-        // Recode the scalar into signed-digit form
-        {
-            int c1 = Nat.cadd(SCALAR_INTS, ~n[0] & 1, n, L, n);
-            //int c2 =
-            Nat.shiftDownBit(SCALAR_INTS, n, c1);           //assert c2 == (1 << 31);
+        int[] n = new int[SCALAR_INTS + 1];
+        Scalar448.decode(k, n);
+        Scalar448.toSignedDigits(449, n, n);
 
-            // NOTE: Bit 448 is implicitly set after the signed-digit recoding
-        }
+        // NOTE: Bit 448 is handled explicitly by an initial addition
+//        assert n[SCALAR_INTS] == 1;
 
-        int[] table = pointPrecompute(p, 8);
         PointProjective q = new PointProjective();
+        PointTemp t = new PointTemp();
+        int[] table = pointPrecompute(p, 8, t);
 
         // Replace first 4 doublings (2^4 * P) with 1 addition (P + 15 * P)
         pointLookup15(table, r);
-        pointAdd(p, r);
+        pointAdd(p, r, t);
 
         int w = 111;
         for (;;)
         {
             pointLookup(n, w, table, q);
-            pointAdd(q, r);
+            pointAdd(q, r, t);
 
             if (--w < 0)
             {
@@ -1293,7 +1098,7 @@ private static void scalarMult(byte[] k, PointProjective p, PointProjective r)
 
             for (int i = 0; i < 4; ++i)
             {
-                pointDouble(r);
+                pointDouble(r, t);
             }
         }
     }
@@ -1310,18 +1115,11 @@ private static void scalarMultBase(byte[] k, PointProjective r)
         precompute();
 
         int[] n = new int[SCALAR_INTS + 1];
-        decodeScalar(k, 0, n);
-
-        // Recode the scalar into signed-digit form
-        {
-            n[SCALAR_INTS] = (1 << (PRECOMP_RANGE - 448))
-                           + Nat.cadd(SCALAR_INTS, ~n[0] & 1, n, L, n);
-            //int c =
-            Nat.shiftDownBit(n.length, n, 0);
-            //assert c == (1 << 31);
-        }
+        Scalar448.decode(k, n);
+        Scalar448.toSignedDigits(PRECOMP_RANGE, n, n);
 
         PointAffine p = new PointAffine();
+        PointTemp t = new PointTemp();
 
         pointSetNeutral(r);
 
@@ -1330,14 +1128,14 @@ private static void scalarMultBase(byte[] k, PointProjective r)
         {
             int tPos = cOff;
 
-            for (int b = 0; b < PRECOMP_BLOCKS; ++b)
+            for (int block = 0; block < PRECOMP_BLOCKS; ++block)
             {
                 int w = 0;
-                for (int t = 0; t < PRECOMP_TEETH; ++t)
+                for (int tooth = 0; tooth < PRECOMP_TEETH; ++tooth)
                 {
                     int tBit = n[tPos >>> 5] >>> (tPos & 0x1F);
-                    w &= ~(1 << t);
-                    w ^= (tBit << t);
+                    w &= ~(1 << tooth);
+                    w ^= (tBit << tooth);
                     tPos += PRECOMP_SPACING;
                 }
 
@@ -1347,27 +1145,27 @@ private static void scalarMultBase(byte[] k, PointProjective r)
 //                assert sign == 0 || sign == 1;
 //                assert 0 <= abs && abs < PRECOMP_POINTS;
 
-                pointLookup(b, abs, p);
+                pointLookup(block, abs, p);
 
                 F.cnegate(sign, p.x);
 
-                pointAdd(p, r);
+                pointAdd(p, r, t);
             }
 
             if (--cOff < 0)
             {
                 break;
             }
 
-            pointDouble(r);
+            pointDouble(r, t);
         }
     }
 
     private static void scalarMultBaseEncoded(byte[] k, byte[] r, int rOff)
     {
         PointProjective p = new PointProjective();
         scalarMultBase(k, p);
-        if (0 == encodePoint(p, r, rOff))
+        if (0 == encodeResult(p, r, rOff))
         {
             throw new IllegalStateException();
         }
@@ -1388,21 +1186,26 @@ public static void scalarMultBaseXY(X448.Friend friend, byte[] k, int kOff, int[
 
         PointProjective p = new PointProjective();
         scalarMultBase(n, p);
-        if (0 == checkPoint(p.x, p.y, p.z))
+        if (0 == checkPoint(p))
         {
             throw new IllegalStateException();
         }
+
         F.copy(p.x, 0, x, 0);
         F.copy(p.y, 0, y, 0);
     }
 
-    private static void scalarMultOrderVar(PointProjective p, PointProjective r)
+    private static void scalarMultOrderVar(PointAffine p, PointProjective r)
     {
-        byte[] ws_p = getWnafVar(L, WNAF_WIDTH);
+        byte[] ws_p = new byte[447];
 
-        int count = 1 << (WNAF_WIDTH - 2);
+        // NOTE: WNAF_WIDTH_225 because of the special structure of the order 
+        Scalar448.getOrderWnafVar(WNAF_WIDTH_225, ws_p);
+
+        int count = 1 << (WNAF_WIDTH_225 - 2);
         PointProjective[] tp = new PointProjective[count];
-        pointPrecomputeVar(p, tp, count);
+        PointTemp t = new PointTemp();
+        pointPrecompute(p, tp, 0, count, t);
 
         pointSetNeutral(r);
 
@@ -1411,61 +1214,84 @@ private static void scalarMultOrderVar(PointProjective p, PointProjective r)
             int wp = ws_p[bit];
             if (wp != 0)
             {
-                int sign = wp >> 31;
-                int index = (wp ^ sign) >>> 1;
-
-                pointAddVar(sign != 0, tp[index], r);
+                int index = (wp >> 1) ^ (wp >> 31);
+                pointAddVar(wp < 0, tp[index], r, t);
             }
 
             if (--bit < 0)
             {
                 break;
             }
 
-            pointDouble(r);
+            pointDouble(r, t);
         }
     }
 
-    private static void scalarMultStrausVar(int[] nb, int[] np, PointProjective p, PointProjective r)
+    private static void scalarMultStraus225Var(int[] nb, int[] np, PointAffine p, int[] nq, PointAffine q,
+        PointProjective r)
     {
+//        assert nb.length == SCALAR_INTS;
+//        assert nb[SCALAR_INTS - 1] >>> 30 == 0;
+//        assert np.length == 8;
+//        assert np[7] >> 31 == np[7];
+//        assert nq.length == 8;
+//        assert nq[7] >> 31 == nq[7];
+
         precompute();
 
-        byte[] ws_b = getWnafVar(nb, WNAF_WIDTH_BASE);
-        byte[] ws_p = getWnafVar(np, WNAF_WIDTH);
+        byte[] ws_b = new byte[450];
+        byte[] ws_p = new byte[225];
+        byte[] ws_q = new byte[225];
+
+        Wnaf.getSignedVar(nb, WNAF_WIDTH_BASE, ws_b);
+        Wnaf.getSignedVar(np, WNAF_WIDTH_225, ws_p);
+        Wnaf.getSignedVar(nq, WNAF_WIDTH_225, ws_q);
 
-        int count = 1 << (WNAF_WIDTH - 2);
+        int count = 1 << (WNAF_WIDTH_225 - 2);
         PointProjective[] tp = new PointProjective[count];
-        pointPrecomputeVar(p, tp, count);
+        PointProjective[] tq = new PointProjective[count];
+        PointTemp t = new PointTemp();
+        pointPrecompute(p, tp, 0, count, t);
+        pointPrecompute(q, tq, 0, count, t);
 
         pointSetNeutral(r);
 
-        for (int bit = 446;;)
+        int bit = 225;
+        while (--bit >= 0)
         {
             int wb = ws_b[bit];
             if (wb != 0)
             {
-                int sign = wb >> 31;
-                int index = (wb ^ sign) >>> 1;
+                int index = (wb >> 1) ^ (wb >> 31);
+                pointAddVar(wb < 0, PRECOMP_BASE_WNAF[index], r, t);
+            }
 
-                pointAddVar(sign != 0, PRECOMP_BASE_WNAF[index], r);
+            int wb225 = ws_b[225 + bit];
+            if (wb225 != 0)
+            {
+                int index = (wb225 >> 1) ^ (wb225 >> 31);
+                pointAddVar(wb225 < 0, PRECOMP_BASE225_WNAF[index], r, t);
             }
 
             int wp = ws_p[bit];
             if (wp != 0)
             {
-                int sign = wp >> 31;
-                int index = (wp ^ sign) >>> 1;
-
-                pointAddVar(sign != 0, tp[index], r);
+                int index = (wp >> 1) ^ (wp >> 31);
+                pointAddVar(wp < 0, tp[index], r, t);
             }
 
-            if (--bit < 0)
+            int wq = ws_q[bit];
+            if (wq != 0)
             {
-                break;
+                int index = (wq >> 1) ^ (wq >> 31);
+                pointAddVar(wq < 0, tq[index], r, t);
             }
 
-            pointDouble(r);
+            pointDouble(r, t);
         }
+
+        // NOTE: Together with the final pointDouble of the loop, this clears the cofactor of 4
+        pointDouble(r, t);
     }
 
     public static void sign(byte[] sk, int skOff, byte[] ctx, byte[] m, int mOff, int mLen, byte[] sig, int sigOff)
@@ -1475,7 +1301,8 @@ public static void sign(byte[] sk, int skOff, byte[] ctx, byte[] m, int mOff, in
         implSign(sk, skOff, ctx, phflag, 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)
+    public static void sign(byte[] sk, int skOff, byte[] pk, int pkOff, byte[] ctx, byte[] m, int mOff, int mLen,
+        byte[] sig, int sigOff)
     {
         byte phflag = 0x00;
 
@@ -1489,7 +1316,8 @@ public static void signPrehash(byte[] sk, int skOff, byte[] ctx, byte[] ph, int
         implSign(sk, skOff, ctx, phflag, ph, phOff, PREHASH_SIZE, sig, sigOff);
     }
 
-    public static void signPrehash(byte[] sk, int skOff, byte[] pk, int pkOff, byte[] ctx, byte[] ph, int phOff, byte[] sig, int sigOff)
+    public static void signPrehash(byte[] sk, int skOff, byte[] pk, int pkOff, byte[] ctx, byte[] ph, int phOff,
+        byte[] sig, int sigOff)
     {
         byte phflag = 0x01;
 
@@ -1509,7 +1337,8 @@ public static void signPrehash(byte[] sk, int skOff, byte[] ctx, Xof ph, byte[]
         implSign(sk, skOff, ctx, phflag, m, 0, m.length, sig, sigOff);
     }
 
