-
Notifications
You must be signed in to change notification settings - Fork 11
/
gf128mul_lb.c
551 lines (470 loc) · 17.4 KB
/
gf128mul_lb.c
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
/*
---------------------------------------------------------------------------
Copyright (c) 1998-2008, Brian Gladman, Worcester, UK. All rights reserved.
LICENSE TERMS
The redistribution and use of this software (with or without changes)
is allowed without the payment of fees or royalties provided that:
1. source code distributions include the above copyright notice, this
list of conditions and the following disclaimer;
2. binary distributions include the above copyright notice, this list
of conditions and the following disclaimer in their documentation;
3. the name of the copyright holder is not used to endorse products
built using this software without specific written permission.
DISCLAIMER
This software is provided 'as is' with no explicit or implied warranties
in respect of its properties, including, but not limited to, correctness
and/or fitness for purpose.
---------------------------------------------------------------------------
Issue Date: 20/12/2007
This file provides fast multiplication in GF(128) as required by several
cryptographic authentication modes. The galois field representation is
LB (see gfmul128.h) with the following in memory layout.
LB (favours BE)
===============
BE-8
x[0] x[1] x[2] x[3] x[4] x[5] x[6] x[7]
ms ls ms ls ms ls ms ls ms ls ms ls ms ls ms ls
....... ....... ....... ....... ....... ....... ....... .......
00...07 08...15 16...23 24...31 32...39 40...47 48...55 56...63
x[8] x[9] x[10] x[11] x[12] x[13] x[14] x[15]
ms ls ms ls ms ls ms ls ms ls ms ls ms ls ms ls
....... ....... ....... ....... ....... ....... ....... .......
64...71 72...79 80...87 88...95 96..103 104.111 112.119 120.127
BE-16
ms x[0] ls ms x[1] ls ms x[2] ls ms x[3] ls
............... ............... ............... ...............
00...07 08...15 16...23 24...31 32...39 40...47 48...55 56...63
ms x[4] ls ms x[5] ls ms x[6] ls ms x[7] ls
............... ............... ............... ...............
64...71 72...79 80...87 88...95 96..103 104.111 112.119 120.127
BE-32
ms x[0] ls ms x[1] ls
............................... ...............................
00...07 08...15 16...23 24...31 32...39 40...47 48...55 56...63
ms x[2] ls ms x[3] ls
............................... ...............................
64...71 72...79 80...87 88...95 96..103 104.111 112.119 120.127
BE-64
ms x[0] ls
...............................................................
00...07 08...15 16...23 24...31 32...39 40...47 48...55 56...63
ms x[1] ls
...............................................................
64...71 72...79 80...87 88...95 96..103 104.111 112.119 120.127
LE-16
ms x[0] ls ms x[1] ls ms x[2] ls ms x[3] ls
............... ............... ............... ...............
08...15 00...07 24...31 16...23 40...47 32...39 56...63 48...55
ms x[4] ls ms x[5] ls ms x[6] ls ms x[7] ls
............... ............... ............... ...............
72...79 64...71 88...95 80...87 104.111 96..103 120.127 112.119
LE-32
ms x[0] ls ms x[1] ls
............................... ...............................
24...31 16...23 08...15 00...07 56...63 48...55 40...47 32...39
ms x[2] ls ms x[3] ls
............................... ...............................
88...95 80...87 72...79 64...71 120.127 112.119 104.111 96..103
LE-64
ms x[0] ls
...............................................................
56...63 48...55 40...47 32...39 24...31 16...23 08...15 00...07
ms x[1] ls
...............................................................
120.127 112.119 104.111 96..103 88...95 80...87 72...79 64...71
These functions multiply a field element x, by x^4 and by x^8 in
the polynomial field representation. It uses 32-bit word operations
to gain speed but compensates for machine endianess and hence works
correctly on both styles of machine.
