root/crypto/gf128mul.c

DEFINITIONS

1. gf128mul_x8_lle
2. gf128mul_x8_bbe
3. gf128mul_x8_ble
4. gf128mul_lle
5. gf128mul_bbe
6. gf128mul_init_64k_bbe
7. gf128mul_free_64k
8. gf128mul_64k_bbe
9. gf128mul_init_4k_lle
10. gf128mul_init_4k_bbe
11. gf128mul_4k_lle
12. gf128mul_4k_bbe

   1 /* gf128mul.c - GF(2^128) multiplication functions
   2  *
   3  * Copyright (c) 2003, Dr Brian Gladman, Worcester, UK.
   4  * Copyright (c) 2006, Rik Snel <rsnel@cube.dyndns.org>
   5  *
   6  * Based on Dr Brian Gladman's (GPL'd) work published at
   7  * http://gladman.plushost.co.uk/oldsite/cryptography_technology/index.php
   8  * See the original copyright notice below.
   9  *
  10  * This program is free software; you can redistribute it and/or modify it
  11  * under the terms of the GNU General Public License as published by the Free
  12  * Software Foundation; either version 2 of the License, or (at your option)
  13  * any later version.
  14  */
  15 
  16 /*
  17  ---------------------------------------------------------------------------
  18  Copyright (c) 2003, Dr Brian Gladman, Worcester, UK.   All rights reserved.
  19 
  20  LICENSE TERMS
  21 
  22  The free distribution and use of this software in both source and binary
  23  form is allowed (with or without changes) provided that:
  24 
  25    1. distributions of this source code include the above copyright
  26       notice, this list of conditions and the following disclaimer;
  27 
  28    2. distributions in binary form include the above copyright
  29       notice, this list of conditions and the following disclaimer
  30       in the documentation and/or other associated materials;
  31 
  32    3. the copyright holder's name is not used to endorse products
  33       built using this software without specific written permission.
  34 
  35  ALTERNATIVELY, provided that this notice is retained in full, this product
  36  may be distributed under the terms of the GNU General Public License (GPL),
  37  in which case the provisions of the GPL apply INSTEAD OF those given above.
  38 
  39  DISCLAIMER
  40 
  41  This software is provided 'as is' with no explicit or implied warranties
  42  in respect of its properties, including, but not limited to, correctness
  43  and/or fitness for purpose.
  44  ---------------------------------------------------------------------------
  45  Issue 31/01/2006
  46 
  47  This file provides fast multiplication in GF(2^128) as required by several
  48  cryptographic authentication modes
  49 */
  50 
  51 #include <crypto/gf128mul.h>
  52 #include <linux/kernel.h>
  53 #include <linux/module.h>
  54 #include <linux/slab.h>
  55 
  56 #define gf128mul_dat(q) { \
  57         q(0x00), q(0x01), q(0x02), q(0x03), q(0x04), q(0x05), q(0x06), q(0x07),\
  58         q(0x08), q(0x09), q(0x0a), q(0x0b), q(0x0c), q(0x0d), q(0x0e), q(0x0f),\
  59         q(0x10), q(0x11), q(0x12), q(0x13), q(0x14), q(0x15), q(0x16), q(0x17),\
  60         q(0x18), q(0x19), q(0x1a), q(0x1b), q(0x1c), q(0x1d), q(0x1e), q(0x1f),\
  61         q(0x20), q(0x21), q(0x22), q(0x23), q(0x24), q(0x25), q(0x26), q(0x27),\
  62         q(0x28), q(0x29), q(0x2a), q(0x2b), q(0x2c), q(0x2d), q(0x2e), q(0x2f),\
  63         q(0x30), q(0x31), q(0x32), q(0x33), q(0x34), q(0x35), q(0x36), q(0x37),\
  64         q(0x38), q(0x39), q(0x3a), q(0x3b), q(0x3c), q(0x3d), q(0x3e), q(0x3f),\