-    public static void signPrehash(byte[] sk, int skOff, byte[] pk, int pkOff, byte[] ctx, Xof ph, byte[] sig, int sigOff)
+    public static void signPrehash(byte[] sk, int skOff, byte[] pk, int pkOff, byte[] ctx, Xof ph, byte[] sig,
+        int sigOff)
     {
         byte[] m = new byte[PREHASH_SIZE];
         if (PREHASH_SIZE != ph.doFinal(m, 0, PREHASH_SIZE))
@@ -1524,35 +1353,74 @@ public static void signPrehash(byte[] sk, int skOff, byte[] pk, int pkOff, byte[
 
     public static boolean validatePublicKeyFull(byte[] pk, int pkOff)
     {
-        PointProjective p = new PointProjective();
-        if (!decodePointVar(pk, pkOff, false, p))
+        byte[] A = copy(pk, pkOff, PUBLIC_KEY_SIZE);
+
+        if (!checkPointFullVar(A))
         {
             return false;
         }
 
-        F.normalize(p.x);
-        F.normalize(p.y);
-        F.normalize(p.z);
-
-        if (isNeutralElementVar(p.x, p.y, p.z))
+        PointAffine pA = new PointAffine();
+        if (!decodePointVar(A, false, pA))
         {
             return false;
         }
 
-        PointProjective r = new PointProjective();
-        scalarMultOrderVar(p, r);
+        return checkPointOrderVar(pA);
+    }
 
-        F.normalize(r.x);
-        F.normalize(r.y);
-        F.normalize(r.z);
+    public static PublicPoint validatePublicKeyFullExport(byte[] pk, int pkOff)
+    {
+        byte[] A = copy(pk, pkOff, PUBLIC_KEY_SIZE);
 
-        return isNeutralElementVar(r.x, r.y, r.z);
+        if (!checkPointFullVar(A))
+        {
+            return null;
+        }
+
+        PointAffine pA = new PointAffine();
+        if (!decodePointVar(A, false, pA))
+        {
+            return null;
+        }
+
+        if (!checkPointOrderVar(pA))
+        {
+            return null;
+        }
+
+        return exportPoint(pA);
     }
 
     public static boolean validatePublicKeyPartial(byte[] pk, int pkOff)
     {
-        PointProjective p = new PointProjective();
-        return decodePointVar(pk, pkOff, false, p);
+        byte[] A = copy(pk, pkOff, PUBLIC_KEY_SIZE);
+
+        if (!checkPointFullVar(A))
+        {
+            return false;
+        }
+
+        PointAffine pA = new PointAffine();
+        return decodePointVar(A, false, pA);
+    }
+
+    public static PublicPoint validatePublicKeyPartialExport(byte[] pk, int pkOff)
+    {
+        byte[] A = copy(pk, pkOff, PUBLIC_KEY_SIZE);
+
+        if (!checkPointFullVar(A))
+        {
+            return null;
+        }
+
+        PointAffine pA = new PointAffine();
+        if (!decodePointVar(A, false, pA))
+        {
+            return null;
+        }
+
+        return exportPoint(pA);
     }
 
     public static boolean verify(byte[] sig, int sigOff, byte[] pk, int pkOff, byte[] ctx, byte[] m, int mOff, int mLen)
@@ -1562,13 +1430,29 @@ public static boolean verify(byte[] sig, int sigOff, byte[] pk, int pkOff, byte[
         return implVerify(sig, sigOff, pk, pkOff, ctx, phflag, m, mOff, mLen);
     }
 
+    public static boolean verify(byte[] sig, int sigOff, PublicPoint publicPoint, byte[] ctx, byte[] m, int mOff,
+        int mLen)
+    {
+        byte phflag = 0x00;
+
+        return implVerify(sig, sigOff, publicPoint, ctx, phflag, m, mOff, mLen);
+    }
+
     public static boolean verifyPrehash(byte[] sig, int sigOff, byte[] pk, int pkOff, byte[] ctx, byte[] ph, int phOff)
     {
         byte phflag = 0x01;
 
         return implVerify(sig, sigOff, pk, pkOff, ctx, phflag, ph, phOff, PREHASH_SIZE);
     }
 
+    public static boolean verifyPrehash(byte[] sig, int sigOff, PublicPoint publicPoint, byte[] ctx, byte[] ph,
+        int phOff)
+    {
+        byte phflag = 0x01;
+
+        return implVerify(sig, sigOff, publicPoint, ctx, phflag, ph, phOff, PREHASH_SIZE);
+    }
+
     public static boolean verifyPrehash(byte[] sig, int sigOff, byte[] pk, int pkOff, byte[] ctx, Xof ph)
     {
         byte[] m = new byte[PREHASH_SIZE];
@@ -1581,4 +1465,17 @@ public static boolean verifyPrehash(byte[] sig, int sigOff, byte[] pk, int pkOff
 
         return implVerify(sig, sigOff, pk, pkOff, ctx, phflag, m, 0, m.length);
     }
+
+    public static boolean verifyPrehash(byte[] sig, int sigOff, PublicPoint publicPoint, byte[] ctx, Xof ph)
+    {
+        byte[] m = new byte[PREHASH_SIZE];
+        if (PREHASH_SIZE != ph.doFinal(m, 0, PREHASH_SIZE))
+        {
+            throw new IllegalArgumentException("ph");
+        }
+
+        byte phflag = 0x01;
+
+        return implVerify(sig, sigOff, publicPoint, ctx, phflag, m, 0, m.length);
+    }
 }

@@ -0,0 +1,260 @@
+package org.bouncycastle.math.ec.rfc8032;
+
+import org.bouncycastle.math.raw.Nat;
+import org.bouncycastle.math.raw.Nat256;
+
+abstract class Scalar25519
+{
+    static final int SIZE = 8;
+
+    private static final long M08L = 0x000000FFL;
+    private static final long M28L = 0x0FFFFFFFL;
+    private static final long M32L = 0xFFFFFFFFL;
+
+    private static final int TARGET_LENGTH = 254;
+
+    private static final int[] L = new int[]{ 0x5CF5D3ED, 0x5812631A, 0xA2F79CD6, 0x14DEF9DE, 0x00000000, 0x00000000,
+        0x00000000, 0x10000000 };
+    private static final int[] LSq = new int[]{ 0xAB128969, 0xE2EDF685, 0x2298A31D, 0x68039276, 0xD217F5BE, 0x3DCEEC73,
+        0x1B7C309A, 0xA1B39941, 0x4B9EBA7D, 0xCB024C63, 0xD45EF39A, 0x029BDF3B, 0x00000000, 0x00000000, 0x00000000,
+        0x01000000 };
+
+    private static final int L0 = -0x030A2C13;      // L0:26/--
+    private static final int L1 =  0x012631A6;      // L1:24/22
+    private static final int L2 =  0x079CD658;      // L2:27/--
+    private static final int L3 = -0x006215D1;      // L3:23/--
+    private static final int L4 =  0x000014DF;      // L4:12/11
+
+    static boolean checkVar(byte[] s, int[] n)
+    {
+        decode(s, n);
+        return !Nat256.gte(n, L);
+    }
+
+    static void decode(byte[] k, int[] n)
+    {
+        Codec.decode32(k, 0, n, 0, SIZE);
+    }
+
+    static void getOrderWnafVar(int width, byte[] ws)
+    {
+        Wnaf.getSignedVar(L, width, ws);
+    }
+
+    static void multiply128Var(int[] x, int[] y128, int[] z)
+    {
+        int[] tt = new int[12];
+        Nat256.mul128(x, y128, tt);
+
+        if ((int)y128[3] < 0)
+        {
+            Nat256.addTo(L, 0, tt, 4, 0);
+            Nat256.subFrom(x, 0, tt, 4, 0);
+        }
+
+        byte[] bytes = new byte[64];
+        Codec.encode32(tt, 0, 12, bytes, 0);
+
+        byte[] r = reduce(bytes);
+        decode(r, z);
+    }
+
+    static byte[] reduce(byte[] n)
+    {
+        long x00 =  Codec.decode32(n,  0)       & M32L;         // x00:32/--
+        long x01 = (Codec.decode24(n,  4) << 4) & M32L;         // x01:28/--
+        long x02 =  Codec.decode32(n,  7)       & M32L;         // x02:32/--
+        long x03 = (Codec.decode24(n, 11) << 4) & M32L;         // x03:28/--
+        long x04 =  Codec.decode32(n, 14)       & M32L;         // x04:32/--
+        long x05 = (Codec.decode24(n, 18) << 4) & M32L;         // x05:28/--
+        long x06 =  Codec.decode32(n, 21)       & M32L;         // x06:32/--
+        long x07 = (Codec.decode24(n, 25) << 4) & M32L;         // x07:28/--
+        long x08 =  Codec.decode32(n, 28)       & M32L;         // x08:32/--
+        long x09 = (Codec.decode24(n, 32) << 4) & M32L;         // x09:28/--
+        long x10 =  Codec.decode32(n, 35)       & M32L;         // x10:32/--
+        long x11 = (Codec.decode24(n, 39) << 4) & M32L;         // x11:28/--
+        long x12 =  Codec.decode32(n, 42)       & M32L;         // x12:32/--
+        long x13 = (Codec.decode24(n, 46) << 4) & M32L;         // x13:28/--
+        long x14 =  Codec.decode32(n, 49)       & M32L;         // x14:32/--
+        long x15 = (Codec.decode24(n, 53) << 4) & M32L;         // x15:28/--
+        long x16 =  Codec.decode32(n, 56)       & M32L;         // x16:32/--
+        long x17 = (Codec.decode24(n, 60) << 4) & M32L;         // x17:28/--
+        long x18 =                 n[63]        & M08L;         // 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;
+        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;
+
+//        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[64];
+        Codec.encode56(x00 | (x01 << 28), r,  0);
+        Codec.encode56(x02 | (x03 << 28), r,  7);
+        Codec.encode56(x04 | (x05 << 28), r, 14);
+        Codec.encode56(x06 | (x07 << 28), r, 21);
+        Codec.encode32((int)x08,          r, 28);
+        return r;
+    }
+
+    static void reduceBasisVar(int[] k, int[] z0, int[] z1)
+    {
+        /*
+         * Split scalar k into two half-size scalars z0 and z1, such that z1 * k == z0 mod L.
+         * 
+         * See https://ia.cr/2020/454 (Pornin).
+         */
+
+        int[] Nu = new int[16];     System.arraycopy(LSq, 0, Nu, 0, 16);
+        int[] Nv = new int[16];     Nat256.square(k, Nv); ++Nv[0];
+        int[] p  = new int[16];     Nat256.mul(L, k, p);
+        int[] u0 = new int[4];      System.arraycopy(L, 0, u0, 0, 4);
+        int[] u1 = new int[4];
+        int[] v0 = new int[4];      System.arraycopy(k, 0, v0, 0, 4);
+        int[] v1 = new int[4];      v1[0] = 1;
+
+        int last = 15;
+        int len_Nv = ScalarUtil.getBitLengthPositive(last, Nv);
+
+        while (len_Nv > TARGET_LENGTH)
+        {
+            int len_p = ScalarUtil.getBitLength(last, p);
+            int s = len_p - len_Nv;
+            s &= ~(s >> 31);
+
+            if (p[last] < 0)
+            {
+                ScalarUtil.addShifted_NP(last, s, Nu, Nv, p);
+                ScalarUtil.addShifted_UV(3, s, u0, u1, v0, v1);
+            }
+            else
+            {
+                ScalarUtil.subShifted_NP(last, s, Nu, Nv, p);
+                ScalarUtil.subShifted_UV(3, s, u0, u1, v0, v1);
+            }
+
+            if (ScalarUtil.lessThan(last, Nu, Nv))
+            {
+                int[] t0 = u0; u0 = v0; v0 = t0;
+                int[] t1 = u1; u1 = v1; v1 = t1;
+                int[] tN = Nu; Nu = Nv; Nv = tN;
+
+                last = len_Nv >>> 5;
+                len_Nv = ScalarUtil.getBitLengthPositive(last, Nv);
+            }
+        }
+
+        // v1 * k == v0 mod L
+        System.arraycopy(v0, 0, z0, 0, 4);
+        System.arraycopy(v1, 0, z1, 0, 4);
+    }
+
+    static void toSignedDigits(int bits, int[] x, int[] z)
+    {
+//        assert bits == 256;
+//        assert z.length >= SIZE;
+
+//        int c1 =
+        Nat.cadd(SIZE, ~x[0] & 1, x, L, z);     //assert c1 == 0;
+//        int c2 =
+        Nat.shiftDownBit(SIZE, z, 1);           //assert c2 == (1 << 31);
+    }
+}

