Initial work on the Curve25519 field implementation

3 files changed, 299 insertions, 19 deletions

diff --git a/crypto/src/math/ec/Nat.cs b/crypto/src/math/ec/Nat.cs
index 821d5065d..91d86b674 100644
--- a/crypto/src/math/ec/Nat.cs
+++ b/crypto/src/math/ec/Nat.cs
@@ -365,6 +365,17 @@ namespace Org.BouncyCastle.Math.EC
             return c >> 31;
         }
 
+        public static uint ShiftUpBit(int len, uint[] x, int xOff, uint c, uint[] z)
+        {
+            for (int i = 0; i < len; ++i)
+            {
+                uint next = x[xOff + i];
+                z[i] = (next << 1) | (c >> 31);
+                c = next;
+            }
+            return c >> 31;
+        }
+
         public static uint ShiftUpBits(int len, uint[] z, int bits, uint c)
         {
             Debug.Assert(bits > 0 && bits < 32);
diff --git a/crypto/src/math/ec/custom/sec/Curve25519Field.cs b/crypto/src/math/ec/custom/sec/Curve25519Field.cs
new file mode 100644
index 000000000..be9878911
--- /dev/null
+++ b/crypto/src/math/ec/custom/sec/Curve25519Field.cs
@@ -0,0 +1,159 @@
+using System;
+using System.Diagnostics;
+
+namespace Org.BouncyCastle.Math.EC.Custom.Sec
+{
+    internal class Curve25519Field
+    {
+        // 2^255 - 2^4 - 2^1 - 1
+        internal static readonly uint[] P = new uint[]{ 0xFFFFFFED, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF,
+            0xFFFFFFFF, 0x7FFFFFFF };
+        private const int P7 = 0x7FFFFFFF;
+        private static readonly uint[] PExt = new uint[]{ 0x00000169, 0x00000000, 0x00000000, 0x00000000, 0x00000000,
+            0x00000000, 0x00000000, 0x00000000, 0xFFFFFFED, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF,
+            0xFFFFFFFF, 0x3FFFFFFF };
+        private const uint PInv = 0x13;
+
+        public static void Add(uint[] x, uint[] y, uint[] z)
+        {
+            Nat256.Add(x, y, z);
+            if (Nat256.Gte(z, P))
+            {
+                Nat256.AddWord(PInv, z, 0);
+                z[7] &= P7;
+            }
+        }
+
+        public static void AddExt(uint[] xx, uint[] yy, uint[] zz)
+        {
+            Nat256.AddExt(xx, yy, zz);
+            if (Nat256.GteExt(zz, PExt))
+            {
+                Nat256.SubExt(zz, PExt, zz);
+            }
+        }
+
+        public static void AddOne(uint[] x, uint[] z)
+        {
+            Nat256.Copy(x, z);
+            Nat256.Inc(z, 0);
+            if (Nat256.Gte(z, P))
+            {
+                Nat256.AddWord(PInv, z, 0);
+                z[7] &= P7;
+            }
+        }
+
+        public static uint[] FromBigInteger(BigInteger x)
+        {
+            uint[] z = Nat256.FromBigInteger(x);
+            if (Nat256.Gte(z, P))
+            {
+                Nat256.AddWord(PInv, z, 0);
+                z[7] &= P7;
+            }
+            return z;
+        }
+
+        public static void Half(uint[] x, uint[] z)
+        {
+            if ((x[0] & 1) == 0)
+            {
