Remove some length-specific methods in favour of the Nat class

Add more method variations to Nat
Use customized reductions in various fields

12 files changed, 487 insertions, 558 deletions

diff --git a/crypto/src/math/ec/Nat.cs b/crypto/src/math/ec/Nat.cs
index 8dbd6780d..17b632f26 100644
--- a/crypto/src/math/ec/Nat.cs
+++ b/crypto/src/math/ec/Nat.cs
@@ -21,6 +21,52 @@ namespace Org.BouncyCastle.Math.EC
             return (uint)c;
         }
 
+        public static uint Add33At(int len, uint x, uint[] z, int zPos)
+        {
+            Debug.Assert(zPos <= (len - 2));
+            ulong c = (ulong)z[zPos + 0] + x;
+            z[zPos + 0] = (uint)c;
+            c >>= 32;
+            c += (ulong)z[zPos + 1] + 1;
+            z[zPos + 1] = (uint)c;
+            c >>= 32;
+            return c == 0 ? 0 : IncAt(len, z, zPos + 2);
+        }
+
+        public static uint Add33At(int len, uint x, uint[] z, int zOff, int zPos)
+        {
+            Debug.Assert(zPos <= (len - 2));
+            ulong c = (ulong)z[zOff + zPos] + x;
+            z[zOff + zPos] = (uint)c;
+            c >>= 32;
+            c += (ulong)z[zOff + zPos + 1] + 1;
+            z[zOff + zPos + 1] = (uint)c;
+            c >>= 32;
+            return c == 0 ? 0 : IncAt(len, z, zOff, zPos + 2);
+        }
+
+        public static uint Add33To(int len, uint x, uint[] z)
+        {
+            ulong c = (ulong)z[0] + x;
+            z[0] = (uint)c;
+            c >>= 32;
+            c += (ulong)z[1] + 1;
+            z[1] = (uint)c;
+            c >>= 32;
+            return c == 0 ? 0 : IncAt(len, z, 2);
+        }
+
+        public static uint Add33To(int len, uint x, uint[] z, int zOff)
+        {
+            ulong c = (ulong)z[zOff + 0] + x;
+            z[zOff + 0] = (uint)c;
+            c >>= 32;
+            c += (ulong)z[zOff + 1] + 1;
+            z[zOff + 1] = (uint)c;
+            c >>= 32;
+            return c == 0 ? 0 : IncAt(len, z, zOff, 2);
+        }
+
         public static uint AddBothTo(int len, uint[] x, uint[] y, uint[] z)
         {
             ulong c = 0;
@@ -57,6 +103,40 @@ namespace Org.BouncyCastle.Math.EC
             return c == 0 ? 0 : IncAt(len, z, zPos + 2);
         }
 
+        public static uint AddDWordAt(int len, ulong x, uint[] z, int zOff, int zPos)
+        {
+            Debug.Assert(zPos <= (len - 2));
+            ulong c = (ulong)z[zOff + zPos] + (x & M);
+            z[zOff + zPos] = (uint)c;
+            c >>= 32;
+            c += (ulong)z[zOff + zPos + 1] + (x >> 32);
+            z[zOff + zPos + 1] = (uint)c;
+            c >>= 32;
+            return c == 0 ? 0 : IncAt(len, z, zOff, zPos + 2);
+        }
+
+        public static uint AddDWordTo(int len, ulong x, uint[] z)
+        {
+            ulong c = (ulong)z[0] + (x & M);
+            z[0] = (uint)c;
+            c >>= 32;
+            c += (ulong)z[1] + (x >> 32);
+            z[1] = (uint)c;
+            c >>= 32;
+            return c == 0 ? 0 : IncAt(len, z, 2);
+        }
+
+        public static uint AddDWordTo(int len, ulong x, uint[] z, int zOff)
+        {
+            ulong c = (ulong)z[zOff + 0] + (x & M);
+            z[zOff + 0] = (uint)c;
+            c >>= 32;
+            c += (ulong)z[zOff + 1] + (x >> 32);
+            z[zOff + 1] = (uint)c;
+            c >>= 32;
+            return c == 0 ? 0 : IncAt(len, z, zOff, 2);
+        }
+
         public static uint AddTo(int len, uint[] x, uint[] z)
         {
             ulong c = 0;
@@ -99,6 +179,22 @@ namespace Org.BouncyCastle.Math.EC
             return c == 0 ? 0 : IncAt(len, z, zOff, zPos + 1);
         }
 
+        public static uint AddWordTo(int len, uint x, uint[] z)
+        {
+            ulong c = (ulong)x + z[0];
+            z[0] = (uint)c;
+            c >>= 32;
+            return c == 0 ? 0 : IncAt(len, z, 1);
+        }
+
+        public static uint AddWordTo(int len, uint x, uint[] z, int zOff)
+        {
+            ulong c = (ulong)x + z[zOff];
+            z[zOff] = (uint)c;
+            c >>= 32;
+            return c == 0 ? 0 : IncAt(len, z, zOff, 1);
+        }
+
         public static void Copy(int len, uint[] x, uint[] z)
         {
             Array.Copy(x, 0, z, 0, len);
@@ -134,10 +230,15 @@ namespace Org.BouncyCastle.Math.EC
             while (i < len)
             {
                 uint c = x[i] - 1;
-                z[i++] = c;
+                z[i] = c;
+                ++i;
                 if (c != uint.MaxValue)
                 {
-                    Array.Copy(x, i, z, i, len - i);
+                    while (i < len)
+                    {
+                        z[i] = x[i];
+                        ++i;
+                    }
                     return 0;
                 }
             }
@@ -244,10 +345,15 @@ namespace Org.BouncyCastle.Math.EC
             while (i < len)
             {
                 uint c = x[i] + 1;
-                z[i++] = c;
+                z[i] = c;
+                ++i;
                 if (c != 0)
                 {
-                    Array.Copy(x, i, z, i, len - i);
+                    while (i < len)
+                    {
+                        z[i] = x[i];
+                        ++i;
+                    }
                     return 0;
                 }
             }
@@ -708,6 +814,51 @@ namespace Org.BouncyCastle.Math.EC
             }
             return (int)c;
         }
+        public static int Sub33At(int len, uint x, uint[] z, int zPos)
+        {
+            Debug.Assert(zPos <= (len - 2));
+            long c = (long)z[zPos + 0] - x;
+            z[zPos + 0] = (uint)c;
+            c >>= 32;
+            c += (long)z[zPos + 1] - 1;
+            z[zPos + 1] = (uint)c;
+            c >>= 32;
+            return c == 0 ? 0 : DecAt(len, z, zPos + 2);
+        }
+
+        public static int Sub33At(int len, uint x, uint[] z, int zOff, int zPos)
+        {
+            Debug.Assert(zPos <= (len - 2));
+            long c = (long)z[zOff + zPos] - x;
+            z[zOff + zPos] = (uint)c;
+            c >>= 32;
+            c += (long)z[zOff + zPos + 1] - 1;
+            z[zOff + zPos + 1] = (uint)c;
+            c >>= 32;
+            return c == 0 ? 0 : DecAt(len, z, zOff, zPos + 2);
+        }
+
+        public static int Sub33From(int len, uint x, uint[] z)
+        {
+            long c = (long)z[0] - x;
+            z[0] = (uint)c;
+            c >>= 32;
+            c += (long)z[1] - 1;
+            z[1] = (uint)c;
+            c >>= 32;
+            return c == 0 ? 0 : DecAt(len, z, 2);
+        }
+
+        public static int Sub33From(int len, uint x, uint[] z, int zOff)
+        {
+            long c = (long)z[zOff + 0] - x;
+            z[zOff + 0] = (uint)c;
+            c >>= 32;
+            c += (long)z[zOff + 1] - 1;
+            z[zOff + 1] = (uint)c;
+            c >>= 32;
+            return c == 0 ? 0 : DecAt(len, z, zOff, 2);
+        }
 
         public static int SubBothFrom(int len, uint[] x, uint[] y, uint[] z)
         {
@@ -745,6 +896,40 @@ namespace Org.BouncyCastle.Math.EC
             return c == 0 ? 0 : DecAt(len, z, zPos + 2);
         }
 