@@ -0,0 +1,429 @@
+package org.bouncycastle.math.ec.rfc8032;
+
+import org.bouncycastle.math.raw.Nat;
+import org.bouncycastle.math.raw.Nat448;
+
+abstract class Scalar448
+{
+    static final int SIZE = 14;
+
+    private static final int SCALAR_BYTES = SIZE * 4 + 1;
+
+    private static final long M26L = 0x03FFFFFFL;
+    private static final long M28L = 0x0FFFFFFFL;
+    private static final long M32L = 0xFFFFFFFFL;
+
+    private static final int TARGET_LENGTH = 447;
+
+    private static final int[] L = new int[]{ 0xAB5844F3, 0x2378C292, 0x8DC58F55, 0x216CC272, 0xAED63690, 0xC44EDB49,
+        0x7CCA23E9, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0x3FFFFFFF };
+    private static final int[] LSq = new int[]{ 0x1BA1FEA9, 0xC1ADFBB8, 0x49E0A8B2, 0xB91BF537, 0xE764D815, 0x4525492B,
+        0xA2B8716D, 0x4AE17CF6, 0xBA3C47C4, 0xF1A9CC14, 0x7E4D070A, 0x92052BCB, 0x9F823B72, 0xC3402A93, 0x55AC2279,
+        0x91BC6149, 0x46E2C7AA, 0x10B66139, 0xD76B1B48, 0xE2276DA4, 0xBE6511F4, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF,
+        0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0x0FFFFFFF };
+
+    private static final int L_0 = 0x04A7BB0D;      // L_0:26/24
+    private static final int L_1 = 0x0873D6D5;      // L_1:27/23
+    private static final int L_2 = 0x0A70AADC;      // L_2:27/26
+    private static final int L_3 = 0x03D8D723;      // L_3:26/--
+    private static final int L_4 = 0x096FDE93;      // L_4:27/25
+    private static final int L_5 = 0x0B65129C;      // L_5:27/26
+    private static final int L_6 = 0x063BB124;      // L_6:27/--
+    private static final int L_7 = 0x08335DC1;      // L_7:27/22
+
+    private static final int L4_0 = 0x029EEC34;     // L4_0:25/24
+    private static final int L4_1 = 0x01CF5B55;     // L4_1:25/--
+    private static final int L4_2 = 0x09C2AB72;     // L4_2:27/25
+    private static final int L4_3 = 0x0F635C8E;     // L4_3:28/--
+    private static final int L4_4 = 0x05BF7A4C;     // L4_4:26/25
+    private static final int L4_5 = 0x0D944A72;     // L4_5:28/--
+    private static final int L4_6 = 0x08EEC492;     // L4_6:27/24
+    private static final int L4_7 = 0x20CD7705;     // L4_7:29/24
+
+    static boolean checkVar(byte[] s, int[] n)
+    {
+        if (s[SCALAR_BYTES - 1] != 0x00)
+        {
+            return false;
+        }
+
+        decode(s, n);
+        return !Nat.gte(SIZE, n, L);
+    }
+
+    static void decode(byte[] k, int[] n)
+    {
+//        assert k[SCALAR_BYTES - 1] == 0x00;
+
+        Codec.decode32(k, 0, n, 0, SIZE);
+    }
+
+    static void getOrderWnafVar(int width, byte[] ws)
+    {
+        Wnaf.getSignedVar(L, width, ws);
+    }
+
+    static void multiply225Var(int[] x, int[] y225, int[] z)
+    {
+//        assert y225[7] >> 31 == y225[7];
+
+        int[] tt = new int[22];
+        Nat.mul(y225, 0, 8, x, 0, SIZE, tt, 0);
+
+        if (y225[7] < 0)
+        {
+            Nat.addTo(SIZE, L, 0, tt, 8);
+            Nat.subFrom(SIZE, x, 0, tt, 8);
+        }
+
+        byte[] bytes = new byte[114];
+        Codec.encode32(tt, 0, 22, bytes, 0);
+
+        byte[] r = reduce(bytes);
+        decode(r, z);
+    }
+
+    static byte[] reduce(byte[] n)
+    {
+        long x00 =  Codec.decode32(n,   0)       & M32L;    // x00:32/--
+        long x01 = (Codec.decode24(n,   4) << 4) & M32L;    // x01:28/--
+        long x02 =  Codec.decode32(n,   7)       & M32L;    // x02:32/--
+        long x03 = (Codec.decode24(n,  11) << 4) & M32L;    // x03:28/--
+        long x04 =  Codec.decode32(n,  14)       & M32L;    // x04:32/--
+        long x05 = (Codec.decode24(n,  18) << 4) & M32L;    // x05:28/--
+        long x06 =  Codec.decode32(n,  21)       & M32L;    // x06:32/--
+        long x07 = (Codec.decode24(n,  25) << 4) & M32L;    // x07:28/--
+        long x08 =  Codec.decode32(n,  28)       & M32L;    // x08:32/--
+        long x09 = (Codec.decode24(n,  32) << 4) & M32L;    // x09:28/--
+        long x10 =  Codec.decode32(n,  35)       & M32L;    // x10:32/--
+        long x11 = (Codec.decode24(n,  39) << 4) & M32L;    // x11:28/--
+        long x12 =  Codec.decode32(n,  42)       & M32L;    // x12:32/--
+        long x13 = (Codec.decode24(n,  46) << 4) & M32L;    // x13:28/--
+        long x14 =  Codec.decode32(n,  49)       & M32L;    // x14:32/--
+        long x15 = (Codec.decode24(n,  53) << 4) & M32L;    // x15:28/--
+        long x16 =  Codec.decode32(n,  56)       & M32L;    // x16:32/--
+        long x17 = (Codec.decode24(n,  60) << 4) & M32L;    // x17:28/--
+        long x18 =  Codec.decode32(n,  63)       & M32L;    // x18:32/--
+        long x19 = (Codec.decode24(n,  67) << 4) & M32L;    // x19:28/--
+        long x20 =  Codec.decode32(n,  70)       & M32L;    // x20:32/--
+        long x21 = (Codec.decode24(n,  74) << 4) & M32L;    // x21:28/--
+        long x22 =  Codec.decode32(n,  77)       & M32L;    // x22:32/--
+        long x23 = (Codec.decode24(n,  81) << 4) & M32L;    // x23:28/--
+        long x24 =  Codec.decode32(n,  84)       & M32L;    // x24:32/--
+        long x25 = (Codec.decode24(n,  88) << 4) & M32L;    // x25:28/--
+        long x26 =  Codec.decode32(n,  91)       & M32L;    // x26:32/--
+        long x27 = (Codec.decode24(n,  95) << 4) & M32L;    // x27:28/--
+        long x28 =  Codec.decode32(n,  98)       & M32L;    // x28:32/--
+        long x29 = (Codec.decode24(n, 102) << 4) & M32L;    // x29:28/--
+        long x30 =  Codec.decode32(n, 105)       & M32L;    // x30:32/--
+        long x31 = (Codec.decode24(n, 109) << 4) & M32L;    // x31:28/--
+        long x32 =  Codec.decode16(n, 112)       & M32L;    // x32:16/--
+
+//        x32 += (x31 >>> 28); x31 &= M28L;
+        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 &= M28L;           // 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 &= M28L;
+        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 &= M28L;           // 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 &= M28L;
+        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 &= M28L;           // 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 &= M28L;
+        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 &= M28L;           // 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 &= M28L;           // x21:58/--, x20:28/--
+        x22 += (x21 >>> 28); x21 &= M28L;           // x22:57/54, x21:28/--
+        x23 += (x22 >>> 28); x22 &= M28L;           // x23:45/42, x22:28/--
+        x24 += (x23 >>> 28); x23 &= M28L;           // 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 &= M28L;           // x18:59/31, x17:28/--
+        x19 += (x18 >>> 28); x18 &= M28L;           // x19:58/54, x18:28/--
+        x20 += (x19 >>> 28); x19 &= M28L;           // x20:30/29, x19:28/--
+        x21 += (x20 >>> 28); x20 &= M28L;           // 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 &= M28L;           // x15:59/31, x14:28/--
+        x16 += (x15 >>> 28); x15 &= M28L;           // x16:59/32, x15:28/--
+        x17 += (x16 >>> 28); x16 &= M28L;           // x17:31/29, x16:28/--
+        x18 += (x17 >>> 28); x17 &= M28L;           // 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 &= M26L;
+        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 &= 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;
+        x10 += (x09 >>> 28); x09 &= M28L;
+        x11 += (x10 >>> 28); x10 &= M28L;
+        x12 += (x11 >>> 28); x11 &= M28L;
+        x13 += (x12 >>> 28); x12 &= M28L;
+        x14 += (x13 >>> 28); x13 &= M28L;
+        x15 += (x14 >>> 28); x14 &= M28L;
+        x16  = (x15 >>> 26); x15 &= M26L;
+
+        x16 -= 1;
+
+//        assert x16 == 0L || x16 == -1L;
+
+        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 &= 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;
+        x10 += (x09 >> 28); x09 &= M28L;
+        x11 += (x10 >> 28); x10 &= M28L;
+        x12 += (x11 >> 28); x11 &= M28L;
+        x13 += (x12 >> 28); x12 &= M28L;
+        x14 += (x13 >> 28); x13 &= M28L;
+        x15 += (x14 >> 28); x14 &= M28L;
+
+//        assert x15 >>> 26 == 0L;
+
+        byte[] r = new byte[SCALAR_BYTES];
+        Codec.encode56(x00 | (x01 << 28), r,  0);
+        Codec.encode56(x02 | (x03 << 28), r,  7);
+        Codec.encode56(x04 | (x05 << 28), r, 14);
+        Codec.encode56(x06 | (x07 << 28), r, 21);
+        Codec.encode56(x08 | (x09 << 28), r, 28);
+        Codec.encode56(x10 | (x11 << 28), r, 35);
+        Codec.encode56(x12 | (x13 << 28), r, 42);
+        Codec.encode56(x14 | (x15 << 28), r, 49);
+//        r[SCALAR_BYTES - 1] = 0;
+        return r;
+    }
+
+    static void reduceBasisVar(int[] k, int[] z0, int[] z1)
+    {
+        /*
+         * Split scalar k into two half-size scalars z0 and z1, such that z1 * k == z0 mod L.
+         * 
+         * See https://ia.cr/2020/454 (Pornin).
+         */
+
+        int[] Nu = new int[28];     System.arraycopy(LSq, 0, Nu, 0, 28);
+        int[] Nv = new int[28];     Nat448.square(k, Nv); ++Nv[0];
+        int[] p  = new int[28];     Nat448.mul(L, k, p);
+        int[] u0 = new int[8];      System.arraycopy(L, 0, u0, 0, 8);
+        int[] u1 = new int[8];
+        int[] v0 = new int[8];      System.arraycopy(k, 0, v0, 0, 8);
+        int[] v1 = new int[8];      v1[0] = 1;
+
+        int last = 27;
+        int len_Nv = ScalarUtil.getBitLengthPositive(last, Nv);
+
+        while (len_Nv > TARGET_LENGTH)
+        {
+            int len_p = ScalarUtil.getBitLength(last, p);
+            int s = len_p - len_Nv;
+            s &= ~(s >> 31);
+
+            if (p[last] < 0)
+            {
+                ScalarUtil.addShifted_NP(last, s, Nu, Nv, p);
+                ScalarUtil.addShifted_UV(7, s, u0, u1, v0, v1);
+            }
+            else
+            {
+                ScalarUtil.subShifted_NP(last, s, Nu, Nv, p);
+                ScalarUtil.subShifted_UV(7, s, u0, u1, v0, v1);
+            }
+
+            if (ScalarUtil.lessThan(last, Nu, Nv))
+            {
+                int[] t0 = u0; u0 = v0; v0 = t0;
+                int[] t1 = u1; u1 = v1; v1 = t1;
+                int[] tN = Nu; Nu = Nv; Nv = tN;
+
+                last = len_Nv >>> 5;
+                len_Nv = ScalarUtil.getBitLengthPositive(last, Nv);
+            }
+        }
+
+//        assert v0[7] >> 31 == v0[7];
+//        assert v1[7] >> 31 == v1[7];
+
+        // v1 * k == v0 mod L
+        System.arraycopy(v0, 0, z0, 0, 8);
+        System.arraycopy(v1, 0, z1, 0, 8);
+    }
+
+    static void toSignedDigits(int bits, int[] x, int[] z)
+    {
+//        assert 448 < bits && bits < 480;
+//        assert z.length > SIZE;
+
+        z[SIZE] = (1 << (bits - 448))
+                + Nat.cadd(SIZE, ~x[0] & 1, x, L, z);
+//        int c =
+        Nat.shiftDownBit(SIZE + 1, z, 0);
+//        assert c == (1 << 31);
+    }
+}

