Add custom implementations of SEC binary curves

1 files changed, 335 insertions, 0 deletions

diff --git a/crypto/src/math/ec/custom/sec/SecT283Field.cs b/crypto/src/math/ec/custom/sec/SecT283Field.cs
new file mode 100644
index 000000000..9afb27461
--- /dev/null
+++ b/crypto/src/math/ec/custom/sec/SecT283Field.cs
@@ -0,0 +1,335 @@
+using System;
+using System.Diagnostics;
+
+using Org.BouncyCastle.Math.Raw;
+
+namespace Org.BouncyCastle.Math.EC.Custom.Sec
+{
+    internal class SecT283Field
+    {
+        private const ulong M27 = ulong.MaxValue >> 37;
+        private const ulong M57 = ulong.MaxValue >> 7;
+
+        public static void Add(ulong[] x, ulong[] y, ulong[] z)
+        {
+            z[0] = x[0] ^ y[0];
+            z[1] = x[1] ^ y[1];
+            z[2] = x[2] ^ y[2];
+            z[3] = x[3] ^ y[3];
+            z[4] = x[4] ^ y[4];
+        }
+
+        public static void AddExt(ulong[] xx, ulong[] yy, ulong[] zz)
+        {
+            zz[0] = xx[0] ^ yy[0];
+            zz[1] = xx[1] ^ yy[1];
+            zz[2] = xx[2] ^ yy[2];
+            zz[3] = xx[3] ^ yy[3];
+            zz[4] = xx[4] ^ yy[4];
+            zz[5] = xx[5] ^ yy[5];
+            zz[6] = xx[6] ^ yy[6];
+            zz[7] = xx[7] ^ yy[7];
+            zz[8] = xx[8] ^ yy[8];
+        }
+
+        public static void AddOne(ulong[] x, ulong[] z)
+        {
+            z[0] = x[0] ^ 1UL;
+            z[1] = x[1];
+            z[2] = x[2];
+            z[3] = x[3];
+            z[4] = x[4];
+        }
+
+        public static ulong[] FromBigInteger(BigInteger x)
+        {
+            ulong[] z = Nat320.FromBigInteger64(x);
+            Reduce37(z, 0);
+            return z;
+        }
+
+        public static void Multiply(ulong[] x, ulong[] y, ulong[] z)
+        {
+            ulong[] tt = Nat320.CreateExt64();
+            ImplMultiply(x, y, tt);
+            Reduce(tt, z);
+        }
+
+        public static void MultiplyAddToExt(ulong[] x, ulong[] y, ulong[] zz)
+        {
+            ulong[] tt = Nat320.CreateExt64();
+            ImplMultiply(x, y, tt);
+            AddExt(zz, tt, zz);
+        }
+
+        public static void Reduce(ulong[] xx, ulong[] z)
+        {
+            ulong x0 = xx[0], x1 = xx[1], x2 = xx[2], x3 = xx[3], x4 = xx[4];
+            ulong x5 = xx[5], x6 = xx[6], x7 = xx[7], x8 = xx[8];
+
+            x3 ^= (x8 << 37) ^ (x8 << 42) ^ (x8 << 44) ^ (x8 << 49);
+            x4 ^= (x8 >> 27) ^ (x8 >> 22) ^ (x8 >> 20) ^ (x8 >> 15);
+
+            x2 ^= (x7 << 37) ^ (x7 << 42) ^ (x7 << 44) ^ (x7 << 49);
+            x3 ^= (x7 >> 27) ^ (x7 >> 22) ^ (x7 >> 20) ^ (x7 >> 15);
+
+            x1 ^= (x6 << 37) ^ (x6 << 42) ^ (x6 << 44) ^ (x6 << 49);
+            x2 ^= (x6 >> 27) ^ (x6 >> 22) ^ (x6 >> 20) ^ (x6 >> 15);
+
+            x0 ^= (x5 << 37) ^ (x5 << 42) ^ (x5 << 44) ^ (x5 << 49);
+            x1 ^= (x5 >> 27) ^ (x5 >> 22) ^ (x5 >> 20) ^ (x5 >> 15);
+
+            ulong t = x4 >> 27;
+            z[0]    = x0 ^ t ^ (t << 5) ^ (t << 7) ^ (t << 12);
+            z[1]    = x1; 
+            z[2]    = x2; 
+            z[3]    = x3; 
+            z[4]    = x4 & M27; 
+        }
+
+        public static void Reduce37(ulong[] z, int zOff)
+        {
+            ulong z4     = z[zOff + 4], t = z4 >> 27;
+            z[zOff    ] ^= t ^ (t << 5) ^ (t << 7) ^ (t << 12);
+            z[zOff + 4]  = z4 & M27;
+        }
+
+        public static void Square(ulong[] x, ulong[] z)
+        {
+            ulong[] tt = Nat.Create64(9);
+            ImplSquare(x, tt);
+            Reduce(tt, z);
+        }
+
+        public static void SquareAddToExt(ulong[] x, ulong[] zz)
+        {
+            ulong[] tt = Nat.Create64(9);
+            ImplSquare(x, tt);
+            AddExt(zz, tt, zz);
+        }
+
+        public static void SquareN(ulong[] x, int n, ulong[] z)
+        {