+        public static int SubDWordAt(int len, ulong x, uint[] z, int zOff, int zPos)
+        {
+            Debug.Assert(zPos <= (len - 2));
+            long c = (long)z[zOff + zPos] - (long)(x & M);
+            z[zOff + zPos] = (uint)c;
+            c >>= 32;
+            c += (long)z[zOff + zPos + 1] - (long)(x >> 32);
+            z[zOff + zPos + 1] = (uint)c;
+            c >>= 32;
+            return c == 0 ? 0 : DecAt(len, z,  zOff, zPos + 2);
+        }
+
+        public static int SubDWordFrom(int len, ulong x, uint[] z)
+        {
+            long c = (long)z[0] - (long)(x & M);
+            z[0] = (uint)c;
+            c >>= 32;
+            c += (long)z[1] - (long)(x >> 32);
+            z[1] = (uint)c;
+            c >>= 32;
+            return c == 0 ? 0 : DecAt(len, z, 2);
+        }
+
+        public static int SubDWordFrom(int len, ulong x, uint[] z, int zOff)
+        {
+            long c = (long)z[zOff + 0] - (long)(x & M);
+            z[zOff + 0] = (uint)c;
+            c >>= 32;
+            c += (long)z[zOff + 1] - (long)(x >> 32);
+            z[zOff + 1] = (uint)c;
+            c >>= 32;
+            return c == 0 ? 0 : DecAt(len, z, zOff, 2);
+        }
+
         public static int SubFrom(int len, uint[] x, uint[] z)
         {
             long c = 0;
@@ -787,6 +972,22 @@ namespace Org.BouncyCastle.Math.EC
             return c == 0 ? 0 : DecAt(len, z, zOff, zPos + 1);
         }
 
+        public static int SubWordFrom(int len, uint x, uint[] z)
+        {
+            long c = (long)z[0] - x;
+            z[0] = (uint)c;
+            c >>= 32;
+            return c == 0 ? 0 : DecAt(len, z, 1);
+        }
+
+        public static int SubWordFrom(int len, uint x, uint[] z, int zOff)
+        {
+            long c = (long)z[zOff + 0] - x;
+            z[zOff + 0] = (uint)c;
+            c >>= 32;
+            return c == 0 ? 0 : DecAt(len, z, zOff, 1);
+        }
+
         public static BigInteger ToBigInteger(int len, uint[] x)
         {
             byte[] bs = new byte[len << 2];
diff --git a/crypto/src/math/ec/custom/sec/Curve25519Field.cs b/crypto/src/math/ec/custom/sec/Curve25519Field.cs
index c272cbc38..c2924a2a0 100644
--- a/crypto/src/math/ec/custom/sec/Curve25519Field.cs
+++ b/crypto/src/math/ec/custom/sec/Curve25519Field.cs
@@ -19,28 +19,25 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             Nat256.Add(x, y, z);
             if (Nat256.Gte(z, P))
             {
-                Nat256.AddWord(PInv, z, 0);
-                z[7] &= P7;
+                AddPInvTo(z);
             }
         }
 
         public static void AddExt(uint[] xx, uint[] yy, uint[] zz)
         {
-            Nat256.AddExt(xx, yy, zz);
+            Nat.Add(16, xx, yy, zz);
             if (Nat256.GteExt(zz, PExt))
             {
-                Nat256.SubExt(zz, PExt, zz);
+                Nat.SubFrom(16, PExt, zz);
             }
         }
 
         public static void AddOne(uint[] x, uint[] z)
         {
-            Nat256.Copy(x, z);
-            Nat256.Inc(z, 0);
+            Nat.Inc(8, x, z);
             if (Nat256.Gte(z, P))
             {
-                Nat256.AddWord(PInv, z, 0);
-                z[7] &= P7;
+                AddPInvTo(z);
             }
         }
 
@@ -96,11 +93,10 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             uint z07 = z[7];
             z[7] = z07 & P7;
             c += (z07 >> 31) - (xx07 >> 31);
-            Nat256.AddWord(c * PInv, z, 0);
+            Nat.AddWordTo(8, c * PInv, z);
             if (Nat256.Gte(z, P))
             {
-                Nat256.AddWord(PInv, z, 0);
-                z[7] &= P7;
+                AddPInvTo(z);
             }
         }
 
@@ -131,17 +127,16 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             int c = Nat256.Sub(x, y, z);
             if (c != 0)
             {
-                Nat256.SubWord(PInv, z, 0);
-                z[7] &= P7;
+                SubPInvFrom(z);
             }
         }
 
         public static void SubtractExt(uint[] xx, uint[] yy, uint[] zz)
         {
-            int c = Nat256.SubExt(xx, yy, zz);
+            int c = Nat.Sub(16, xx, yy, zz);
             if (c != 0)
             {
-                Nat256.AddExt(zz, PExt, zz);
+                Nat.AddTo(16, PExt, zz);
             }
         }
 
@@ -150,9 +145,32 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             Nat.ShiftUpBit(8, x, 0, z);
             if (Nat256.Gte(z, P))
             {
-                Nat256.AddWord(PInv, z, 0);
-                z[7] &= P7;
+                AddPInvTo(z);
             }
         }
+
+        private static void AddPInvTo(uint[] z)
+        {
+            ulong c = (ulong)z[0] + PInv;
+            z[0] = (uint)c;
+            c >>= 32;
+            if (c != 0)
+            {
+                Nat.IncAt(7, z, 1);
+            }
+            z[7] &= P7;
+        }
+
+        private static void SubPInvFrom(uint[] z)
+        {
+            long c = (long)z[0] - PInv;
+            z[0] = (uint)c;
+            c >>= 32;
+            if (c != 0)
+            {
+                Nat.DecAt(7, z, 1);
+            }
+            z[7] &= P7;
+        }
     }
 }
diff --git a/crypto/src/math/ec/custom/sec/Nat192.cs b/crypto/src/math/ec/custom/sec/Nat192.cs
index 1a6e557f8..0ecbc06de 100644
--- a/crypto/src/math/ec/custom/sec/Nat192.cs
+++ b/crypto/src/math/ec/custom/sec/Nat192.cs
@@ -57,32 +57,6 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             return (uint)c;
         }
 
-        // TODO Re-write to allow full range for x?
-        public static uint AddDWord(ulong x, uint[] z, int zOff)
-        {
-            Debug.Assert(zOff <= 4);
-            ulong c = x;
-            c += (ulong)z[zOff + 0];
-            z[zOff + 0] = (uint)c;
-            c >>= 32;
-            c += (ulong)z[zOff + 1];
-            z[zOff + 1] = (uint)c;
-            c >>= 32;
-            return c == 0 ? 0 : Inc(z, zOff + 2);
-        }
-
-        public static uint AddExt(uint[] xx, uint[] yy, uint[] zz)
-        {
-            ulong c = 0;
-            for (int i = 0; i < 12; ++i)
-            {
-                c += (ulong)xx[i] + yy[i];
-                zz[i] = (uint)c;
-                c >>= 32;
-            }
-            return (uint)c;
-        }
-
         public static uint AddTo(uint[] x, uint[] z)
         {
             ulong c = 0;
@@ -161,24 +135,6 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             return (uint)c;
         }
 
-        public static uint AddWord(uint x, uint[] z, int zOff)
-        {
-            Debug.Assert(zOff <= 5);
-            ulong c = (ulong)x + z[zOff + 0];
-            z[zOff + 0] = (uint)c;
-            c >>= 32;
-            return c == 0 ? 0 : Inc(z, zOff + 1);
-        }
-
-        public static uint AddWordExt(uint x, uint[] zz, int zzOff)
-        {
-            Debug.Assert(zzOff <= 11);
-            ulong c = (ulong)x + zz[zzOff + 0];
-            zz[zzOff + 0] = (uint)c;
-            c >>= 32;
-            return c == 0 ? 0 : IncExt(zz, zzOff + 1);
-        }
-
         public static void Copy(uint[] x, uint[] z)
         {
             z[0] = x[0];
@@ -199,32 +155,6 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             return new uint[12];
         }
 