@@ -0,0 +1,241 @@
+package org.bouncycastle.math.ec.rfc8032;
+
+import org.bouncycastle.util.Integers;
+
+abstract class ScalarUtil
+{
+    private static final long M = 0xFFFFFFFFL;
+
+    static void addShifted_NP(int last, int s, int[] Nu, int[] Nv, int[] _p)
+    {
+        int sWords = s >>> 5, sBits = s & 31;
+
+        long cc__p = 0L;
+        long cc_Nu = 0L;
+
+        if (sBits == 0)
+        {
+            for (int i = sWords; i <= last; ++i)
+            {
+                cc_Nu += Nu[i] & M;
+                cc_Nu += _p[i - sWords] & M;
+
+                cc__p += _p[i] & M;
+                cc__p += Nv[i - sWords] & M;
+                _p[i]  = (int)cc__p; cc__p >>>= 32;
+
+                cc_Nu += _p[i - sWords] & M;
+                Nu[i]  = (int)cc_Nu; cc_Nu >>>= 32;
+            }
+        }
+        else
+        {
+            int prev_p = 0;
+            int prev_q = 0;
+            int prev_v = 0;
+
+            for (int i = sWords; i <= last; ++i)
+            {
+                int next_p = _p[i - sWords];
+                int p_s = (next_p << sBits) | (prev_p >>> -sBits);
+                prev_p = next_p;
+
+                cc_Nu += Nu[i] & M;
+                cc_Nu += p_s & M;
+
+                int next_v = Nv[i - sWords];
+                int v_s = (next_v << sBits) | (prev_v >>> -sBits);
+                prev_v = next_v;
+
+                cc__p += _p[i] & M;
+                cc__p += v_s & M;
+                _p[i]  = (int)cc__p; cc__p >>>= 32;
+
+                int next_q = _p[i - sWords];
+                int q_s = (next_q << sBits) | (prev_q >>> -sBits);
+                prev_q = next_q;
+
+                cc_Nu += q_s & M;
+                Nu[i]  = (int)cc_Nu; cc_Nu >>>= 32;
+            }
+        }
+    }
+
+    static void addShifted_UV(int last, int s, int[] u0, int[] u1, int[] v0, int[] v1)
+    {
+        int sWords = s >>> 5, sBits = s & 31;
+
+        long cc_u0 = 0L;
+        long cc_u1 = 0L;
+
+        if (sBits == 0)
+        {
+            for (int i = sWords; i <= last; ++i)
+            {
+                cc_u0 += u0[i] & M;
+                cc_u1 += u1[i] & M;
+                cc_u0 += v0[i - sWords] & M;
+                cc_u1 += v1[i - sWords] & M;
+                u0[i]  = (int)cc_u0; cc_u0 >>>= 32;
+                u1[i]  = (int)cc_u1; cc_u1 >>>= 32;
+            }
+        }
+        else
+        {
+            int prev_v0 = 0;
+            int prev_v1 = 0;
+
+            for (int i = sWords; i <= last; ++i)
+            {
+                int next_v0 = v0[i - sWords];
+                int next_v1 = v1[i - sWords];
+                int v0_s = (next_v0 << sBits) | (prev_v0 >>> -sBits);
+                int v1_s = (next_v1 << sBits) | (prev_v1 >>> -sBits);
+                prev_v0 = next_v0;
+                prev_v1 = next_v1;
+
+                cc_u0 += u0[i] & M;
+                cc_u1 += u1[i] & M;
+                cc_u0 += v0_s & M;
+                cc_u1 += v1_s & M;
+                u0[i]  = (int)cc_u0; cc_u0 >>>= 32;
+                u1[i]  = (int)cc_u1; cc_u1 >>>= 32;
+            }
+        }
+    }
+
+    static int getBitLength(int last, int[] x)
+    {
+        int i = last;
+        int sign = x[i] >> 31;
+        while (i > 0 && x[i] == sign)
+        {
+            --i;
+        }
+        return i * 32 + 32 - Integers.numberOfLeadingZeros(x[i] ^ sign);
+    }
+
+    static int getBitLengthPositive(int last, int[] x)
+    {
+        int i = last;
+        while (i > 0 && x[i] == 0)
+        {
+            --i;
+        }
+        return i * 32 + 32 - Integers.numberOfLeadingZeros(x[i]);
+    }
+
+    static boolean lessThan(int last, int[] x, int[] y)
+    {
+        int i = last;
+        do
+        {
+            int x_i = x[i] + Integer.MIN_VALUE;
+            int y_i = y[i] + Integer.MIN_VALUE;
+            if (x_i < y_i)
+                return true;
+            if (x_i > y_i)
+                return false;
+        }
+        while (--i >= 0);
+        return false;
+    }
+
+    static void subShifted_NP(int last, int s, int[] Nu, int[] Nv, int[] _p)
+    {
+        int sWords = s >>> 5, sBits = s & 31;
+
+        long cc__p = 0L;
+        long cc_Nu = 0L;
+
+        if (sBits == 0)
+        {
+            for (int i = sWords; i <= last; ++i)
+            {
+                cc_Nu += Nu[i] & M;
+                cc_Nu -= _p[i - sWords] & M;
+
+                cc__p += _p[i] & M;
+                cc__p -= Nv[i - sWords] & M;
+                _p[i]  = (int)cc__p; cc__p >>= 32;
+
+                cc_Nu -= _p[i - sWords] & M;
+                Nu[i]  = (int)cc_Nu; cc_Nu >>= 32;
+            }
+        }
+        else
+        {
+            int prev_p = 0;
+            int prev_q = 0;
+            int prev_v = 0;
+
+            for (int i = sWords; i <= last; ++i)
+            {
+                int next_p = _p[i - sWords];
+                int p_s = (next_p << sBits) | (prev_p >>> -sBits);
+                prev_p = next_p;
+
+                cc_Nu += Nu[i] & M;
+                cc_Nu -= p_s & M;
+
+                int next_v = Nv[i - sWords];
+                int v_s = (next_v << sBits) | (prev_v >>> -sBits);
+                prev_v = next_v;
+
+                cc__p += _p[i] & M;
+                cc__p -= v_s & M;
+                _p[i]  = (int)cc__p; cc__p >>= 32;
+
+                int next_q = _p[i - sWords];
+                int q_s = (next_q << sBits) | (prev_q >>> -sBits);
+                prev_q = next_q;
+
+                cc_Nu -= q_s & M;
+                Nu[i]  = (int)cc_Nu; cc_Nu >>= 32;
+            }
+        }
+    }
+
+    static void subShifted_UV(int last, int s, int[] u0, int[] u1, int[] v0, int[] v1)
+    {
+        int sWords = s >>> 5, sBits = s & 31;
+
+        long cc_u0 = 0L;
+        long cc_u1 = 0L;
+
+        if (sBits == 0)
+        {
+            for (int i = sWords; i <= last; ++i)
+            {
+                cc_u0 += u0[i] & M;
+                cc_u1 += u1[i] & M;
+                cc_u0 -= v0[i - sWords] & M;
+                cc_u1 -= v1[i - sWords] & M;
+                u0[i]  = (int)cc_u0; cc_u0 >>= 32;
+                u1[i]  = (int)cc_u1; cc_u1 >>= 32;
+            }
+        }
+        else
+        {
+            int prev_v0 = 0;
+            int prev_v1 = 0;
+
+            for (int i = sWords; i <= last; ++i)
+            {
+                int next_v0 = v0[i - sWords];
+                int next_v1 = v1[i - sWords];
+                int v0_s = (next_v0 << sBits) | (prev_v0 >>> -sBits);
+                int v1_s = (next_v1 << sBits) | (prev_v1 >>> -sBits);
+                prev_v0 = next_v0;
+                prev_v1 = next_v1;
+
+                cc_u0 += u0[i] & M;
+                cc_u1 += u1[i] & M;
+                cc_u0 -= v0_s & M;
+                cc_u1 -= v1_s & M;
+                u0[i]  = (int)cc_u0; cc_u0 >>= 32;
+                u1[i]  = (int)cc_u1; cc_u1 >>= 32;
+            }
+        }
+    }
+}