  65         q(0x40), q(0x41), q(0x42), q(0x43), q(0x44), q(0x45), q(0x46), q(0x47),\
  66         q(0x48), q(0x49), q(0x4a), q(0x4b), q(0x4c), q(0x4d), q(0x4e), q(0x4f),\
  67         q(0x50), q(0x51), q(0x52), q(0x53), q(0x54), q(0x55), q(0x56), q(0x57),\
  68         q(0x58), q(0x59), q(0x5a), q(0x5b), q(0x5c), q(0x5d), q(0x5e), q(0x5f),\
  69         q(0x60), q(0x61), q(0x62), q(0x63), q(0x64), q(0x65), q(0x66), q(0x67),\
  70         q(0x68), q(0x69), q(0x6a), q(0x6b), q(0x6c), q(0x6d), q(0x6e), q(0x6f),\
  71         q(0x70), q(0x71), q(0x72), q(0x73), q(0x74), q(0x75), q(0x76), q(0x77),\
  72         q(0x78), q(0x79), q(0x7a), q(0x7b), q(0x7c), q(0x7d), q(0x7e), q(0x7f),\
  73         q(0x80), q(0x81), q(0x82), q(0x83), q(0x84), q(0x85), q(0x86), q(0x87),\
  74         q(0x88), q(0x89), q(0x8a), q(0x8b), q(0x8c), q(0x8d), q(0x8e), q(0x8f),\
  75         q(0x90), q(0x91), q(0x92), q(0x93), q(0x94), q(0x95), q(0x96), q(0x97),\
  76         q(0x98), q(0x99), q(0x9a), q(0x9b), q(0x9c), q(0x9d), q(0x9e), q(0x9f),\
  77         q(0xa0), q(0xa1), q(0xa2), q(0xa3), q(0xa4), q(0xa5), q(0xa6), q(0xa7),\
  78         q(0xa8), q(0xa9), q(0xaa), q(0xab), q(0xac), q(0xad), q(0xae), q(0xaf),\
  79         q(0xb0), q(0xb1), q(0xb2), q(0xb3), q(0xb4), q(0xb5), q(0xb6), q(0xb7),\
  80         q(0xb8), q(0xb9), q(0xba), q(0xbb), q(0xbc), q(0xbd), q(0xbe), q(0xbf),\
  81         q(0xc0), q(0xc1), q(0xc2), q(0xc3), q(0xc4), q(0xc5), q(0xc6), q(0xc7),\
  82         q(0xc8), q(0xc9), q(0xca), q(0xcb), q(0xcc), q(0xcd), q(0xce), q(0xcf),\
  83         q(0xd0), q(0xd1), q(0xd2), q(0xd3), q(0xd4), q(0xd5), q(0xd6), q(0xd7),\
  84         q(0xd8), q(0xd9), q(0xda), q(0xdb), q(0xdc), q(0xdd), q(0xde), q(0xdf),\
  85         q(0xe0), q(0xe1), q(0xe2), q(0xe3), q(0xe4), q(0xe5), q(0xe6), q(0xe7),\
  86         q(0xe8), q(0xe9), q(0xea), q(0xeb), q(0xec), q(0xed), q(0xee), q(0xef),\
  87         q(0xf0), q(0xf1), q(0xf2), q(0xf3), q(0xf4), q(0xf5), q(0xf6), q(0xf7),\
  88         q(0xf8), q(0xf9), q(0xfa), q(0xfb), q(0xfc), q(0xfd), q(0xfe), q(0xff) \
  89 }
  90 
  91 /*
  92  * Given a value i in 0..255 as the byte overflow when a field element
  93  * in GF(2^128) is multiplied by x^8, the following macro returns the
  94  * 16-bit value that must be XOR-ed into the low-degree end of the
  95  * product to reduce it modulo the polynomial x^128 + x^7 + x^2 + x + 1.
  96  *
  97  * There are two versions of the macro, and hence two tables: one for
  98  * the "be" convention where the highest-order bit is the coefficient of
  99  * the highest-degree polynomial term, and one for the "le" convention
 100  * where the highest-order bit is the coefficient of the lowest-degree
 101  * polynomial term.  In both cases the values are stored in CPU byte
 102  * endianness such that the coefficients are ordered consistently across
 103  * bytes, i.e. in the "be" table bits 15..0 of the stored value
 104  * correspond to the coefficients of x^15..x^0, and in the "le" table
 105  * bits 15..0 correspond to the coefficients of x^0..x^15.
 106  *
 107  * Therefore, provided that the appropriate byte endianness conversions
 108  * are done by the multiplication functions (and these must be in place
 109  * anyway to support both little endian and big endian CPUs), the "be"
 110  * table can be used for multiplications of both "bbe" and "ble"
 111  * elements, and the "le" table can be used for multiplications of both
 112  * "lle" and "lbe" elements.