-        public static int Dec(uint[] z, int zOff)
-        {
-            Debug.Assert(zOff <= 6);
-            for (int i = zOff; i < 6; ++i)
-            {
-                if (--z[i] != uint.MaxValue)
-                {
-                    return 0;
-                }
-            }
-            return -1;
-        }
-
-        public static int DecExt(uint[] z, int zOff)
-        {
-            Debug.Assert(zOff <= 12);
-            for (int i = zOff; i < 12; ++i)
-            {
-                if (--z[i] != uint.MaxValue)
-                {
-                    return 0;
-                }
-            }
-            return -1;
-        }
-
         public static bool Diff(uint[] x, int xOff, uint[] y, int yOff, uint[] z, int zOff)
         {
             bool pos = Gte(x, xOff, y, yOff);
@@ -318,32 +248,6 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             return true;
         }
 
-        public static uint Inc(uint[] z, int zOff)
-        {
-            Debug.Assert(zOff <= 6);
-            for (int i = zOff; i < 6; ++i)
-            {
-                if (++z[i] != uint.MinValue)
-                {
-                    return 0;
-                }
-            }
-            return 1;
-        }
-
-        public static uint IncExt(uint[] zz, int zzOff)
-        {
-            Debug.Assert(zzOff <= 12);
-            for (int i = zzOff; i < 12; ++i)
-            {
-                if (++zz[i] != uint.MinValue)
-                {
-                    return 0;
-                }
-            }
-            return 1;
-        }
-
         public static bool IsOne(uint[] x)
         {
             if (x[0] != 1)
@@ -654,7 +558,7 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             c += z[zOff + 3];
             z[zOff + 3] = (uint)c;
             c >>= 32;
-            return c == 0 ? 0 : Inc(z, zOff + 4);
+            return c == 0 ? 0 : Nat.IncAt(6, z, zOff, 4);
         }
 
         public static uint Mul33WordAdd(uint x, uint y, uint[] z, int zOff)
@@ -671,7 +575,7 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             c += z[zOff + 2];
             z[zOff + 2] = (uint)c;
             c >>= 32;
-            return c == 0 ? 0 : Inc(z, zOff + 3);
+            return c == 0 ? 0 : Nat.IncAt(6, z, zOff, 3);
         }
 
         public static uint MulWordDwordAdd(uint x, ulong y, uint[] z, int zOff)
@@ -687,7 +591,7 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             c += z[zOff + 2];
             z[zOff + 2] = (uint)c;
             c >>= 32;
-            return c == 0 ? 0 : Inc(z, zOff + 3);
+            return c == 0 ? 0 : Nat.IncAt(6, z, zOff, 3);
         }
 
         public static uint MulWord(uint x, uint[] y, uint[] z, int zOff)
@@ -968,31 +872,6 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             return (int)c;
         }
 
-        // TODO Re-write to allow full range for x?
-        public static int SubDWord(ulong x, uint[] z)
-        {
-            long c = -(long)x;
-            c += (long)z[0];
-            z[0] = (uint)c;
-            c >>= 32;
-            c += (long)z[1];
-            z[1] = (uint)c;
-            c >>= 32;
-            return c == 0 ? 0 : Dec(z, 2);
-        }
-
-        public static int SubExt(uint[] xx, uint[] yy, uint[] zz)
-        {
-            long c = 0;
-            for (int i = 0; i < 12; ++i)
-            {
-                c += (long)xx[i] - yy[i];
-                zz[i] = (uint)c;
-                c >>= 32;
-            }
-            return (int)c;
-        }
-
         public static int SubFrom(uint[] x, uint[] z)
         {
             long c = 0;
@@ -1041,24 +920,6 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             return (int)c;
         }
 
-        public static int SubWord(uint x, uint[] z, int zOff)
-        {
-            Debug.Assert(zOff <= 5);
-            long c = (long)z[zOff + 0] - x;
-            z[zOff + 0] = (uint)c;
-            c >>= 32;
-            return c == 0 ? 0 : Dec(z, zOff + 1);
-        }
-
-        public static int SubWordExt(uint x, uint[] zz, int zzOff)
-        {
-            Debug.Assert(zzOff <= 11);
-            long c = (long)zz[zzOff + 0] - x;
-            zz[zzOff + 0] = (uint)c;
-            c >>= 32;
-            return c == 0 ? 0 : DecExt(zz, zzOff + 1);
-        }
-
         public static BigInteger ToBigInteger(uint[] x)
         {
             byte[] bs = new byte[24];
diff --git a/crypto/src/math/ec/custom/sec/Nat224.cs b/crypto/src/math/ec/custom/sec/Nat224.cs
index 7027f1162..f8021b19a 100644
--- a/crypto/src/math/ec/custom/sec/Nat224.cs
+++ b/crypto/src/math/ec/custom/sec/Nat224.cs
@@ -117,32 +117,6 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             return (uint)c;
         }
 
-        // TODO Re-write to allow full range for x?
-        public static uint AddDWord(ulong x, uint[] z, int zOff)
-        {
-            Debug.Assert(zOff <= 5);
-            ulong c = x;
-            c += (ulong)z[zOff + 0];
-            z[zOff + 0] = (uint)c;
-            c >>= 32;
-            c += (ulong)z[zOff + 1];
-            z[zOff + 1] = (uint)c;
-            c >>= 32;
-            return c == 0 ? 0 : Inc(z, zOff + 2);
-        }
-
-        public static uint AddExt(uint[] xx, uint[] yy, uint[] zz)
-        {
-            ulong c = 0;
-            for (int i = 0; i < 14; ++i)
-            {
-                c += (ulong)xx[i] + yy[i];
-                zz[i] = (uint)c;
-                c >>= 32;
-            }
-            return (uint)c;
-        }
-
         public static uint AddTo(uint[] x, uint[] z)
         {
             ulong c = 0;
@@ -231,24 +205,6 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             return (uint)c;
         }
 
-        public static uint AddWord(uint x, uint[] z, int zOff)
-        {
-            Debug.Assert(zOff <= 6);
-            ulong c = (ulong)x + z[zOff + 0];
-            z[zOff + 0] = (uint)c;
-            c >>= 32;
-            return c == 0 ? 0 : Inc(z, zOff + 1);
-        }
-
-        public static uint AddWordExt(uint x, uint[] zz, int zzOff)
-        {
-            Debug.Assert(zzOff <= 13);
-            ulong c = (ulong)x + zz[zzOff + 0];
-            zz[zzOff + 0] = (uint)c;
-            c >>= 32;
-            return c == 0 ? 0 : IncExt(zz, zzOff + 1);
-        }
-
         public static void Copy(uint[] x, uint[] z)
         {
             z[0] = x[0];
@@ -270,32 +226,6 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             return new uint[14];
         }
 
-        public static int Dec(uint[] z, int zOff)
-        {
-            Debug.Assert(zOff <= 7);
-            for (int i = zOff; i < 7; ++i)
-            {
-                if (--z[i] != uint.MaxValue)
-                {
-                    return 0;
-                }
-            }
-            return -1;
-        }
-
-        public static int DecExt(uint[] zz, int zzOff)
-        {
-            Debug.Assert(zzOff <= 14);
-            for (int i = zzOff; i < 14; ++i)
-            {
-                if (--zz[i] != uint.MaxValue)
-                {
-                    return 0;
-                }
-            }
-            return -1;
-        }
-
         public static bool Diff(uint[] x, int xOff, uint[] y, int yOff, uint[] z, int zOff)
         {
             bool pos = Gte(x, xOff, y, yOff);
@@ -389,32 +319,6 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             return true;
         }
 