@@ -0,0 +1,49 @@
+package org.bouncycastle.math.ec.rfc8032;
+
+abstract class Wnaf
+{
+    static void getSignedVar(int[] n, int width, byte[] ws)
+    {
+//        assert 2 <= width && width <= 8;
+
+        int[] t = new int[n.length * 2];
+        {
+            int c = n[n.length - 1] >> 31, i = n.length, tPos = t.length;
+            while (--i >= 0)
+            {
+                int next = n[i];
+                t[--tPos] = (next >>> 16) | (c << 16);
+                t[--tPos] = c = next;
+            }
+        }
+
+        final int lead = 32 - width;
+
+        int j = 0, carry = 0;
+        for (int i = 0; i < t.length; ++i, j -= 16)
+        {
+            int word = t[i];
+            while (j < 16)
+            {
+                int word16 = word >>> j;
+
+                // TODO Consider trailing-zeros approach from bc-csharp
+                int bit = word16 & 1;
+                if (bit == carry)
+                {
+                    ++j;
+                    continue;
+                }
+
+                int digit = (word16 | 1) << lead;
+                carry = digit >>> 31;
+
+                ws[(i << 4) + j] = (byte)(digit >> lead);
+
+                j += width;
+            }
+        }
+
+//        assert carry == n[n.length - 1] >>> 31;
+    }
+}

@@ -143,6 +143,33 @@ public static int addTo(int[] x, int[] z)
         return (int)c;
     }
 
+    public static int addTo(int[] x, int[] z, int cIn)
+    {
+        long c = cIn & M;
+        c += (x[0] & M) + (z[0] & M);
+        z[0] = (int)c;
+        c >>>= 32;
+        c += (x[1] & M) + (z[1] & M);
+        z[1] = (int)c;
+        c >>>= 32;
+        c += (x[2] & M) + (z[2] & M);
+        z[2] = (int)c;
+        c >>>= 32;
+        c += (x[3] & M) + (z[3] & M);
+        z[3] = (int)c;
+        c >>>= 32;
+        c += (x[4] & M) + (z[4] & M);
+        z[4] = (int)c;
+        c >>>= 32;
+        c += (x[5] & M) + (z[5] & M);
+        z[5] = (int)c;
+        c >>>= 32;
+        c += (x[6] & M) + (z[6] & M);
+        z[6] = (int)c;
+        c >>>= 32;
+        return (int)c;
+    }
+
     public static int addTo(int[] x, int xOff, int[] z, int zOff, int cIn)
     {
         long c = cIn & M;

@@ -158,6 +158,36 @@ public static int addTo(int[] x, int[] z)
         return (int)c;
     }
 
+    public static int addTo(int[] x, int[] z, int cIn)
+    {
+        long c = cIn & M;
+        c += (x[0] & M) + (z[0] & M);
+        z[0] = (int)c;
+        c >>>= 32;
+        c += (x[1] & M) + (z[1] & M);
+        z[1] = (int)c;
+        c >>>= 32;
+        c += (x[2] & M) + (z[2] & M);
+        z[2] = (int)c;
+        c >>>= 32;
+        c += (x[3] & M) + (z[3] & M);
+        z[3] = (int)c;
+        c >>>= 32;
+        c += (x[4] & M) + (z[4] & M);
+        z[4] = (int)c;
+        c >>>= 32;
+        c += (x[5] & M) + (z[5] & M);
+        z[5] = (int)c;
+        c >>>= 32;
+        c += (x[6] & M) + (z[6] & M);
+        z[6] = (int)c;
+        c >>>= 32;
+        c += (x[7] & M) + (z[7] & M);
+        z[7] = (int)c;
+        c >>>= 32;
+        return (int)c;
+    }
+
     public static int addTo(int[] x, int xOff, int[] z, int zOff, int cIn)
     {
         long c = cIn & M;
@@ -602,6 +632,77 @@ public static void mul(int[] x, int xOff, int[] y, int yOff, int[] zz, int zzOff
         }
     }
 
+    public static void mul128(int[] x, int[] y128, int[] zz)
+    {
+        long x_0 = x[0] & M;
+        long x_1 = x[1] & M;
+        long x_2 = x[2] & M;
+        long x_3 = x[3] & M;
+        long x_4 = x[4] & M;
+        long x_5 = x[5] & M;
+        long x_6 = x[6] & M;
+        long x_7 = x[7] & M;
+
+        {
+            long c = 0, y_0 = y128[0] & M;
+            c += y_0 * x_0;
+            zz[0] = (int)c;
+            c >>>= 32;
+            c += y_0 * x_1;
+            zz[1] = (int)c;
+            c >>>= 32;
+            c += y_0 * x_2;
+            zz[2] = (int)c;
+            c >>>= 32;
+            c += y_0 * x_3;
+            zz[3] = (int)c;
+            c >>>= 32;
+            c += y_0 * x_4;
+            zz[4] = (int)c;
+            c >>>= 32;
+            c += y_0 * x_5;
+            zz[5] = (int)c;
+            c >>>= 32;
+            c += y_0 * x_6;
+            zz[6] = (int)c;
+            c >>>= 32;
+            c += y_0 * x_7;
+            zz[7] = (int)c;
+            c >>>= 32;
+            zz[8] = (int)c;
+        }
+
+        for (int i = 1; i < 4; ++i)
+        {
+            long c = 0, y_i = y128[i] & M;
+            c += y_i * x_0 + (zz[i + 0] & M);
+            zz[i + 0] = (int)c;
+            c >>>= 32;
+            c += y_i * x_1 + (zz[i + 1] & M);
+            zz[i + 1] = (int)c;
+            c >>>= 32;
+            c += y_i * x_2 + (zz[i + 2] & M);
+            zz[i + 2] = (int)c;
+            c >>>= 32;
+            c += y_i * x_3 + (zz[i + 3] & M);
+            zz[i + 3] = (int)c;
+            c >>>= 32;
+            c += y_i * x_4 + (zz[i + 4] & M);
+            zz[i + 4] = (int)c;
+            c >>>= 32;
+            c += y_i * x_5 + (zz[i + 5] & M);
+            zz[i + 5] = (int)c;
+            c >>>= 32;
+            c += y_i * x_6 + (zz[i + 6] & M);
+            zz[i + 6] = (int)c;
+            c >>>= 32;
+            c += y_i * x_7 + (zz[i + 7] & M);
+            zz[i + 7] = (int)c;
+            c >>>= 32;
+            zz[i + 8] = (int)c;
+        }
+    }
+
     public static int mulAddTo(int[] x, int[] y, int[] zz)
     {
         long y_0 = y[0] & M;
@@ -1347,6 +1448,36 @@ public static int subFrom(int[] x, int[] z)
         return (int)c;
     }
 
+    public static int subFrom(int[] x, int[] z, int cIn)
+    {
+        long c = cIn & M;
+        c += (z[0] & M) - (x[0] & M);
+        z[0] = (int)c;
+        c >>= 32;
+        c += (z[1] & M) - (x[1] & M);
+        z[1] = (int)c;
+        c >>= 32;
+        c += (z[2] & M) - (x[2] & M);
+        z[2] = (int)c;
+        c >>= 32;
+        c += (z[3] & M) - (x[3] & M);
+        z[3] = (int)c;
+        c >>= 32;
+        c += (z[4] & M) - (x[4] & M);
+        z[4] = (int)c;
+        c >>= 32;
+        c += (z[5] & M) - (x[5] & M);
+        z[5] = (int)c;
+        c >>= 32;
+        c += (z[6] & M) - (x[6] & M);
+        z[6] = (int)c;
+        c >>= 32;
+        c += (z[7] & M) - (x[7] & M);
+        z[7] = (int)c;
+        c >>= 32;
+        return (int)c;
+    }
+
     public static int subFrom(int[] x, int xOff, int[] z, int zOff)
     {
         long c = 0;
@@ -1377,6 +1508,36 @@ public static int subFrom(int[] x, int xOff, int[] z, int zOff)
         return (int)c;
     }
 
+    public static int subFrom(int[] x, int xOff, int[] z, int zOff, int cIn)
+    {
+        long c = cIn & M;
+        c += (z[zOff + 0] & M) - (x[xOff + 0] & M);
+        z[zOff + 0] = (int)c;
+        c >>= 32;
+        c += (z[zOff + 1] & M) - (x[xOff + 1] & M);
+        z[zOff + 1] = (int)c;
+        c >>= 32;
+        c += (z[zOff + 2] & M) - (x[xOff + 2] & M);
+        z[zOff + 2] = (int)c;
+        c >>= 32;
+        c += (z[zOff + 3] & M) - (x[xOff + 3] & M);
+        z[zOff + 3] = (int)c;
+        c >>= 32;
+        c += (z[zOff + 4] & M) - (x[xOff + 4] & M);
+        z[zOff + 4] = (int)c;
+        c >>= 32;
+        c += (z[zOff + 5] & M) - (x[xOff + 5] & M);
+        z[zOff + 5] = (int)c;
+        c >>= 32;
+        c += (z[zOff + 6] & M) - (x[xOff + 6] & M);
+        z[zOff + 6] = (int)c;
+        c >>= 32;
+        c += (z[zOff + 7] & M) - (x[xOff + 7] & M);
+        z[zOff + 7] = (int)c;
+        c >>= 32;
+        return (int)c;
+    }
+
     public static BigInteger toBigInteger(int[] x)
     {
         byte[] bs = new byte[32];