+            Debug.Assert(n > 0);
+
+            ulong[] tt = Nat.Create64(9);
+            ImplSquare(x, tt);
+            Reduce(tt, z);
+
+            while (--n > 0)
+            {
+                ImplSquare(z, tt);
+                Reduce(tt, z);
+            }
+        }
+
+        protected static void ImplCompactExt(ulong[] zz)
+        {
+            ulong z0 = zz[0], z1 = zz[1], z2 = zz[2], z3 = zz[3], z4 = zz[4];
+            ulong z5 = zz[5], z6 = zz[6], z7 = zz[7], z8 = zz[8], z9 = zz[9];
+            zz[0] =  z0        ^ (z1 << 57);
+            zz[1] = (z1 >>  7) ^ (z2 << 50);
+            zz[2] = (z2 >> 14) ^ (z3 << 43);
+            zz[3] = (z3 >> 21) ^ (z4 << 36);
+            zz[4] = (z4 >> 28) ^ (z5 << 29);
+            zz[5] = (z5 >> 35) ^ (z6 << 22);
+            zz[6] = (z6 >> 42) ^ (z7 << 15);
+            zz[7] = (z7 >> 49) ^ (z8 <<  8);
+            zz[8] = (z8 >> 56) ^ (z9 <<  1);
+            zz[9] = (z9 >> 63); // Zero!
+        }
+
+        protected static void ImplExpand(ulong[] x, ulong[] z)
+        {
+            ulong x0 = x[0], x1 = x[1], x2 = x[2], x3 = x[3], x4 = x[4];
+            z[0] = x0 & M57;
+            z[1] = ((x0 >> 57) ^ (x1 <<  7)) & M57;
+            z[2] = ((x1 >> 50) ^ (x2 << 14)) & M57;
+            z[3] = ((x2 >> 43) ^ (x3 << 21)) & M57;
+            z[4] = ((x3 >> 36) ^ (x4 << 28));
+        }
+
+        //protected static void AddMs(ulong[] zz, int zOff, ulong[] p, params int[] ms)
+        //{
+        //    ulong t0 = 0, t1 = 0;
+        //    foreach (int m in ms)
+        //    {
+        //        int i = (m - 1) << 1;
+        //        t0 ^= p[i    ];
+        //        t1 ^= p[i + 1];
+        //    }
+        //    zz[zOff    ] ^= t0;
+        //    zz[zOff + 1] ^= t1;
+        //}
+
+        protected static void ImplMultiply(ulong[] x, ulong[] y, ulong[] zz)
+        {
+            /*
+             * Formula (17) from "Some New Results on Binary Polynomial Multiplication",
+             * Murat Cenk and M. Anwar Hasan.
+             * 
+             * The formula as given contained an error in the term t25, as noted below
+             */
+            ulong[] a = new ulong[5], b = new ulong[5];
+            ImplExpand(x, a);
+            ImplExpand(y, b);
+
+            ulong[] p = new ulong[26];
+
+            ImplMulw(a[0], b[0], p, 0);                                 // m1
+            ImplMulw(a[1], b[1], p, 2);                                 // m2
+            ImplMulw(a[2], b[2], p, 4);                                 // m3
+            ImplMulw(a[3], b[3], p, 6);                                 // m4
+            ImplMulw(a[4], b[4], p, 8);                                 // m5
+
+            ulong u0 = a[0] ^ a[1], v0 = b[0] ^ b[1];
+            ulong u1 = a[0] ^ a[2], v1 = b[0] ^ b[2];
+            ulong u2 = a[2] ^ a[4], v2 = b[2] ^ b[4];
+            ulong u3 = a[3] ^ a[4], v3 = b[3] ^ b[4];
+
+            ImplMulw(u1 ^ a[3], v1 ^ b[3], p, 18);                      // m10
+            ImplMulw(u2 ^ a[1], v2 ^ b[1], p, 20);                      // m11
+
+            ulong A4 = u0 ^ u3  , B4 = v0 ^ v3;
+            ulong A5 = A4 ^ a[2], B5 = B4 ^ b[2];
+
+            ImplMulw(A4, B4, p, 22);                                    // m12
+            ImplMulw(A5, B5, p, 24);                                    // m13
+
+            ImplMulw(u0, v0, p, 10);                                    // m6
+            ImplMulw(u1, v1, p, 12);                                    // m7
+            ImplMulw(u2, v2, p, 14);                                    // m8
+            ImplMulw(u3, v3, p, 16);                                    // m9
+
+
+            // Original method, corresponding to formula (16)
+            //AddMs(zz, 0, p, 1);
+            //AddMs(zz, 1, p, 1, 2, 6);
+            //AddMs(zz, 2, p, 1, 2, 3, 7);