-        public static uint Inc(uint[] z, int zOff)
-        {
-            Debug.Assert(zOff <= 7);
-            for (int i = zOff; i < 7; ++i)
-            {
-                if (++z[i] != uint.MinValue)
-                {
-                    return 0;
-                }
-            }
-            return 1;
-        }
-
-        public static uint IncExt(uint[] zz, int zzOff)
-        {
-            Debug.Assert(zzOff <= 14);
-            for (int i = zzOff; i < 14; ++i)
-            {
-                if (++zz[i] != uint.MinValue)
-                {
-                    return 0;
-                }
-            }
-            return 1;
-        }
-
         public static bool IsOne(uint[] x)
         {
             if (x[0] != 1)
@@ -806,7 +710,7 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             c += z[zOff + 3];
             z[zOff + 3] = (uint)c;
             c >>= 32;
-            return c == 0 ? 0 : Inc(z, zOff + 4);
+            return c == 0 ? 0 : Nat.IncAt(7, z, zOff, 4);
         }
 
         public static uint Mul33WordAdd(uint x, uint y, uint[] z, int zOff)
@@ -823,7 +727,7 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             c += z[zOff + 2];
             z[zOff + 2] = (uint)c;
             c >>= 32;
-            return c == 0 ? 0 : Inc(z, zOff + 3);
+            return c == 0 ? 0 : Nat.IncAt(7, z, zOff, 3);
         }
 
         public static uint MulWordDwordAdd(uint x, ulong y, uint[] z, int zOff)
@@ -839,7 +743,7 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             c += z[zOff + 2];
             z[zOff + 2] = (uint)c;
             c >>= 32;
-            return c == 0 ? 0 : Inc(z, zOff + 3);
+            return c == 0 ? 0 : Nat.IncAt(7, z, zOff, 3);
         }
 
         public static uint MulWord(uint x, uint[] y, uint[] z, int zOff)
@@ -1167,31 +1071,6 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             return (int)c;
         }
 
-        // TODO Re-write to allow full range for x?
-        public static int SubDWord(ulong x, uint[] z)
-        {
-            long c = -(long)x;
-            c += (long)z[0];
-            z[0] = (uint)c;
-            c >>= 32;
-            c += (long)z[1];
-            z[1] = (uint)c;
-            c >>= 32;
-            return c == 0 ? 0 : Dec(z, 2);
-        }
-
-        public static int SubExt(uint[] xx, uint[] yy, uint[] zz)
-        {
-            long c = 0;
-            for (int i = 0; i < 14; ++i)
-            {
-                c += (long)xx[i] - yy[i];
-                zz[i] = (uint)c;
-                c >>= 32;
-            }
-            return (int)c;
-        }
-
         public static int SubFrom(uint[] x, uint[] z)
         {
             long c = 0;
@@ -1246,24 +1125,6 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             return (int)c;
         }
 
-        public static int SubWord(uint x, uint[] z, int zOff)
-        {
-            Debug.Assert(zOff <= 6);
-            long c = (long)z[zOff + 0] - x;
-            z[zOff + 0] = (uint)c;
-            c >>= 32;
-            return c == 0 ? 0 : Dec(z, zOff + 1);
-        }
-
-        public static int SubWordExt(uint x, uint[] zz, int zzOff)
-        {
-            Debug.Assert(zzOff <= 13);
-            long c = (long)zz[zzOff + 0] - x;
-            zz[zzOff + 0] = (uint)c;
-            c >>= 32;
-            return c == 0 ? 0 : DecExt(zz, zzOff + 1);
-        }
-
         public static BigInteger ToBigInteger(uint[] x)
         {
             byte[] bs = new byte[28];
diff --git a/crypto/src/math/ec/custom/sec/Nat256.cs b/crypto/src/math/ec/custom/sec/Nat256.cs
index f4599b988..9c19f41ba 100644
--- a/crypto/src/math/ec/custom/sec/Nat256.cs
+++ b/crypto/src/math/ec/custom/sec/Nat256.cs
@@ -69,17 +69,6 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             return (uint)c;
         }
 
-        public static uint Add33To(uint x, uint[] z)
-        {
-            ulong c = (ulong)z[0] + x;
-            z[0] = (uint)c;
-            c >>= 32;
-            c += (ulong)z[1] + 1;
-            z[1] = (uint)c;
-            c >>= 32;
-            return c == 0 ? 0 : Inc(z, 2);
-        }
-
         public static uint AddBothTo(uint[] x, uint[] y, uint[] z)
         {
             ulong c = 0;
@@ -140,30 +129,6 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             return (uint)c;
         }
 
-        public static uint AddDWordAt(ulong x, uint[] z, int zPos)
-        {
-            Debug.Assert(zPos <= 6);
-            ulong c = (ulong)z[zPos + 0] + (x & M);
-            z[zPos + 0] = (uint)c;
-            c >>= 32;
-            c += (ulong)z[zPos + 1] + (x >> 32);
-            z[zPos + 1] = (uint)c;
-            c >>= 32;
-            return c == 0 ? 0 : Inc(z, zPos + 2);
-        }
-
-        public static uint AddExt(uint[] xx, uint[] yy, uint[] zz)
-        {
-            ulong c = 0;
-            for (int i = 0; i < 16; ++i)
-            {
-                c += (ulong)xx[i] + yy[i];
-                zz[i] = (uint)c;
-                c >>= 32;
-            }
-            return (uint)c;
-        }
-
         public static uint AddTo(uint[] x, uint[] z)
         {
             ulong c = 0;
@@ -262,24 +227,6 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             return (uint)c;
         }
 
-        public static uint AddWord(uint x, uint[] z, int zOff)
-        {
-            Debug.Assert(zOff <= 7);
-            ulong c = (ulong)x + z[zOff + 0];
-            z[zOff + 0] = (uint)c;
-            c >>= 32;
-            return c == 0 ? 0 : Inc(z, zOff + 1);
-        }
-
-        public static uint AddWordExt(uint x, uint[] zz, int zzOff)
-        {
-            Debug.Assert(zzOff <= 15);
-            ulong c = (ulong)x + zz[zzOff + 0];
-            zz[zzOff + 0] = (uint)c;
-            c >>= 32;
-            return c == 0 ? 0 : IncExt(zz, zzOff + 1);
-        }
-
         public static void Copy(uint[] x, uint[] z)
         {
             z[0] = x[0];
@@ -302,32 +249,6 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             return new uint[16];
         }
 
-        public static int Dec(uint[] z, int zOff)
-        {
-            Debug.Assert(zOff <= 8);
-            for (int i = zOff; i < 8; ++i)
-            {
-                if (--z[i] != uint.MaxValue)
-                {
-                    return 0;
-                }
-            }
-            return -1;
-        }
-
-        public static int DecExt(uint[] zz, int zzOff)
-        {
-            Debug.Assert(zzOff <= 16);
-            for (int i = zzOff; i < 16; ++i)
-            {
-                if (--zz[i] != uint.MaxValue)
-                {
-                    return 0;
-                }
-            }
-            return -1;
-        }
-
         public static bool Diff(uint[] x, int xOff, uint[] y, int yOff, uint[] z, int zOff)
         {
             bool pos = Gte(x, xOff, y, yOff);
@@ -421,32 +342,6 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             return true;
         }
 