@@ -2,20 +2,19 @@
 
 import java.security.SecureRandom;
 
-import junit.framework.TestCase;
 import org.bouncycastle.crypto.Digest;
 import org.bouncycastle.math.ec.rfc8032.Ed25519;
 import org.bouncycastle.util.Arrays;
 import org.bouncycastle.util.Strings;
 import org.bouncycastle.util.encoders.Hex;
 
+import junit.framework.TestCase;
+
 public class Ed25519Test
     extends TestCase
 {
     private static final SecureRandom RANDOM = new SecureRandom();
 
-    private static final byte[] NEUTRAL = Hex.decodeStrict("0100000000000000000000000000000000000000000000000000000000000000");
-
 //    @BeforeClass
 //    public static void init()
     public void setUp()
@@ -28,6 +27,7 @@ public void testEd25519Consistency()
     {
         byte[] sk = new byte[Ed25519.SECRET_KEY_SIZE];
         byte[] pk = new byte[Ed25519.PUBLIC_KEY_SIZE];
+        byte[] pk2 = new byte[Ed25519.PUBLIC_KEY_SIZE];
         byte[] m = new byte[255];
         byte[] sig1 = new byte[Ed25519.SIGNATURE_SIZE];
         byte[] sig2 = new byte[Ed25519.SIGNATURE_SIZE];
@@ -37,7 +37,14 @@ public void testEd25519Consistency()
         for (int i = 0; i < 10; ++i)
         {
             RANDOM.nextBytes(sk);
-            Ed25519.generatePublicKey(sk, 0, pk, 0);
+            Ed25519.PublicPoint publicPoint = Ed25519.generatePublicKey(sk, 0);
+            Ed25519.encodePublicPoint(publicPoint, pk, 0);
+
+            {
+                Ed25519.generatePublicKey(sk, 0, pk2, 0);
+
+                assertTrue("Ed25519 consistent generation #" + i, Arrays.areEqual(pk, pk2));
+            }
 
             int mLen = RANDOM.nextInt() & 255;
 
@@ -46,14 +53,29 @@ public void testEd25519Consistency()
 
             assertTrue("Ed25519 consistent signatures #" + i, Arrays.areEqual(sig1, sig2));
 
-            boolean shouldVerify = Ed25519.verify(sig1, 0, pk, 0, m, 0, mLen);
+            {
+                boolean shouldVerify = Ed25519.verify(sig1, 0, pk, 0, m, 0, mLen);
 
-            assertTrue("Ed25519 consistent sign/verify #" + i, shouldVerify);
+                assertTrue("Ed25519 consistent sign/verify #" + i, shouldVerify);
+            }
+            {
+                boolean shouldVerify = Ed25519.verify(sig1, 0, publicPoint, m, 0, mLen);
+
+                assertTrue("Ed25519 consistent sign/verify #" + i, shouldVerify);
+            }
 
             sig1[Ed25519.PUBLIC_KEY_SIZE - 1] ^= 0x80;
-            boolean shouldNotVerify = Ed25519.verify(sig1, 0, pk, 0, m, 0, mLen);
 
-            assertFalse("Ed25519 consistent verification failure #" + i, shouldNotVerify);
+            {
+                boolean shouldNotVerify = Ed25519.verify(sig1, 0, pk, 0, m, 0, mLen);
+
+                assertFalse("Ed25519 consistent verification failure #" + i, shouldNotVerify);
+            }
+            {
+                boolean shouldNotVerify = Ed25519.verify(sig1, 0, publicPoint, m, 0, mLen);
+
+                assertFalse("Ed25519 consistent verification failure #" + i, shouldNotVerify);
+            }
         }
     }
     
@@ -62,6 +84,7 @@ public void testEd25519ctxConsistency()
     {
         byte[] sk = new byte[Ed25519.SECRET_KEY_SIZE];
         byte[] pk = new byte[Ed25519.PUBLIC_KEY_SIZE];
+        byte[] pk2 = new byte[Ed25519.PUBLIC_KEY_SIZE];
         byte[] ctx = new byte[RANDOM.nextInt() & 7];
         byte[] m = new byte[255];
         byte[] sig1 = new byte[Ed25519.SIGNATURE_SIZE];
@@ -73,7 +96,14 @@ public void testEd25519ctxConsistency()
         for (int i = 0; i < 10; ++i)
         {
             RANDOM.nextBytes(sk);
-            Ed25519.generatePublicKey(sk, 0, pk, 0);
+            Ed25519.PublicPoint publicPoint = Ed25519.generatePublicKey(sk, 0);
+            Ed25519.encodePublicPoint(publicPoint, pk, 0);
+
+            {
+                Ed25519.generatePublicKey(sk, 0, pk2, 0);
+
+                assertTrue("Ed25519 consistent generation #" + i, Arrays.areEqual(pk, pk2));
+            }
 
             int mLen = RANDOM.nextInt() & 255;
 
@@ -82,14 +112,29 @@ public void testEd25519ctxConsistency()
 
             assertTrue("Ed25519ctx consistent signatures #" + i, Arrays.areEqual(sig1, sig2));
 
-            boolean shouldVerify = Ed25519.verify(sig1, 0, pk, 0, ctx, m, 0, mLen);
+            {
+                boolean shouldVerify = Ed25519.verify(sig1, 0, pk, 0, ctx, m, 0, mLen);
+
+                assertTrue("Ed25519ctx consistent sign/verify #" + i, shouldVerify);
+            }
+            {
+                boolean shouldVerify = Ed25519.verify(sig1, 0, publicPoint, ctx, m, 0, mLen);
 
-            assertTrue("Ed25519ctx consistent sign/verify #" + i, shouldVerify);
+                assertTrue("Ed25519ctx consistent sign/verify #" + i, shouldVerify);
+            }
 
             sig1[Ed25519.PUBLIC_KEY_SIZE - 1] ^= 0x80;
-            boolean shouldNotVerify = Ed25519.verify(sig1, 0, pk, 0, ctx, m, 0, mLen);
 
-            assertFalse("Ed25519ctx consistent verification failure #" + i, shouldNotVerify);
+            {
+                boolean shouldNotVerify = Ed25519.verify(sig1, 0, pk, 0, ctx, m, 0, mLen);
+
+                assertFalse("Ed25519ctx consistent verification failure #" + i, shouldNotVerify);
+            }
+            {
+                boolean shouldNotVerify = Ed25519.verify(sig1, 0, publicPoint, ctx, m, 0, mLen);
+
+                assertFalse("Ed25519ctx consistent verification failure #" + i, shouldNotVerify);
+            }
         }
     }
     
@@ -98,6 +143,7 @@ public void testEd25519phConsistency()
     {
         byte[] sk = new byte[Ed25519.SECRET_KEY_SIZE];
         byte[] pk = new byte[Ed25519.PUBLIC_KEY_SIZE];
+        byte[] pk2 = new byte[Ed25519.PUBLIC_KEY_SIZE];
         byte[] ctx = new byte[RANDOM.nextInt() & 7];
         byte[] m = new byte[255];
         byte[] ph = new byte[Ed25519.PREHASH_SIZE];
@@ -110,7 +156,14 @@ public void testEd25519phConsistency()
         for (int i = 0; i < 10; ++i)
         {
             RANDOM.nextBytes(sk);
-            Ed25519.generatePublicKey(sk, 0, pk, 0);
+            Ed25519.PublicPoint publicPoint = Ed25519.generatePublicKey(sk, 0);
+            Ed25519.encodePublicPoint(publicPoint, pk, 0);
+
+            {
+                Ed25519.generatePublicKey(sk, 0, pk2, 0);
+
+                assertTrue("Ed25519 consistent generation #" + i, Arrays.areEqual(pk, pk2));
+            }
 
             int mLen = RANDOM.nextInt() & 255;
 
@@ -123,14 +176,29 @@ public void testEd25519phConsistency()
 
             assertTrue("Ed25519ph consistent signatures #" + i, Arrays.areEqual(sig1, sig2));
 
-            boolean shouldVerify = Ed25519.verifyPrehash(sig1, 0, pk, 0, ctx, ph, 0);
+            {
+                boolean shouldVerify = Ed25519.verifyPrehash(sig1, 0, pk, 0, ctx, ph, 0);
+
+                assertTrue("Ed25519ph consistent sign/verify #" + i, shouldVerify);
+            }
+            {
+                boolean shouldVerify = Ed25519.verifyPrehash(sig1, 0, publicPoint, ctx, ph, 0);
 
-            assertTrue("Ed25519ph consistent sign/verify #" + i, shouldVerify);
+                assertTrue("Ed25519ph consistent sign/verify #" + i, shouldVerify);
+            }
 
             sig1[Ed25519.PUBLIC_KEY_SIZE - 1] ^= 0x80;
-            boolean shouldNotVerify = Ed25519.verifyPrehash(sig1, 0, pk, 0, ctx, ph, 0);
 
-            assertFalse("Ed25519ph consistent verification failure #" + i, shouldNotVerify);
+            {
+                boolean shouldNotVerify = Ed25519.verifyPrehash(sig1, 0, pk, 0, ctx, ph, 0);
+
+                assertFalse("Ed25519ph consistent verification failure #" + i, shouldNotVerify);
+            }
+            {
+                boolean shouldNotVerify = Ed25519.verifyPrehash(sig1, 0, publicPoint, ctx, ph, 0);
+
+                assertFalse("Ed25519ph consistent verification failure #" + i, shouldNotVerify);
+            }
         }
     }
 
@@ -370,8 +438,6 @@ public void testEd25519phVector1()
 
     public void testPublicKeyValidationFull()
     {
-        assertFalse(Ed25519.validatePublicKeyFull(NEUTRAL, 0));
-
         byte[] sk = new byte[Ed25519.SECRET_KEY_SIZE];
         byte[] pk = new byte[Ed25519.PUBLIC_KEY_SIZE];
 