+            //AddMs(zz, 3, p, 1, 3, 4, 5, 8, 10, 12, 13);
+            //AddMs(zz, 4, p, 1, 2, 4, 5, 6, 9, 10, 11, 13);
+            //AddMs(zz, 5, p, 1, 2, 3, 5, 7, 11, 12, 13);
+            //AddMs(zz, 6, p, 3, 4, 5, 8);
+            //AddMs(zz, 7, p, 4, 5, 9);
+            //AddMs(zz, 8, p, 5);
+
+            // Improved method factors out common single-word terms
+            // NOTE: p1,...,p26 in the paper maps to p[0],...,p[25] here
+
+            zz[0]     = p[ 0];
+            zz[9]     = p[ 9];
+
+            ulong t1  = p[ 0] ^ p[ 1];
+            ulong t2  = t1    ^ p[ 2];
+            ulong t3  = t2    ^ p[10];
+        
+            zz[1]     = t3;
+
+            ulong t4  = p[ 3] ^ p[ 4];
+            ulong t5  = p[11] ^ p[12];
+            ulong t6  = t4    ^ t5;
+            ulong t7  = t2    ^ t6;
+
+            zz[2]     = t7;
+
+            ulong t8  = t1    ^ t4;
+            ulong t9  = p[ 5] ^ p[ 6];
+            ulong t10 = t8    ^ t9;
+            ulong t11 = t10   ^ p[ 8];
+            ulong t12 = p[13] ^ p[14];
+            ulong t13 = t11   ^ t12;
+            ulong t14 = p[18] ^ p[22];
+            ulong t15 = t14   ^ p[24];
+            ulong t16 = t13   ^ t15;
+
+            zz[3]     = t16;
+
+            ulong t17 = p[ 7] ^ p[ 8];
+            ulong t18 = t17   ^ p[ 9];
+            ulong t19 = t18   ^ p[17];
+
+            zz[8]     = t19;
+
+            ulong t20 = t18   ^ t9;
+            ulong t21 = p[15] ^ p[16];
+            ulong t22 = t20   ^ t21;
+
+            zz[7]     = t22;
+
+            ulong t23 = t22   ^ t3;
+            ulong t24 = p[19] ^ p[20];
+    //      ulong t25 = p[23] ^ p[24];
+            ulong t25 = p[25] ^ p[24];       // Fixes an error in the paper: p[23] -> p{25]
+            ulong t26 = p[18] ^ p[23];
+            ulong t27 = t24   ^ t25;
+            ulong t28 = t27   ^ t26;
+            ulong t29 = t28   ^ t23;
+
+            zz[4]     = t29;
+        
+            ulong t30 = t7    ^ t19;
+            ulong t31 = t27   ^ t30;
+            ulong t32 = p[21] ^ p[22];
+            ulong t33 = t31   ^ t32;
+
+            zz[5]     = t33;
+
+            ulong t34 = t11   ^ p[0];
+            ulong t35 = t34   ^ p[9];
+            ulong t36 = t35   ^ t12;
+            ulong t37 = t36   ^ p[21];
+            ulong t38 = t37   ^ p[23];
+            ulong t39 = t38   ^ p[25];
+
+            zz[6]     = t39;
+
+            ImplCompactExt(zz);
+        }
+
+        protected static void ImplMulw(ulong x, ulong y, ulong[] z, int zOff)
+        {
+            Debug.Assert(x >> 57 == 0);
+            Debug.Assert(y >> 57 == 0);
+
+            ulong[] u = new ulong[8];
+    //      u[0] = 0;
+            u[1] = y;
+            u[2] = u[1] << 1;
+            u[3] = u[2] ^  y;
+            u[4] = u[2] << 1;
+            u[5] = u[4] ^  y;
+            u[6] = u[3] << 1;
+            u[7] = u[6] ^  y;
+
+            uint j = (uint)x;
+            ulong g, h = 0, l = u[j & 7];
+            int k = 48;
+            do
+            {
+                j = (uint)(x >> k);
+                g  = u[j & 7]
+                   ^ u[(j >> 3) & 7] << 3
+                   ^ u[(j >> 6) & 7] << 6;
+                l ^= (g <<  k);
+                h ^= (g >> -k);
+            }
+            while ((k -= 9) > 0);
+
+            h ^= ((x & 0x0100804020100800L) & (ulong)(((long)y << 7) >> 63)) >> 8;
+
+            Debug.Assert(h >> 49 == 0);
+
+            z[zOff    ] = l & M57;
+            z[zOff + 1] = (l >> 57) ^ (h << 7);
+        }
+
+        protected static void ImplSquare(ulong[] x, ulong[] zz)
+        {
+            for (int i = 0; i < 4; ++i)
+            {
+                Interleave.Expand64To128(x[i], zz, i << 1);
+            }
+            zz[8] = Interleave.Expand32to64((uint)x[4]);
+        }
+    }
+}