-        public static uint Inc(uint[] z, int zOff)
-        {
-            Debug.Assert(zOff <= 8);
-            for (int i = zOff; i < 8; ++i)
-            {
-                if (++z[i] != uint.MinValue)
-                {
-                    return 0;
-                }
-            }
-            return 1;
-        }
-
-        public static uint IncExt(uint[] zz, int zzOff)
-        {
-            Debug.Assert(zzOff <= 16);
-            for (int i = zzOff; i < 16; ++i)
-            {
-                if (++zz[i] != uint.MinValue)
-                {
-                    return 0;
-                }
-            }
-            return 1;
-        }
-
         public static bool IsOne(uint[] x)
         {
             if (x[0] != 1)
@@ -873,7 +768,7 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             c += z[zOff + 3];
             z[zOff + 3] = (uint)c;
             c >>= 32;
-            return c == 0 ? 0 : Inc(z, zOff + 4);
+            return c == 0 ? 0 : Nat.IncAt(8, z, zOff, 4);
         }
 
         public static uint Mul33WordAdd(uint x, uint y, uint[] z, int zOff)
@@ -890,7 +785,7 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             c += z[zOff + 2];
             z[zOff + 2] = (uint)c;
             c >>= 32;
-            return c == 0 ? 0 : Inc(z, zOff + 3);
+            return c == 0 ? 0 : Nat.IncAt(8, z, zOff, 3);
         }
 
         public static uint MulWordDwordAdd(uint x, ulong y, uint[] z, int zOff)
@@ -906,7 +801,7 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             c += z[zOff + 2];
             z[zOff + 2] = (uint)c;
             c >>= 32;
-            return c == 0 ? 0 : Inc(z, zOff + 3);
+            return c == 0 ? 0 : Nat.IncAt(8, z, zOff, 3);
         }
 
         public static uint MulWord(uint x, uint[] y, uint[] z, int zOff)
@@ -1255,17 +1150,6 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             return (int)c;
         }
 
-        public static int Sub33From(uint x, uint[] z)
-        {
-            long c = (long)z[0] - x;
-            z[0] = (uint)c;
-            c >>= 32;
-            c += (long)z[1] - 1;
-            z[1] = (uint)c;
-            c >>= 32;
-            return c == 0 ? 0 : Dec(z, 2);
-        }
-
         public static int SubBothFrom(uint[] x, uint[] y, uint[] z)
         {
             long c = 0;
@@ -1296,30 +1180,6 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             return (int)c;
         }
 
-        public static int SubDWordAt(ulong x, uint[] z, int zPos)
-        {
-            Debug.Assert(zPos <= 6);
-            long c = (long)z[zPos + 0] - (long)(x & M);
-            z[zPos + 0] = (uint)c;
-            c >>= 32;
-            c += (long)z[zPos + 1] - (long)(x >> 32);
-            z[zPos + 1] = (uint)c;
-            c >>= 32;
-            return c == 0 ? 0 : Dec(z, zPos + 2);
-        }
-
-        public static int SubExt(uint[] xx, uint[] yy, uint[] zz)
-        {
-            long c = 0;
-            for (int i = 0; i < 16; ++i)
-            {
-                c += (long)xx[i] - yy[i];
-                zz[i] = (uint)c;
-                c >>= 32;
-            }
-            return (int)c;
-        }
-
         public static int SubFrom(uint[] x, uint[] z)
         {
             long c = 0;
@@ -1380,24 +1240,6 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             return (int)c;
         }
 
-        public static int SubWord(uint x, uint[] z, int zOff)
-        {
-            Debug.Assert(zOff <= 7);
-            long c = (long)z[zOff + 0] - x;
-            z[zOff + 0] = (uint)c;
-            c >>= 32;
-            return c == 0 ? 0 : Dec(z, zOff + 1);
-        }
-
-        public static int SubWordExt(uint x, uint[] zz, int zzOff)
-        {
-            Debug.Assert(zzOff <= 15);
-            long c = (long)zz[zzOff + 0] - x;
-            zz[zzOff + 0] = (uint)c;
-            c >>= 32;
-            return c == 0 ? 0 : DecExt(zz, zzOff + 1);
-        }
-
         public static BigInteger ToBigInteger(uint[] x)
         {
             byte[] bs = new byte[32];
diff --git a/crypto/src/math/ec/custom/sec/SecP192K1Field.cs b/crypto/src/math/ec/custom/sec/SecP192K1Field.cs
index 99e4cf999..8ce5619a0 100644
--- a/crypto/src/math/ec/custom/sec/SecP192K1Field.cs
+++ b/crypto/src/math/ec/custom/sec/SecP192K1Field.cs
@@ -9,9 +9,10 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
         internal static readonly uint[] P = new uint[]{ 0xFFFFEE37, 0xFFFFFFFE, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF };
         internal static readonly uint[] PExt = new uint[]{ 0x013C4FD1, 0x00002392, 0x00000001, 0x00000000, 0x00000000,
             0x00000000, 0xFFFFDC6E, 0xFFFFFFFD, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF };
+        private static readonly uint[] PExtInv = new uint[]{ 0xFEC3B02F, 0xFFFFDC6D, 0xFFFFFFFE, 0xFFFFFFFF, 0xFFFFFFFF,
+            0xFFFFFFFF, 0x00002391, 0x00000002 };
         private const uint P5 = 0xFFFFFFFF;
         private const uint PExt11 = 0xFFFFFFFF;
-        private const ulong PInv = 0x00000001000011C9L;
         private const uint PInv33 = 0x11C9;
 
         public static void Add(uint[] x, uint[] y, uint[] z)
@@ -19,26 +20,28 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             uint c = Nat192.Add(x, y, z);
             if (c != 0 || (z[5] == P5 && Nat192.Gte(z, P)))
             {
-                Nat192.AddDWord(PInv, z, 0);
+                Nat.Add33To(6, PInv33, z);
             }
         }
 
         public static void AddExt(uint[] xx, uint[] yy, uint[] zz)
         {
-            uint c = Nat192.AddExt(xx, yy, zz);
+            uint c = Nat.Add(12, xx, yy, zz);
             if (c != 0 || (zz[11] == PExt11 && Nat192.GteExt(zz, PExt)))
             {
-                Nat192.SubExt(zz, PExt, zz);
+                if (Nat.AddTo(PExtInv.Length, PExtInv, zz) != 0)
+                {
+                    Nat.IncAt(12, zz, PExtInv.Length);
+                }
             }
         }
 
         public static void AddOne(uint[] x, uint[] z)
         {
-            Nat192.Copy(x, z);
-            uint c = Nat192.Inc(z, 0);
+            uint c = Nat.Inc(6, x, z);
             if (c != 0 || (z[5] == P5 && Nat192.Gte(z, P)))
             {
-                Nat192.AddDWord(PInv, z, 0);
+                Nat.Add33To(6, PInv33, z);
             }
         }
 
@@ -93,7 +96,7 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
 
             if (c != 0 || (z[5] == P5 && Nat192.Gte(z, P)))
             {
-                Nat192.AddDWord(PInv, z, 0);
+                Nat.Add33To(6, PInv33, z);
             }
         }
 
@@ -102,7 +105,7 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             if ((x != 0 && Nat192.Mul33WordAdd(PInv33, x, z, 0) != 0)
                 || (z[5] == P5 && Nat192.Gte(z, P)))
             {
-                Nat192.AddDWord(PInv, z, 0);
+                Nat.Add33To(6, PInv33, z);
             }
         }
 
@@ -133,16 +136,19 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             int c = Nat192.Sub(x, y, z);
             if (c != 0)
             {
-                Nat192.SubDWord(PInv, z);
+                Nat.Sub33From(6, PInv33, z);
             }
         }
 
         public static void SubtractExt(uint[] xx, uint[] yy, uint[] zz)
         {
-            int c = Nat192.SubExt(xx, yy, zz);
+            int c = Nat.Sub(12, xx, yy, zz);
             if (c != 0)
             {
-                Nat192.AddExt(zz, PExt, zz);
+                if (Nat.SubFrom(PExtInv.Length, PExtInv, zz) != 0)
+                {
+                    Nat.DecAt(12, zz, PExtInv.Length);
+                }
             }
         }
 
@@ -151,7 +157,7 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             uint c = Nat.ShiftUpBit(6, x, 0, z);
             if (c != 0 || (z[5] == P5 && Nat192.Gte(z, P)))
             {
-                Nat192.AddDWord(PInv, z, 0);
+                Nat.Add33To(6, PInv33, z);
             }
         }
     }
diff --git a/crypto/src/math/ec/custom/sec/SecP192R1Field.cs b/crypto/src/math/ec/custom/sec/SecP192R1Field.cs
index 71ccfc4b7..8e2aad5af 100644
--- a/crypto/src/math/ec/custom/sec/SecP192R1Field.cs
+++ b/crypto/src/math/ec/custom/sec/SecP192R1Field.cs
@@ -9,6 +9,8 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
         internal static readonly uint[] P = new uint[]{ 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFE, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF };
         internal static readonly uint[] PExt = new uint[]{ 0x00000001, 0x00000000, 0x00000002, 0x00000000, 0x00000001,
             0x00000000, 0xFFFFFFFE, 0xFFFFFFFF, 0xFFFFFFFD, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF };
+        private static readonly uint[] PExtInv = new uint[]{ 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFD, 0xFFFFFFFF, 0xFFFFFFFE,
+            0xFFFFFFFF, 0x00000001, 0x00000000, 0x00000002 };
         private const uint P5 = 0xFFFFFFFF;
         private const uint PExt11 = 0xFFFFFFFF;
 