 113  */
 114 
 115 #define xda_be(i) ( \
 116         (i & 0x80 ? 0x4380 : 0) ^ (i & 0x40 ? 0x21c0 : 0) ^ \
 117         (i & 0x20 ? 0x10e0 : 0) ^ (i & 0x10 ? 0x0870 : 0) ^ \
 118         (i & 0x08 ? 0x0438 : 0) ^ (i & 0x04 ? 0x021c : 0) ^ \
 119         (i & 0x02 ? 0x010e : 0) ^ (i & 0x01 ? 0x0087 : 0) \
 120 )
 121 
 122 #define xda_le(i) ( \
 123         (i & 0x80 ? 0xe100 : 0) ^ (i & 0x40 ? 0x7080 : 0) ^ \
 124         (i & 0x20 ? 0x3840 : 0) ^ (i & 0x10 ? 0x1c20 : 0) ^ \
 125         (i & 0x08 ? 0x0e10 : 0) ^ (i & 0x04 ? 0x0708 : 0) ^ \
 126         (i & 0x02 ? 0x0384 : 0) ^ (i & 0x01 ? 0x01c2 : 0) \
 127 )
 128 
 129 static const u16 gf128mul_table_le[256] = gf128mul_dat(xda_le);
 130 static const u16 gf128mul_table_be[256] = gf128mul_dat(xda_be);
 131 
 132 /*
 133  * The following functions multiply a field element by x^8 in
 134  * the polynomial field representation.  They use 64-bit word operations
 135  * to gain speed but compensate for machine endianness and hence work
 136  * correctly on both styles of machine.
 137  */
 138 
 139 static void gf128mul_x8_lle(be128 *x)
 140 {
 141         u64 a = be64_to_cpu(x->a);
 142         u64 b = be64_to_cpu(x->b);
 143         u64 _tt = gf128mul_table_le[b & 0xff];
 144 
 145         x->b = cpu_to_be64((b >> 8) | (a << 56));
 146         x->a = cpu_to_be64((a >> 8) ^ (_tt << 48));
 147 }
 148 
 149 static void gf128mul_x8_bbe(be128 *x)
 150 {
 151         u64 a = be64_to_cpu(x->a);
 152         u64 b = be64_to_cpu(x->b);
 153         u64 _tt = gf128mul_table_be[a >> 56];
 154 
 155         x->a = cpu_to_be64((a << 8) | (b >> 56));
 156         x->b = cpu_to_be64((b << 8) ^ _tt);
 157 }
 158 
 159 void gf128mul_x8_ble(le128 *r, const le128 *x)
 160 {
 161         u64 a = le64_to_cpu(x->a);
 162         u64 b = le64_to_cpu(x->b);
 163         u64 _tt = gf128mul_table_be[a >> 56];
 164 
 165         r->a = cpu_to_le64((a << 8) | (b >> 56));
 166         r->b = cpu_to_le64((b << 8) ^ _tt);
 167 }
 168 EXPORT_SYMBOL(gf128mul_x8_ble);
 169 
 170 void gf128mul_lle(be128 *r, const be128 *b)
 171 {
 172         be128 p[8];
 173         int i;
 174 
 175         p[0] = *r;
 176         for (i = 0; i < 7; ++i)
 177                 gf128mul_x_lle(&p[i + 1], &p[i]);
 178 
 179         memset(r, 0, sizeof(*r));
 180         for (i = 0;;) {
 181                 u8 ch = ((u8 *)b)[15 - i];
 182 
 183                 if (ch & 0x80)
 184                         be128_xor(r, r, &p[0]);
 185                 if (ch & 0x40)
 186                         be128_xor(r, r, &p[1]);
 187                 if (ch & 0x20)
 188                         be128_xor(r, r, &p[2]);
 189                 if (ch & 0x10)
 190                         be128_xor(r, r, &p[3]);
 191                 if (ch & 0x08)
 192                         be128_xor(r, r, &p[4]);
 193                 if (ch & 0x04)
 194                         be128_xor(r, r, &p[5]);
 195                 if (ch & 0x02)
 196                         be128_xor(r, r, &p[6]);
 197                 if (ch & 0x01)
 198                         be128_xor(r, r, &p[7]);
 199 
 200                 if (++i >= 16)
 201                         break;
 202 
 203                 gf128mul_x8_lle(r);
 204         }
 205 }
 206 EXPORT_SYMBOL(gf128mul_lle);
 207 
 208 void gf128mul_bbe(be128 *r, const be128 *b)
 209 {
 210         be128 p[8];
 211         int i;
 212 
 213         p[0] = *r;
 214         for (i = 0; i < 7; ++i)
 215                 gf128mul_x_bbe(&p[i + 1], &p[i]);
 216 
 217         memset(r, 0, sizeof(*r));
 218         for (i = 0;;) {
 219                 u8 ch = ((u8 *)b)[i];
 220 