+                Nat.ShiftDownBit(8, x, 0, z);
+            }
+            else
+            {
+                Nat256.Add(x, P, z);
+                Nat.ShiftDownBit(8, z, 0);
+            }
+        }
+
+        public static void Multiply(uint[] x, uint[] y, uint[] z)
+        {
+            uint[] tt = Nat256.CreateExt();
+            Nat256.Mul(x, y, tt);
+            Reduce(tt, z);
+        }
+
+        public static void Negate(uint[] x, uint[] z)
+        {
+            if (Nat256.IsZero(x))
+            {
+                Nat256.Zero(z);
+            }
+            else
+            {
+                Nat256.Sub(P, x, z);
+            }
+        }
+
+        public static void Reduce(uint[] xx, uint[] z)
+        {
+            Debug.Assert(xx[15] >> 30 == 0);
+
+            uint xx07 = xx[7];
+            Nat.ShiftUpBit(8, xx, 8, xx07, z);
+            uint c = Nat256.MulByWordAddTo(PInv, xx, z) << 1;
+            uint z07 = z[7];
+            z[7] = z07 & P7;
+            c += (z07 >> 31) - (xx07 >> 31);
+            Nat256.AddWord(c * PInv, z, 0);
+            if (Nat256.Gte(z, P))
+            {
+                Nat256.AddWord(PInv, z, 0);
+                z[7] &= P7;
+            }
+        }
+
+        public static void Square(uint[] x, uint[] z)
+        {
+            uint[] tt = Nat256.CreateExt();
+            Nat256.Square(x, tt);
+            Reduce(tt, z);
+        }
+
+        public static void SquareN(uint[] x, int n, uint[] z)
+        {
+    //        assert n > 0;
+
+            uint[] tt = Nat256.CreateExt();
+            Nat256.Square(x, tt);
+            Reduce(tt, z);
+
+            while (--n > 0)
+            {
+                Nat256.Square(z, tt);
+                Reduce(tt, z);
+            }
+        }
+
+        public static void Subtract(uint[] x, uint[] y, uint[] z)
+        {
+            int c = Nat256.Sub(x, y, z);
+            if (c != 0)
+            {
+                Nat256.SubWord(PInv, z, 0);
+                z[7] &= P7;
+            }
+        }
+
+        public static void SubtractExt(uint[] xx, uint[] yy, uint[] zz)
+        {
+            int c = Nat256.SubExt(xx, yy, zz);
+            if (c != 0)
+            {
+                Nat256.AddExt(zz, PExt, zz);
+            }
+        }
+
+        public static void Twice(uint[] x, uint[] z)
+        {
+            Nat256.ShiftUpBit(x, 0, z);
+            if (Nat256.Gte(z, P))
+            {
+                Nat256.AddWord(PInv, z, 0);
+                z[7] &= P7;
+            }
+        }
+    }
+}
diff --git a/crypto/src/math/ec/custom/sec/Nat256.cs b/crypto/src/math/ec/custom/sec/Nat256.cs
index 3bd329251..4e3741886 100644
--- a/crypto/src/math/ec/custom/sec/Nat256.cs
+++ b/crypto/src/math/ec/custom/sec/Nat256.cs
@@ -223,6 +223,15 @@ 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);
@@ -232,6 +241,18 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             return c == 0 ? 0 : IncExt(zz, zzOff + 1);
         }
 