@@ -17,26 +19,28 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             uint c = Nat192.Add(x, y, z);
             if (c != 0 || (z[5] == P5 && Nat192.Gte(z, P)))
             {
-                Nat192.SubFrom(P, z);
+                AddPInvTo(z);
             }
         }
 
         public static void AddExt(uint[] xx, uint[] yy, uint[] zz)
         {
-            uint c = Nat192.AddExt(xx, yy, zz);
+            uint c = Nat.Add(12, xx, yy, zz);
             if (c != 0 || (zz[11] == PExt11 && Nat192.GteExt(zz, PExt)))
             {
-                Nat192.SubExt(zz, PExt, zz);
+                if (Nat.AddTo(PExtInv.Length, PExtInv, zz) != 0)
+                {
+                    Nat.IncAt(12, zz, PExtInv.Length);
+                }
             }
         }
 
         public static void AddOne(uint[] x, uint[] z)
         {
-            Nat192.Copy(x, z);
-            uint c = Nat192.Inc(z, 0);
+            uint c = Nat.Inc(6, x, z);
             if (c != 0 || (z[5] == P5 && Nat192.Gte(z, P)))
             {
-                Nat192.SubFrom(P, z);
+                AddPInvTo(z);
             }
         }
 
@@ -123,10 +127,10 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
 
         public static void Reduce32(uint x, uint[] z)
         {
-            if ((x != 0 && (Nat192.AddWord(x, z, 0) + Nat192.AddWord(x, z, 2) != 0))
+            if ((x != 0 && (Nat.AddWordTo(6, x, z) + Nat.AddWordAt(6, x, z, 2) != 0))
                 || (z[5] == P5 && Nat192.Gte(z, P)))
             {
-                Nat192.SubFrom(P, z);
+                AddPInvTo(z);
             }
         }
 
@@ -157,16 +161,19 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             int c = Nat192.Sub(x, y, z);
             if (c != 0)
             {
-                Nat192.AddTo(P, z);
+                SubPInvFrom(z);
             }
         }
 
         public static void SubtractExt(uint[] xx, uint[] yy, uint[] zz)
         {
-            int c = Nat192.SubExt(xx, yy, zz);
+            int c = Nat.Sub(12, xx, yy, zz);
             if (c != 0)
             {
-                Nat192.AddExt(zz, PExt, zz);
+                if (Nat.SubFrom(PExtInv.Length, PExtInv, zz) != 0)
+                {
+                    Nat.DecAt(12, zz, PExtInv.Length);
+                }
             }
         }
 
@@ -175,7 +182,47 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             uint c = Nat.ShiftUpBit(6, x, 0, z);
             if (c != 0 || (z[5] == P5 && Nat192.Gte(z, P)))
             {
-                Nat192.SubFrom(P, z);
+                AddPInvTo(z);
+            }
+        }
+
+        private static void AddPInvTo(uint[] z)
+        {
+            long c = (long)z[0] + 1;
+            z[0] = (uint)c;
+            c >>= 32;
+            if (c != 0)
+            {
+                c += (long)z[1];
+                z[1] = (uint)c;
+                c >>= 32;
+            }
+            c += (long)z[2] + 1;
+            z[2] = (uint)c;
+            c >>= 32;
+            if (c != 0)
+            {
+                Nat.IncAt(6, z, 3);
+            }
+        }
+
+        private static void SubPInvFrom(uint[] z)
+        {
+            long c = (long)z[0] - 1;
+            z[0] = (uint)c;
+            c >>= 32;
+            if (c != 0)
+            {
+                c += (long)z[1];
+                z[1] = (uint)c;
+                c >>= 32;
+            }
+            c += (long)z[2] - 1;
+            z[2] = (uint)c;
+            c >>= 32;
+            if (c != 0)
+            {
+                Nat.DecAt(6, z, 3);
             }
         }
     }
diff --git a/crypto/src/math/ec/custom/sec/SecP224K1Field.cs b/crypto/src/math/ec/custom/sec/SecP224K1Field.cs
index 03df35d36..57fd1179a 100644
--- a/crypto/src/math/ec/custom/sec/SecP224K1Field.cs
+++ b/crypto/src/math/ec/custom/sec/SecP224K1Field.cs
@@ -10,9 +10,10 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             0xFFFFFFFF };
         internal static readonly uint[] PExt = new uint[]{ 0x02C23069, 0x00003526, 0x00000001, 0x00000000, 0x00000000,
             0x00000000, 0x00000000, 0xFFFFCADA, 0xFFFFFFFD, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF };
+        private static readonly uint[] PExtInv = new uint[]{ 0xFD3DCF97, 0xFFFFCAD9, 0xFFFFFFFE, 0xFFFFFFFF, 0xFFFFFFFF,
+            0xFFFFFFFF, 0xFFFFFFFF, 0x00003525, 0x00000002 };
         private const uint P6 = 0xFFFFFFFF;
         private const uint PExt13 = 0xFFFFFFFF;
-        private const ulong PInv = 0x0000000100001A93L; 
         private const uint PInv33 = 0x1A93;
 
         public static void Add(uint[] x, uint[] y, uint[] z)
@@ -20,26 +21,28 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             uint c = Nat224.Add(x, y, z);
             if (c != 0 || (z[6] == P6 && Nat224.Gte(z, P)))
             {
-                Nat224.AddDWord(PInv, z, 0);
+                Nat.Add33To(7, PInv33, z);
             }
         }
 
         public static void AddExt(uint[] xx, uint[] yy, uint[] zz)
         {
-            uint c = Nat224.AddExt(xx, yy, zz);
+            uint c = Nat.Add(14, xx, yy, zz);
             if (c != 0 || (zz[13] == PExt13 && Nat224.GteExt(zz, PExt)))
             {
-                Nat224.SubExt(zz, PExt, zz);
+                if (Nat.AddTo(PExtInv.Length, PExtInv, zz) != 0)
+                {
+                    Nat.IncAt(14, zz, PExtInv.Length);
+                }
             }
         }
 
         public static void AddOne(uint[] x, uint[] z)
         {
-            Nat224.Copy(x, z);
-            uint c = Nat224.Inc(z, 0);
+            uint c = Nat.Inc(7, x, z);
             if (c != 0 || (z[6] == P6 && Nat224.Gte(z, P)))
             {
-                Nat224.AddDWord(PInv, z, 0);
+                Nat.Add33To(7, PInv33, z);
             }
         }
 
@@ -94,7 +97,7 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
 
             if (c != 0 || (z[6] == P6 && Nat224.Gte(z, P)))
             {
-                Nat224.AddDWord(PInv, z, 0);
+                Nat.Add33To(7, PInv33, z);
             }
         }
 
@@ -103,7 +106,7 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             if ((x != 0 && Nat224.Mul33WordAdd(PInv33, x, z, 0) != 0)
                 || (z[6] == P6 && Nat224.Gte(z, P)))
             {
-                Nat224.AddDWord(PInv, z, 0);
+                Nat.Add33To(7, PInv33, z);
             }
         }
 