 221                 if (ch & 0x80)
 222                         be128_xor(r, r, &p[7]);
 223                 if (ch & 0x40)
 224                         be128_xor(r, r, &p[6]);
 225                 if (ch & 0x20)
 226                         be128_xor(r, r, &p[5]);
 227                 if (ch & 0x10)
 228                         be128_xor(r, r, &p[4]);
 229                 if (ch & 0x08)
 230                         be128_xor(r, r, &p[3]);
 231                 if (ch & 0x04)
 232                         be128_xor(r, r, &p[2]);
 233                 if (ch & 0x02)
 234                         be128_xor(r, r, &p[1]);
 235                 if (ch & 0x01)
 236                         be128_xor(r, r, &p[0]);
 237 
 238                 if (++i >= 16)
 239                         break;
 240 
 241                 gf128mul_x8_bbe(r);
 242         }
 243 }
 244 EXPORT_SYMBOL(gf128mul_bbe);
 245 
 246 /*      This version uses 64k bytes of table space.
 247     A 16 byte buffer has to be multiplied by a 16 byte key
 248     value in GF(2^128).  If we consider a GF(2^128) value in
 249     the buffer's lowest byte, we can construct a table of
 250     the 256 16 byte values that result from the 256 values
 251     of this byte.  This requires 4096 bytes. But we also
 252     need tables for each of the 16 higher bytes in the
 253     buffer as well, which makes 64 kbytes in total.
 254 */
 255 /* additional explanation
 256  * t[0][BYTE] contains g*BYTE
 257  * t[1][BYTE] contains g*x^8*BYTE
 258  *  ..
 259  * t[15][BYTE] contains g*x^120*BYTE */
 260 struct gf128mul_64k *gf128mul_init_64k_bbe(const be128 *g)
 261 {
 262         struct gf128mul_64k *t;
 263         int i, j, k;
 264 
 265         t = kzalloc(sizeof(*t), GFP_KERNEL);
 266         if (!t)
 267                 goto out;
 268 
 269         for (i = 0; i < 16; i++) {
 270                 t->t[i] = kzalloc(sizeof(*t->t[i]), GFP_KERNEL);
 271                 if (!t->t[i]) {
 272                         gf128mul_free_64k(t);
 273                         t = NULL;
 274                         goto out;
 275                 }
 276         }
 277 
 278         t->t[0]->t[1] = *g;
 279         for (j = 1; j <= 64; j <<= 1)
 280                 gf128mul_x_bbe(&t->t[0]->t[j + j], &t->t[0]->t[j]);
 281 
 282         for (i = 0;;) {
 283                 for (j = 2; j < 256; j += j)
 284                         for (k = 1; k < j; ++k)
 285                                 be128_xor(&t->t[i]->t[j + k],
 286                                           &t->t[i]->t[j], &t->t[i]->t[k]);
 287 
 288                 if (++i >= 16)
 289                         break;
 290 
 291                 for (j = 128; j > 0; j >>= 1) {
 292                         t->t[i]->t[j] = t->t[i - 1]->t[j];
 293                         gf128mul_x8_bbe(&t->t[i]->t[j]);
 294                 }
 295         }
 296 
 297 out:
 298         return t;
 299 }
 300 EXPORT_SYMBOL(gf128mul_init_64k_bbe);
 301 
 302 void gf128mul_free_64k(struct gf128mul_64k *t)
 303 {
 304         int i;
 305 
 306         for (i = 0; i < 16; i++)
 307                 kzfree(t->t[i]);
 308         kzfree(t);
 309 }
 310 EXPORT_SYMBOL(gf128mul_free_64k);
 311 
 312 void gf128mul_64k_bbe(be128 *a, const struct gf128mul_64k *t)
 313 {
 314         u8 *ap = (u8 *)a;
 315         be128 r[1];
 316         int i;
 317 
 318         *r = t->t[0]->t[ap[15]];
 319         for (i = 1; i < 16; ++i)
 320                 be128_xor(r, r, &t->t[i]->t[ap[15 - i]]);
 321         *a = *r;
 322 }
 323 EXPORT_SYMBOL(gf128mul_64k_bbe);
 324 
 325 /*      This version uses 4k bytes of table space.