@@ -382,11 +448,24 @@ public void testPublicKeyValidationFull()
             assertTrue(Ed25519.validatePublicKeyFull(pk, 0));
         }
 
+        // Small order points (canonical encodings)
+        assertFalse(Ed25519.validatePublicKeyFull(Hex.decodeStrict("0000000000000000000000000000000000000000000000000000000000000000"), 0));
+        assertFalse(Ed25519.validatePublicKeyFull(Hex.decodeStrict("0000000000000000000000000000000000000000000000000000000000000080"), 0));
+        assertFalse(Ed25519.validatePublicKeyFull(Hex.decodeStrict("0100000000000000000000000000000000000000000000000000000000000000"), 0));
+        assertFalse(Ed25519.validatePublicKeyFull(Hex.decodeStrict("ECFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7F"), 0));
+        assertFalse(Ed25519.validatePublicKeyFull(Hex.decodeStrict("C7176A703D4DD84FBA3C0B760D10670F2A2053FA2C39CCC64EC7FD7792AC037A"), 0));
+        assertFalse(Ed25519.validatePublicKeyFull(Hex.decodeStrict("C7176A703D4DD84FBA3C0B760D10670F2A2053FA2C39CCC64EC7FD7792AC03FA"), 0));
+        assertFalse(Ed25519.validatePublicKeyFull(Hex.decodeStrict("26E8958FC2B227B045C3F489F2EF98F0D5DFAC05D3C63339B13802886D53FC05"), 0));
+        assertFalse(Ed25519.validatePublicKeyFull(Hex.decodeStrict("26E8958FC2B227B045C3F489F2EF98F0D5DFAC05D3C63339B13802886D53FC85"), 0));
+
+        // Small order points (non-canonical encodings)
         assertFalse(Ed25519.validatePublicKeyFull(Hex.decodeStrict("0100000000000000000000000000000000000000000000000000000000000080"), 0));
+        assertFalse(Ed25519.validatePublicKeyFull(Hex.decodeStrict("ECFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"), 0));
 
-        assertFalse(Ed25519.validatePublicKeyFull(Hex.decodeStrict("ECFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7F"), 0));
+        // Non-canonical encodings
         assertFalse(Ed25519.validatePublicKeyFull(Hex.decodeStrict("EDFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7F"), 0));
-        assertFalse(Ed25519.validatePublicKeyFull(Hex.decodeStrict("EDFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"), 0));        assertFalse(Ed25519.validatePublicKeyFull(Hex.decodeStrict("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7F"), 0));
+        assertFalse(Ed25519.validatePublicKeyFull(Hex.decodeStrict("EDFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"), 0));
+        assertFalse(Ed25519.validatePublicKeyFull(Hex.decodeStrict("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7F"), 0));
         assertFalse(Ed25519.validatePublicKeyFull(Hex.decodeStrict("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"), 0));
 
         assertFalse(Ed25519.validatePublicKeyFull(Hex.decodeStrict("D73D6044821BD0DF4068AE1792F0851170F53062150AA70A87E2A58A05A26115"), 0));
@@ -414,8 +493,6 @@ public void testPublicKeyValidationFull()
 
     public void testPublicKeyValidationPartial()
     {
-        assertTrue(Ed25519.validatePublicKeyPartial(NEUTRAL, 0));
-
         byte[] sk = new byte[Ed25519.SECRET_KEY_SIZE];
         byte[] pk = new byte[Ed25519.PUBLIC_KEY_SIZE];
 
@@ -426,11 +503,23 @@ public void testPublicKeyValidationPartial()
             assertTrue(Ed25519.validatePublicKeyPartial(pk, 0));
         }
 
+        // Small order points (canonical encodings)
+        assertFalse(Ed25519.validatePublicKeyPartial(Hex.decodeStrict("0000000000000000000000000000000000000000000000000000000000000000"), 0));
+        assertFalse(Ed25519.validatePublicKeyPartial(Hex.decodeStrict("0000000000000000000000000000000000000000000000000000000000000080"), 0));
+        assertFalse(Ed25519.validatePublicKeyPartial(Hex.decodeStrict("0100000000000000000000000000000000000000000000000000000000000000"), 0));
+        assertFalse(Ed25519.validatePublicKeyPartial(Hex.decodeStrict("ECFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7F"), 0));
+        assertFalse(Ed25519.validatePublicKeyPartial(Hex.decodeStrict("C7176A703D4DD84FBA3C0B760D10670F2A2053FA2C39CCC64EC7FD7792AC037A"), 0));
+        assertFalse(Ed25519.validatePublicKeyPartial(Hex.decodeStrict("C7176A703D4DD84FBA3C0B760D10670F2A2053FA2C39CCC64EC7FD7792AC03FA"), 0));
+        assertFalse(Ed25519.validatePublicKeyPartial(Hex.decodeStrict("26E8958FC2B227B045C3F489F2EF98F0D5DFAC05D3C63339B13802886D53FC05"), 0));
+        assertFalse(Ed25519.validatePublicKeyPartial(Hex.decodeStrict("26E8958FC2B227B045C3F489F2EF98F0D5DFAC05D3C63339B13802886D53FC85"), 0));
+
+        // Small order points (non-canonical encodings)
         assertFalse(Ed25519.validatePublicKeyPartial(Hex.decodeStrict("0100000000000000000000000000000000000000000000000000000000000080"), 0));
+        assertFalse(Ed25519.validatePublicKeyPartial(Hex.decodeStrict("ECFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"), 0));
 
-        assertTrue (Ed25519.validatePublicKeyPartial(Hex.decodeStrict("ECFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7F"), 0));
+        // Non-canonical encodings
         assertFalse(Ed25519.validatePublicKeyPartial(Hex.decodeStrict("EDFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7F"), 0));
-        assertFalse(Ed25519.validatePublicKeyPartial(Hex.decodeStrict("EDFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"), 0));        
+        assertFalse(Ed25519.validatePublicKeyPartial(Hex.decodeStrict("EDFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"), 0));
         assertFalse(Ed25519.validatePublicKeyPartial(Hex.decodeStrict("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7F"), 0));
         assertFalse(Ed25519.validatePublicKeyPartial(Hex.decodeStrict("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"), 0));
 
@@ -463,22 +552,19 @@ public void testPublicKeyValidationPartial()
 
     public void testTamingNonRepudiation()
     {
-        // TODO Algorithm 2 rejects this because A is one of 8 small order points
-
         byte[] msg1 = Strings.toUTF8ByteArray("Send 100 USD to Alice");
         byte[] msg2 = Strings.toUTF8ByteArray("Send 100000 USD to Alice");
         byte[] pub = Hex.decodeStrict("ecffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7f");
         byte[] sig = Hex.decodeStrict("a9d55260f765261eb9b84e106f665e00b867287a761990d7135963ee0a7d59dc" +
                                       "a5bb704786be79fc476f91d3f3f89b03984d8068dcf1bb7dfc6637b45450ac04");
 
-        assertTrue(Ed25519.verify(sig, 0, pub, 0, msg1, 0, msg1.length));
-        assertTrue(Ed25519.verify(sig, 0, pub, 0, msg2, 0, msg2.length));
+        assertFalse(Ed25519.verify(sig, 0, pub, 0, msg1, 0, msg1.length));
+        assertFalse(Ed25519.verify(sig, 0, pub, 0, msg2, 0, msg2.length));
     }
 
     public void testTamingVector_00()
     {
-        // TODO Algorithm 2 rejects this because A is one of 8 small order points
-        implTamingVector(0, true,
+        implTamingVector(0, false,
             "8c93255d71dcab10e8f379c26200f3c7bd5f09d9bc3068d3ef4edeb4853022b6",
             "c7176a703d4dd84fba3c0b760d10670f2a2053fa2c39ccc64ec7fd7792ac03fa",
             "c7176a703d4dd84fba3c0b760d10670f2a2053fa2c39ccc64ec7fd7792ac037a" +
@@ -487,8 +573,7 @@ public void testTamingVector_00()
 
     public void testTamingVector_01()
     {
-        // TODO Algorithm 2 rejects this because A is one of 8 small order points
-        implTamingVector(1, true,
+        implTamingVector(1, false,
             "9bd9f44f4dcc75bd531b56b2cd280b0bb38fc1cd6d1230e14861d861de092e79",
             "c7176a703d4dd84fba3c0b760d10670f2a2053fa2c39ccc64ec7fd7792ac03fa",
             "f7badec5b8abeaf699583992219b7b223f1df3fbbea919844e3f7c554a43dd43" +
@@ -517,8 +602,7 @@ public void testTamingVector_03()
 
     public void testTamingVector_04()
     {
-        // TODO Algorithm 2 accepts this (cofactored verification)
-        implTamingVector(4, false,
+        implTamingVector(4, true,
             "e47d62c63f830dc7a6851a0b1f33ae4bb2f507fb6cffec4011eaccd55b53f56c",
             "cdb267ce40c5cd45306fa5d2f29731459387dbf9eb933b7bd5aed9a765b88d4d",
             "160a1cb0dc9c0258cd0a7d23e94d8fa878bcb1925f2c64246b2dee1796bed512" +
@@ -527,8 +611,7 @@ public void testTamingVector_04()
 
     public void testTamingVector_05()
     {
-        // TODO Algorithm 2 accepts this (cofactored verification)
-        implTamingVector(5, false,
+        implTamingVector(5, true,
             "e47d62c63f830dc7a6851a0b1f33ae4bb2f507fb6cffec4011eaccd55b53f56c",
             "cdb267ce40c5cd45306fa5d2f29731459387dbf9eb933b7bd5aed9a765b88d4d",
             "21122a84e0b5fca4052f5b1235c80a537878b38f3142356b2c2384ebad4668b7" +

@@ -2,19 +2,18 @@
 
 import java.security.SecureRandom;
 
-import junit.framework.TestCase;
 import org.bouncycastle.crypto.Xof;
 import org.bouncycastle.math.ec.rfc8032.Ed448;
 import org.bouncycastle.util.Arrays;
 import org.bouncycastle.util.encoders.Hex;
 
+import junit.framework.TestCase;
+
 public class Ed448Test
     extends TestCase
 {
     private static final SecureRandom RANDOM = new SecureRandom();
 