@@ -134,16 +137,19 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             int c = Nat224.Sub(x, y, z);
             if (c != 0)
             {
-                Nat224.SubDWord(PInv, z);
+                Nat.Sub33From(7, PInv33, z);
             }
         }
 
         public static void SubtractExt(uint[] xx, uint[] yy, uint[] zz)
         {
-            int c = Nat224.SubExt(xx, yy, zz);
+            int c = Nat.Sub(14, xx, yy, zz);
             if (c != 0)
             {
-                Nat224.AddExt(zz, PExt, zz);
+                if (Nat.SubFrom(PExtInv.Length, PExtInv, zz) != 0)
+                {
+                    Nat.DecAt(14, zz, PExtInv.Length);
+                }
             }
         }
 
@@ -152,7 +158,7 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             uint c = Nat.ShiftUpBit(7, x, 0, z);
             if (c != 0 || (z[6] == P6 && Nat224.Gte(z, P)))
             {
-                Nat224.AddDWord(PInv, z, 0);
+                Nat.Add33To(7, PInv33, z);
             }
         }
     }
diff --git a/crypto/src/math/ec/custom/sec/SecP224R1Field.cs b/crypto/src/math/ec/custom/sec/SecP224R1Field.cs
index 5447ce697..8ffc9aa65 100644
--- a/crypto/src/math/ec/custom/sec/SecP224R1Field.cs
+++ b/crypto/src/math/ec/custom/sec/SecP224R1Field.cs
@@ -9,6 +9,8 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
         internal static readonly uint[] P = new uint[] { 0x00000001, 0x00000000, 0x00000000, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF };
         internal static readonly uint[] PExt = new uint[]{ 0x00000001, 0x00000000, 0x00000000, 0xFFFFFFFE, 0xFFFFFFFF,
             0xFFFFFFFF, 0x00000000, 0x00000002, 0x00000000, 0x00000000, 0xFFFFFFFE, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF };
+        private static readonly uint[] PExtInv = new uint[]{ 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0x00000001, 0x00000000,
+            0x00000000, 0xFFFFFFFF, 0xFFFFFFFD, 0xFFFFFFFF, 0xFFFFFFFF, 0x00000001 };
         private const uint P6 = 0xFFFFFFFF;
         private const uint PExt13 = 0xFFFFFFFF;
 
@@ -17,26 +19,28 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             uint c = Nat224.Add(x, y, z);
             if (c != 0 || (z[6] == P6 && Nat224.Gte(z, P)))
             {
-                Nat224.SubFrom(P, z);
+                AddPInvTo(z);
             }
         }
 
         public static void AddExt(uint[] xx, uint[] yy, uint[] zz)
         {
-            uint c = Nat224.AddExt(xx, yy, zz);
+            uint c = Nat.Add(14, xx, yy, zz);
             if (c != 0 || (zz[13] == PExt13 && Nat224.GteExt(zz, PExt)))
             {
-                Nat224.SubExt(zz, PExt, zz);
+                if (Nat.AddTo(PExtInv.Length, PExtInv, zz) != 0)
+                {
+                    Nat.IncAt(14, zz, PExtInv.Length);
+                }
             }
         }
 
         public static void AddOne(uint[] x, uint[] z)
         {
-            Nat224.Copy(x, z);
-            uint c = Nat224.Inc(z, 0);
+            uint c = Nat.Inc(7, x, z);
             if (c != 0 || (z[6] == P6 && Nat224.Gte(z, P)))
             {
-                Nat224.SubFrom(P, z);
+                AddPInvTo(z);
             }
         }
 
@@ -121,16 +125,16 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             }
             else
             {
-                Nat224.AddTo(P, z);
+                SubPInvFrom(z);
             }
         }
 
         public static void Reduce32(uint x, uint[] z)
         {
-            if ((x != 0 && (Nat224.SubWord(x, z, 0) + Nat224.AddWord(x, z, 3) != 0))
+            if ((x != 0 && (Nat.SubWordFrom(7, x, z) + Nat.AddWordAt(7, x, z, 3) != 0))
                 || (z[6] == P6 && Nat224.Gte(z, P)))
             {
-                Nat224.SubFrom(P, z);
+                AddPInvTo(z);
             }
         }
 
@@ -161,16 +165,19 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             int c = Nat224.Sub(x, y, z);
             if (c != 0)
             {
-                Nat224.AddTo(P, z);
+                SubPInvFrom(z);
             }
         }
 
         public static void SubtractExt(uint[] xx, uint[] yy, uint[] zz)
         {
-            int c = Nat224.SubExt(xx, yy, zz);
+            int c = Nat.Sub(14, xx, yy, zz);
             if (c != 0)
             {
-                Nat224.AddExt(zz, PExt, zz);
+                if (Nat.SubFrom(PExtInv.Length, PExtInv, zz) != 0)
+                {
+                    Nat.DecAt(14, zz, PExtInv.Length);
+                }
             }
         }
 
@@ -179,7 +186,53 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             uint c = Nat.ShiftUpBit(7, x, 0, z);
             if (c != 0 || (z[6] == P6 && Nat224.Gte(z, P)))
             {
-                Nat224.SubFrom(P, z);
+                AddPInvTo(z);
+            }
+        }
+
+        private static void AddPInvTo(uint[] z)
+        {
+            long c = (long)z[0] - 1;
+            z[0] = (uint)c;
+            c >>= 32;
+            if (c != 0)
+            {
+                c += (long)z[1];
+                z[1] = (uint)c;
+                c >>= 32;
+                c += (long)z[2];
+                z[2] = (uint)c;
+                c >>= 32;
+            }
+            c += (long)z[3] + 1;
+            z[3] = (uint)c;
+            c >>= 32;
+            if (c != 0)
+            {
+                Nat.IncAt(7, z, 4);
+            }
+        }
+
+        private static void SubPInvFrom(uint[] z)
+        {
+            long c = (long)z[0] + 1;
+            z[0] = (uint)c;
+            c >>= 32;
+            if (c != 0)
+            {
+                c += (long)z[1];
+                z[1] = (uint)c;
+                c >>= 32;
+                c += (long)z[2];
+                z[2] = (uint)c;
+                c >>= 32;
+            }
+            c += (long)z[3] - 1;
+            z[3] = (uint)c;
+            c >>= 32;
+            if (c != 0)
+            {
+                Nat.DecAt(7, z, 4);
             }
         }
     }
diff --git a/crypto/src/math/ec/custom/sec/SecP256K1Field.cs b/crypto/src/math/ec/custom/sec/SecP256K1Field.cs
index 6e834beb3..aa82013b2 100644
--- a/crypto/src/math/ec/custom/sec/SecP256K1Field.cs
+++ b/crypto/src/math/ec/custom/sec/SecP256K1Field.cs
@@ -22,29 +22,28 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             uint c = Nat256.Add(x, y, z);
             if (c != 0 || (z[7] == P7 && Nat256.Gte(z, P)))
             {
-                Nat256.Add33To(PInv33, z);
+                Nat.Add33To(8, PInv33, z);
             }
         }
 
         public static void AddExt(uint[] xx, uint[] yy, uint[] zz)
         {
-            uint c = Nat256.AddExt(xx, yy, zz);
+            uint c = Nat.Add(16, xx, yy, zz);
             if (c != 0 || (zz[15] == PExt15 && Nat256.GteExt(zz, PExt)))
             {
                 if (Nat.AddTo(PExtInv.Length, PExtInv, zz) != 0)
                 {
-                    Nat256.IncExt(zz, PExtInv.Length);
+                    Nat.IncAt(16, zz, PExtInv.Length);
                 }
             }
         }
 
         public static void AddOne(uint[] x, uint[] z)
         {
-            Nat256.Copy(x, z);
-            uint c = Nat256.Inc(z, 0);
+            uint c = Nat.Inc(8, x, z);
             if (c != 0 || (z[7] == P7 && Nat256.Gte(z, P)))
             {
-                Nat256.Add33To(PInv33, z);
+                Nat.Add33To(8, PInv33, z);
             }
         }
 
@@ -99,7 +98,7 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
 
             if (c != 0 || (z[7] == P7 && Nat256.Gte(z, P)))
             {
-                Nat256.Add33To(PInv33, z);
+                Nat.Add33To(8, PInv33, z);
             }
         }
 