+        public static void Copy(uint[] x, uint[] z)
+        {
+            z[0] = x[0];
+            z[1] = x[1];
+            z[2] = x[2];
+            z[3] = x[3];
+            z[4] = x[4];
+            z[5] = x[5];
+            z[6] = x[6];
+            z[7] = x[7];
+        }
+
         public static uint[] Create()
         {
             return new uint[8];
@@ -255,6 +276,19 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             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);
@@ -637,34 +671,92 @@ namespace Org.BouncyCastle.Math.EC.Custom.Sec
             return c;
         }
 
-        public static uint MulWordAddExt(uint x, uint[] yy, int yyOff, uint[] zz, int zzOff)
+        public static uint MulByWord(uint x, uint[] z)
         {
-            Debug.Assert(yyOff <= 8);
-            Debug.Assert(zzOff <= 8);
             ulong c = 0, xVal = x;
-            c += xVal * yy[yyOff + 0] + zz[zzOff + 0];
-            zz[zzOff + 0] = (uint)c;
+            c += xVal * (ulong)z[0];
+            z[0] = (uint)c;
             c >>= 32;
-            c += xVal * yy[yyOff + 1] + zz[zzOff + 1];
-            zz[zzOff + 1] = (uint)c;
+            c += xVal * (ulong)z[1];
+            z[1] = (uint)c;
             c >>= 32;
-            c += xVal * yy[yyOff + 2] + zz[zzOff + 2];
-            zz[zzOff + 2] = (uint)c;
+            c += xVal * (ulong)z[2];
+            z[2] = (uint)c;
             c >>= 32;
-            c += xVal * yy[yyOff + 3] + zz[zzOff + 3];
-            zz[zzOff + 3] = (uint)c;
+            c += xVal * (ulong)z[3];
+            z[3] = (uint)c;
             c >>= 32;
-            c += xVal * yy[yyOff + 4] + zz[zzOff + 4];
-            zz[zzOff + 4] = (uint)c;
+            c += xVal * (ulong)z[4];
+            z[4] = (uint)c;
             c >>= 32;
-            c += xVal * yy[yyOff + 5] + zz[zzOff + 5];
-            zz[zzOff + 5] = (uint)c;
+            c += xVal * (ulong)z[5];
+            z[5] = (uint)c;
             c >>= 32;
-            c += xVal * yy[yyOff + 6] + zz[zzOff + 6];
-            zz[zzOff + 6] = (uint)c;
+            c += xVal * (ulong)z[6];
+            z[6] = (uint)c;
             c >>= 32;
-            c += xVal * yy[yyOff + 7] + zz[zzOff + 7];
-            zz[zzOff + 7] = (uint)c;
+            c += xVal * (ulong)z[7];
+            z[7] = (uint)c;
+            c >>= 32;
+            return (uint)c;
+        }
+
+        public static uint MulByWordAddTo(uint x, uint[] y, uint[] z)
+        {
+            ulong c = 0, xVal = x;
+            c += xVal * (ulong)z[0] + y[0];
+            z[0] = (uint)c;
+            c >>= 32;
+            c += xVal * (ulong)z[1] + y[1];
+            z[1] = (uint)c;
+            c >>= 32;
+            c += xVal * (ulong)z[2] + y[2];
+            z[2] = (uint)c;
+            c >>= 32;
+            c += xVal * (ulong)z[3] + y[3];
+            z[3] = (uint)c;
+            c >>= 32;
+            c += xVal * (ulong)z[4] + y[4];
+            z[4] = (uint)c;
+            c >>= 32;
+            c += xVal * (ulong)z[5] + y[5];
+            z[5] = (uint)c;
+            c >>= 32;
+            c += xVal * (ulong)z[6] + y[6];
+            z[6] = (uint)c;
+            c >>= 32;
+            c += xVal * (ulong)z[7] + y[7];
+            z[7] = (uint)c;
+            c >>= 32;
+            return (uint)c;
+        }
+
+        public static uint MulWordAddTo(uint x, uint[] y, int yOff, uint[] z, int zOff)
+        {
+            ulong c = 0, xVal = x;
+            c += xVal * y[yOff + 0] + z[zOff + 0];
+            z[zOff + 0] = (uint)c;
+            c >>= 32;
+            c += xVal * y[yOff + 1] + z[zOff + 1];
+            z[zOff + 1] = (uint)c;
+            c >>= 32;
+            c += xVal * y[yOff + 2] + z[zOff + 2];
+            z[zOff + 2] = (uint)c;
+            c >>= 32;
+            c += xVal * y[yOff + 3] + z[zOff + 3];
+            z[zOff + 3] = (uint)c;
+            c >>= 32;
+            c += xVal * y[yOff + 4] + z[zOff + 4];
+            z[zOff + 4] = (uint)c;
+            c >>= 32;
+            c += xVal * y[yOff + 5] + z[zOff + 5];
+            z[zOff + 5] = (uint)c;
+            c >>= 32;
+            c += xVal * y[yOff + 6] + z[zOff + 6];
+            z[zOff + 6] = (uint)c;
+            c >>= 32;
+            c += xVal * y[yOff + 7] + z[zOff + 7];
+            z[zOff + 7] = (uint)c;
             c >>= 32;
             return (uint)c;
         }
@@ -1237,6 +1329,24 @@ 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];