 326     A 16 byte buffer has to be multiplied by a 16 byte key
 327     value in GF(2^128).  If we consider a GF(2^128) value in a
 328     single byte, we can construct a table of the 256 16 byte
 329     values that result from the 256 values of this byte.
 330     This requires 4096 bytes. If we take the highest byte in
 331     the buffer and use this table to get the result, we then
 332     have to multiply by x^120 to get the final value. For the
 333     next highest byte the result has to be multiplied by x^112
 334     and so on. But we can do this by accumulating the result
 335     in an accumulator starting with the result for the top
 336     byte.  We repeatedly multiply the accumulator value by
 337     x^8 and then add in (i.e. xor) the 16 bytes of the next
 338     lower byte in the buffer, stopping when we reach the
 339     lowest byte. This requires a 4096 byte table.
 340 */
 341 struct gf128mul_4k *gf128mul_init_4k_lle(const be128 *g)
 342 {
 343         struct gf128mul_4k *t;
 344         int j, k;
 345 
 346         t = kzalloc(sizeof(*t), GFP_KERNEL);
 347         if (!t)
 348                 goto out;
 349 
 350         t->t[128] = *g;
 351         for (j = 64; j > 0; j >>= 1)
 352                 gf128mul_x_lle(&t->t[j], &t->t[j+j]);
 353 
 354         for (j = 2; j < 256; j += j)
 355                 for (k = 1; k < j; ++k)
 356                         be128_xor(&t->t[j + k], &t->t[j], &t->t[k]);
 357 
 358 out:
 359         return t;
 360 }
 361 EXPORT_SYMBOL(gf128mul_init_4k_lle);
 362 
 363 struct gf128mul_4k *gf128mul_init_4k_bbe(const be128 *g)
 364 {
 365         struct gf128mul_4k *t;
 366         int j, k;
 367 
 368         t = kzalloc(sizeof(*t), GFP_KERNEL);
 369         if (!t)
 370                 goto out;
 371 
 372         t->t[1] = *g;
 373         for (j = 1; j <= 64; j <<= 1)
 374                 gf128mul_x_bbe(&t->t[j + j], &t->t[j]);
 375 
 376         for (j = 2; j < 256; j += j)
 377                 for (k = 1; k < j; ++k)
 378                         be128_xor(&t->t[j + k], &t->t[j], &t->t[k]);
 379 
 380 out:
 381         return t;
 382 }
 383 EXPORT_SYMBOL(gf128mul_init_4k_bbe);
 384 
 385 void gf128mul_4k_lle(be128 *a, const struct gf128mul_4k *t)
 386 {
 387         u8 *ap = (u8 *)a;
 388         be128 r[1];
 389         int i = 15;
 390 
 391         *r = t->t[ap[15]];
 392         while (i--) {
 393                 gf128mul_x8_lle(r);
 394                 be128_xor(r, r, &t->t[ap[i]]);
 395         }
 396         *a = *r;
 397 }
 398 EXPORT_SYMBOL(gf128mul_4k_lle);
 399 
 400 void gf128mul_4k_bbe(be128 *a, const struct gf128mul_4k *t)
 401 {
 402         u8 *ap = (u8 *)a;
 403         be128 r[1];
 404         int i = 0;
 405 
 406         *r = t->t[ap[0]];
 407         while (++i < 16) {
 408                 gf128mul_x8_bbe(r);
 409                 be128_xor(r, r, &t->t[ap[i]]);
 410         }
 411         *a = *r;
 412 }
 413 EXPORT_SYMBOL(gf128mul_4k_bbe);
 414 
 415 MODULE_LICENSE("GPL");
 416 MODULE_DESCRIPTION("Functions for multiplying elements of GF(2^128)");