@@ -108,7 +107,7 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             if ((x != 0 && Nat256.Mul33WordAdd(PInv33, x, z, 0) != 0)
                 || (z[7] == P7 && Nat256.Gte(z, P)))
             {
-                Nat256.Add33To(PInv33, z);
+                Nat.Add33To(8, PInv33, z);
             }
         }
 
@@ -139,18 +138,18 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             int c = Nat256.Sub(x, y, z);
             if (c != 0)
             {
-                Nat256.Sub33From(PInv33, z);
+                Nat.Sub33From(8, PInv33, z);
             }
         }
 
         public static void SubtractExt(uint[] xx, uint[] yy, uint[] zz)
         {
-            int c = Nat256.SubExt(xx, yy, zz);
+            int c = Nat.Sub(16, xx, yy, zz);
             if (c != 0)
             {
                 if (Nat.SubFrom(PExtInv.Length, PExtInv, zz) != 0)
                 {
-                    Nat256.DecExt(zz, PExtInv.Length);
+                    Nat.DecAt(16, zz, PExtInv.Length);
                 }
             }
         }
@@ -160,7 +159,7 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             uint c = Nat.ShiftUpBit(8, x, 0, z);
             if (c != 0 || (z[7] == P7 && Nat256.Gte(z, P)))
             {
-                Nat256.Add33To(PInv33, z);
+                Nat.Add33To(8, PInv33, z);
             }
         }
     }
diff --git a/crypto/src/math/ec/custom/sec/SecP256R1Field.cs b/crypto/src/math/ec/custom/sec/SecP256R1Field.cs
index 9bcb0e98e..de383046d 100644
--- a/crypto/src/math/ec/custom/sec/SecP256R1Field.cs
+++ b/crypto/src/math/ec/custom/sec/SecP256R1Field.cs
@@ -26,17 +26,16 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
 
         public static void AddExt(uint[] xx, uint[] yy, uint[] zz)
         {
-            uint c = Nat256.AddExt(xx, yy, zz);
+            uint c = Nat.Add(16, xx, yy, zz);
             if (c != 0 || Nat256.GteExt(zz, PExt))
             {
-                Nat256.SubExt(zz, PExt, zz);
+                Nat.SubFrom(16, PExt, zz);
             }
         }
 
         public static void AddOne(uint[] x, uint[] z)
         {
-            Nat256.Copy(x, z);
-            uint c = Nat256.Inc(z, 0);
+            uint c = Nat.Inc(8, x, z);
             if (c != 0 || (z[7] == P7 && Nat256.Gte(z, P)))
             {
                 Nat256.SubFrom(P, z);
@@ -217,10 +216,10 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
 
         public static void SubtractExt(uint[] xx, uint[] yy, uint[] zz)
         {
-            int c = Nat256.SubExt(xx, yy, zz);
+            int c = Nat.Sub(16, xx, yy, zz);
             if (c != 0)
             {
-                Nat256.AddExt(zz, PExt, zz);
+                Nat.AddTo(16, PExt, zz);
             }
         }
 
diff --git a/crypto/src/math/ec/custom/sec/SecP384R1Field.cs b/crypto/src/math/ec/custom/sec/SecP384R1Field.cs
index f41c0b8dd..039c18af8 100644
--- a/crypto/src/math/ec/custom/sec/SecP384R1Field.cs
+++ b/crypto/src/math/ec/custom/sec/SecP384R1Field.cs
@@ -11,7 +11,6 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
         internal static readonly uint[] PExt = new uint[]{ 0x00000001, 0xFFFFFFFE, 0x00000000, 0x00000002, 0x00000000, 0xFFFFFFFE,
             0x00000000, 0x00000002, 0x00000001, 0x00000000, 0x00000000, 0x00000000, 0xFFFFFFFE, 0x00000001, 0x00000000,
             0xFFFFFFFE, 0xFFFFFFFD, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF };
-        private static readonly uint[] PInv = new uint[]{ 0x00000001, 0xFFFFFFFF, 0xFFFFFFFF, 0x00000000, 0x00000001 };
         private static readonly uint[] PExtInv = new uint[]{ 0xFFFFFFFF, 0x00000001, 0xFFFFFFFF, 0xFFFFFFFD, 0xFFFFFFFF, 0x00000001,
             0xFFFFFFFF, 0xFFFFFFFD, 0xFFFFFFFE, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0x00000001, 0xFFFFFFFE, 0xFFFFFFFF,
             0x00000001, 0x00000002 };
@@ -23,10 +22,7 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             uint c = Nat.Add(12, x, y, z);
             if (c != 0 || (z[11] == P11 && Nat.Gte(12, z, P)))
             {
-                if (Nat.AddTo(PInv.Length, PInv, z) != 0)
-                {
-                    Nat.IncAt(12, z, PInv.Length);
-                }
+                AddPInvTo(z);
             }
         }
 
@@ -47,10 +43,7 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             uint c = Nat.Inc(12, x, z);
             if (c != 0 || (z[11] == P11 && Nat.Gte(12, z, P)))
             {
-                if (Nat.AddTo(PInv.Length, PInv, z) != 0)
-                {
-                    Nat.IncAt(12, z, PInv.Length);
-                }
+                AddPInvTo(z);
             }
         }
 
@@ -145,9 +138,9 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             {
                 Reduce32((uint)c, z);
             }
-            else if (Nat.SubFrom(PInv.Length, PInv, z) != 0)
+            else
             {
-                Nat.DecAt(12, z, PInv.Length);
+                SubPInvFrom(z);
             }
         }
 
@@ -181,10 +174,7 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             if ((cc != 0 && Nat.IncAt(12, z, 5) != 0)
                 || (z[11] == P11 && Nat.Gte(12, z, P)))
             {
-                if (Nat.AddTo(PInv.Length, PInv, z) != 0)
-                {
-                    Nat.IncAt(12, z, PInv.Length);
-                }
+                AddPInvTo(z);
             }
         }
 
@@ -215,10 +205,7 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             int c = Nat.Sub(12, x, y, z);
             if (c != 0)
             {
-                if (Nat.SubFrom(PInv.Length, PInv, z) != 0)
-                {
-                    Nat.DecAt(12, z, PInv.Length);
-                }
+                SubPInvFrom(z);
             }
         }
 
@@ -239,10 +226,59 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             uint c = Nat.ShiftUpBit(12, x, 0, z);
             if (c != 0 || (z[11] == P11 && Nat.Gte(12, z, P)))
             {
-                if (Nat.AddTo(PInv.Length, PInv, z) != 0)
-                {
-                    Nat.IncAt(12, z, PInv.Length);
-                }
+                AddPInvTo(z);
+            }
+        }
+
+        private static void AddPInvTo(uint[] z)
+        {
+            long c = (long)z[0] + 1;
+            z[0] = (uint)c;
+            c >>= 32;
+            c += (long)z[1] - 1;
+            z[1] = (uint)c;
+            c >>= 32;
+            if (c != 0)
+            {
+                c += (long)z[2];
+                z[2] = (uint)c;
+                c >>= 32;
+            }
+            c += (long)z[3] + 1;
+            z[3] = (uint)c;
+            c >>= 32;
+            c += (long)z[4] + 1;
+            z[4] = (uint)c;
+            c >>= 32;
+            if (c != 0)
+            {
+                Nat.IncAt(12, z, 5);
+            }
+        }
+
+        private static void SubPInvFrom(uint[] z)
+        {
+            long c = (long)z[0] - 1;
+            z[0] = (uint)c;
+            c >>= 32;
+            c += (long)z[1] + 1;
+            z[1] = (uint)c;
+            c >>= 32;
+            if (c != 0)
+            {
+                c += (long)z[2];
+                z[2] = (uint)c;
+                c >>= 32;
+            }
+            c += (long)z[3] - 1;
+            z[3] = (uint)c;
+            c >>= 32;
+            c += (long)z[4] - 1;
+            z[4] = (uint)c;
+            c >>= 32;
+            if (c != 0)
+            {
+                Nat.DecAt(12, z, 5);
             }
         }
     }