-    private static final byte[] NEUTRAL = Hex.decodeStrict("010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000");
-
 //    @BeforeClass
 //    public static void init()
     public void setUp()
@@ -27,6 +26,7 @@ public void testEd448Consistency()
     {
         byte[] sk = new byte[Ed448.SECRET_KEY_SIZE];
         byte[] pk = new byte[Ed448.PUBLIC_KEY_SIZE];
+        byte[] pk2 = new byte[Ed448.PUBLIC_KEY_SIZE];
         byte[] ctx = new byte[RANDOM.nextInt() & 7];
         byte[] m = new byte[255];
         byte[] sig1 = new byte[Ed448.SIGNATURE_SIZE];
@@ -38,7 +38,14 @@ public void testEd448Consistency()
         for (int i = 0; i < 10; ++i)
         {
             RANDOM.nextBytes(sk);
-            Ed448.generatePublicKey(sk, 0, pk, 0);
+            Ed448.PublicPoint publicPoint = Ed448.generatePublicKey(sk, 0);
+            Ed448.encodePublicPoint(publicPoint, pk, 0);
+
+            {
+                Ed448.generatePublicKey(sk, 0, pk2, 0);
+
+                assertTrue("Ed448 consistent generation #" + i, Arrays.areEqual(pk, pk2));
+            }
 
             int mLen = RANDOM.nextInt() & 255;
 
@@ -47,14 +54,29 @@ public void testEd448Consistency()
 
             assertTrue("Ed448 consistent signatures #" + i, Arrays.areEqual(sig1, sig2));
 
-            boolean shouldVerify = Ed448.verify(sig1, 0, pk, 0, ctx, m, 0, mLen);
+            {
+                boolean shouldVerify = Ed448.verify(sig1, 0, pk, 0, ctx, m, 0, mLen);
+
+                assertTrue("Ed448 consistent sign/verify #" + i, shouldVerify);
+            }
+            {
+                boolean shouldVerify = Ed448.verify(sig1, 0, publicPoint, ctx, m, 0, mLen);
 
-            assertTrue("Ed448 consistent sign/verify #" + i, shouldVerify);
+                assertTrue("Ed448 consistent sign/verify #" + i, shouldVerify);
+            }
 
             sig1[Ed448.PUBLIC_KEY_SIZE - 1] ^= 0x80;
-            boolean shouldNotVerify = Ed448.verify(sig1, 0, pk, 0, ctx, m, 0, mLen);
 
-            assertFalse("Ed448 consistent verification failure #" + i, shouldNotVerify);
+            {
+                boolean shouldNotVerify = Ed448.verify(sig1, 0, pk, 0, ctx, m, 0, mLen);
+
+                assertFalse("Ed448 consistent verification failure #" + i, shouldNotVerify);
+            }
+            {
+                boolean shouldNotVerify = Ed448.verify(sig1, 0, publicPoint, ctx, m, 0, mLen);
+
+                assertFalse("Ed448 consistent verification failure #" + i, shouldNotVerify);
+            }
         }
     }
 
@@ -63,6 +85,7 @@ public void testEd448phConsistency()
     {
         byte[] sk = new byte[Ed448.SECRET_KEY_SIZE];
         byte[] pk = new byte[Ed448.PUBLIC_KEY_SIZE];
+        byte[] pk2 = new byte[Ed448.PUBLIC_KEY_SIZE];
         byte[] ctx = new byte[RANDOM.nextInt() & 7];
         byte[] m = new byte[255];
         byte[] ph = new byte[Ed448.PREHASH_SIZE];
@@ -75,7 +98,14 @@ public void testEd448phConsistency()
         for (int i = 0; i < 10; ++i)
         {
             RANDOM.nextBytes(sk);
-            Ed448.generatePublicKey(sk, 0, pk, 0);
+            Ed448.PublicPoint publicPoint = Ed448.generatePublicKey(sk, 0);
+            Ed448.encodePublicPoint(publicPoint, pk, 0);
+
+            {
+                Ed448.generatePublicKey(sk, 0, pk2, 0);
+
+                assertTrue("Ed448 consistent generation #" + i, Arrays.areEqual(pk, pk2));
+            }
 
             int mLen = RANDOM.nextInt() & 255;
 
@@ -88,14 +118,29 @@ public void testEd448phConsistency()
 
             assertTrue("Ed448ph consistent signatures #" + i, Arrays.areEqual(sig1, sig2));
 
-            boolean shouldVerify = Ed448.verifyPrehash(sig1, 0, pk, 0, ctx, ph, 0);
+            {
+                boolean shouldVerify = Ed448.verifyPrehash(sig1, 0, pk, 0, ctx, ph, 0);
 
-            assertTrue("Ed448ph consistent sign/verify #" + i, shouldVerify);
+                assertTrue("Ed448ph consistent sign/verify #" + i, shouldVerify);
+            }
+            {
+                boolean shouldVerify = Ed448.verifyPrehash(sig1, 0, publicPoint, ctx, ph, 0);
+
+                assertTrue("Ed448ph consistent sign/verify #" + i, shouldVerify);
+            }
 
             sig1[Ed448.PUBLIC_KEY_SIZE - 1] ^= 0x80;
-            boolean shouldNotVerify = Ed448.verifyPrehash(sig1, 0, pk, 0, ctx, ph, 0);
 
-            assertFalse("Ed448ph consistent verification failure #" + i, shouldNotVerify);
+            {
+                boolean shouldNotVerify = Ed448.verifyPrehash(sig1, 0, pk, 0, ctx, ph, 0);
+
+                assertFalse("Ed448ph consistent verification failure #" + i, shouldNotVerify);
+            }
+            {
+                boolean shouldNotVerify = Ed448.verifyPrehash(sig1, 0, publicPoint, ctx, ph, 0);
+
+                assertFalse("Ed448ph consistent verification failure #" + i, shouldNotVerify);
+            }
         }
     }
 
@@ -466,8 +511,6 @@ public void testEd448phVector2()
 
     public void testPublicKeyValidationFull()
     {
-        assertFalse(Ed448.validatePublicKeyFull(NEUTRAL, 0));
-
         byte[] sk = new byte[Ed448.SECRET_KEY_SIZE];
         byte[] pk = new byte[Ed448.PUBLIC_KEY_SIZE];
 
@@ -478,13 +521,21 @@ public void testPublicKeyValidationFull()
             assertTrue(Ed448.validatePublicKeyFull(pk, 0));
         }
 
+        // Small order points (canonical encodings)
+        assertFalse(Ed448.validatePublicKeyFull(Hex.decodeStrict("000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), 0));
+        assertFalse(Ed448.validatePublicKeyFull(Hex.decodeStrict("000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000080"), 0));
+        assertFalse(Ed448.validatePublicKeyFull(Hex.decodeStrict("010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), 0));
+        assertFalse(Ed448.validatePublicKeyFull(Hex.decodeStrict("FEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00"), 0));
+
+        // Small order points (non-canonical encodings)
         assertFalse(Ed448.validatePublicKeyFull(Hex.decodeStrict("010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000080"), 0));
+        assertFalse(Ed448.validatePublicKeyFull(Hex.decodeStrict("FEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF80"), 0));
 
-        assertFalse(Ed448.validatePublicKeyFull(Hex.decodeStrict("FEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00"), 0));
-        assertFalse(Ed448.validatePublicKeyFull(Hex.decodeStrict("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00"), 0));
-        assertFalse(Ed448.validatePublicKeyFull(Hex.decodeStrict("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF80"), 0));        
-        assertFalse(Ed448.validatePublicKeyFull(Hex.decodeStrict("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00"), 0));
-        assertFalse(Ed448.validatePublicKeyFull(Hex.decodeStrict("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF80"), 0));
+        // Non-canonical encodings
+        assertFalse(Ed448.validatePublicKeyFull(Hex.decodeStrict("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00"), 0));
+        assertFalse(Ed448.validatePublicKeyFull(Hex.decodeStrict("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF80"), 0));
+        assertFalse(Ed448.validatePublicKeyFull(Hex.decodeStrict("00000000000000000000000000000000000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00"), 0));
+        assertFalse(Ed448.validatePublicKeyFull(Hex.decodeStrict("00000000000000000000000000000000000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF80"), 0));
         assertFalse(Ed448.validatePublicKeyFull(Hex.decodeStrict("000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001"), 0));
         assertFalse(Ed448.validatePublicKeyFull(Hex.decodeStrict("000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000081"), 0));
 
@@ -513,8 +564,6 @@ public void testPublicKeyValidationFull()
 
     public void testPublicKeyValidationPartial()
     {
-        assertTrue(Ed448.validatePublicKeyPartial(NEUTRAL, 0));
-
         byte[] sk = new byte[Ed448.SECRET_KEY_SIZE];
         byte[] pk = new byte[Ed448.PUBLIC_KEY_SIZE];
 
@@ -525,13 +574,21 @@ public void testPublicKeyValidationPartial()
             assertTrue(Ed448.validatePublicKeyPartial(pk, 0));
         }
 
+        // Small order points (canonical encodings)
+        assertFalse(Ed448.validatePublicKeyPartial(Hex.decodeStrict("000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), 0));
+        assertFalse(Ed448.validatePublicKeyPartial(Hex.decodeStrict("000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000080"), 0));
+        assertFalse(Ed448.validatePublicKeyPartial(Hex.decodeStrict("010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), 0));
+        assertFalse(Ed448.validatePublicKeyPartial(Hex.decodeStrict("FEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00"), 0));
+
+        // Small order points (non-canonical encodings)
         assertFalse(Ed448.validatePublicKeyPartial(Hex.decodeStrict("010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000080"), 0));
+        assertFalse(Ed448.validatePublicKeyPartial(Hex.decodeStrict("FEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF80"), 0));
 
-        assertTrue (Ed448.validatePublicKeyPartial(Hex.decodeStrict("FEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00"), 0));
-        assertFalse(Ed448.validatePublicKeyPartial(Hex.decodeStrict("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00"), 0));
-        assertFalse(Ed448.validatePublicKeyPartial(Hex.decodeStrict("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF80"), 0));        
-        assertFalse(Ed448.validatePublicKeyPartial(Hex.decodeStrict("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00"), 0));
-        assertFalse(Ed448.validatePublicKeyPartial(Hex.decodeStrict("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF80"), 0));
+        // Non-canonical encodings
+        assertFalse(Ed448.validatePublicKeyPartial(Hex.decodeStrict("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00"), 0));
+        assertFalse(Ed448.validatePublicKeyPartial(Hex.decodeStrict("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF80"), 0));
+        assertFalse(Ed448.validatePublicKeyPartial(Hex.decodeStrict("00000000000000000000000000000000000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00"), 0));
+        assertFalse(Ed448.validatePublicKeyPartial(Hex.decodeStrict("00000000000000000000000000000000000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF80"), 0));
         assertFalse(Ed448.validatePublicKeyPartial(Hex.decodeStrict("000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001"), 0));
         assertFalse(Ed448.validatePublicKeyPartial(Hex.decodeStrict("000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000081"), 0));