*/
#define GF_MODE_LB
/* Change Galois Field representation (for TESTING, not for production) */
#if 0
# define CHANGE_GF_REPRESENTATION
# define CONVERT (REVERSE_NONE)
#endif
#include "gf128mul.h"
#include "mode_hdr.h"
#include "gf_mul_lo.c"
/* Speed critical loops can be unrolled to gain speed but consume more memory */
#if 1
# define UNROLL_LOOPS
#endif
void gf_mul(gf_t a, const gf_t b)
{ gf_t p[8];
uint_8t *q, ch;
int i;
#ifdef CHANGE_GF_REPRESENTATION
convert_representation(a, a, CONVERT);
if(a != b)
convert_representation(b, b, CONVERT);
#endif
q = (uint_8t*)(a == b ? p[0] : b);
move_block_aligned(p[0], a);
for(i = 0; i < 7; ++i)
gf_mulx1_lb(p[i + 1], p[i]);
memset(a, 0, GF_BYTE_LEN);
for(i = 15; ; )
{
ch = q[i];
if(ch & X_0)
xor_block_aligned(a, a, p[0]);
if(ch & X_1)
xor_block_aligned(a, a, p[1]);
if(ch & X_2)
xor_block_aligned(a, a, p[2]);
if(ch & X_3)
xor_block_aligned(a, a, p[3]);
if(ch & X_4)
xor_block_aligned(a, a, p[4]);
if(ch & X_5)
xor_block_aligned(a, a, p[5]);
if(ch & X_6)
xor_block_aligned(a, a, p[6]);
if(ch & X_7)
xor_block_aligned(a, a, p[7]);
if(!i--)
break;
gf_mulx8_lb(a);
}
#ifdef CHANGE_GF_REPRESENTATION
convert_representation(a, a, CONVERT);
if(a != b)
convert_representation(b, b, CONVERT);
#endif
}
#if defined( TABLES_64K )
/* This version uses 64k bytes of table space on the stack.
An input field value in a[] has to be multiplied by a
key value in g[]. To do this a[] is split up into 16
smaller field values each one byte in length. For the
256 values of each of these smaller field values we can
precompute the result of mulltiplying g by the field
value in question. So for each of 16 bytes we have a
table of 256 field values, each of 16 bytes - 64k bytes
in total.
*/
void init_64k_table(gf_t g, gf_t64k_t t)
{ int i = 0, j, k;
/*
the byte value 0x80 at the lowest byte position in a[]
is unity in this field representation g[] goes into
this position in the table. 0x40 corresponds to a field
value of 2 so we can determine this value by multiplying
the 0x80 value by x, a process we can repeat for 8 field
values.
*/
#ifdef CHANGE_GF_REPRESENTATION
convert_representation(t[0][128], g, CONVERT);
#else
memcpy(t[0][128], g, GF_BYTE_LEN);
#endif
memset(t[0][0], 0, GF_BYTE_LEN);
for(j = 64; j > 0; j >>= 1)
gf_mulx1_lb(t[0][j], t[0][j + j]);
for( ; ; )
{
/* if { n } stands for the field value represented by
the integer n, we can express higher multiplies in
the table as follows:
1. g * { 3} = g * {2} ^ g * {1}
2. g * { 5} = g * {4} ^ g * {1}
g * { 6} = g * {4} ^ g * {2}
g * { 7} = g * {4} ^ g * {3}
3. g * { 9} = g * {8} ^ g * {1}
g * {10} = g * {8} ^ g * {2}
....
and so on
*/
for(j = 2; j < 256; j += j)
for(k = 1; k < j; ++k)
xor_block_aligned(t[i][j + k], t[i][j], t[i][k]);
if(++i == GF_BYTE_LEN) /* all 16 byte positions done */
return;
/* We now move to the next byte up and set up its eight
starting values by multiplying the values in the
lower table by x^8
*/
memset(t[i][0], 0, GF_BYTE_LEN);
for(j = 128; j > 0; j >>= 1)
{
memcpy(t[i][j], t[i - 1][j], GF_BYTE_LEN);
gf_mulx8_lb(t[i][j]);
}
}
}
#define xor_64k(i,ap,t,r) xor_block_aligned(r, r, t[i][ap[i]])
#if defined( UNROLL_LOOPS )
void gf_mul_64k(gf_t a, const gf_t64k_t t, gf_t r)
{ uint_8t *ap = (uint_8t*)a;
#ifdef CHANGE_GF_REPRESENTATION
convert_representation(a, a, CONVERT);
#endif
memset(r, 0, GF_BYTE_LEN);
xor_64k(15, ap, t, r); xor_64k(14, ap, t, r);
xor_64k(13, ap, t, r); xor_64k(12, ap, t, r);
xor_64k(11, ap, t, r); xor_64k(10, ap, t, r);
xor_64k( 9, ap, t, r); xor_64k( 8, ap, t, r);
xor_64k( 7, ap, t, r); xor_64k( 6, ap, t, r);
xor_64k( 5, ap, t, r); xor_64k( 4, ap, t, r);
xor_64k( 3, ap, t, r); xor_64k( 2, ap, t, r);
xor_64k( 1, ap, t, r); xor_64k( 0, ap, t, r);
move_block_aligned(a, r);
#ifdef CHANGE_GF_REPRESENTATION
convert_representation(a, a, CONVERT);
#endif
}
#else
void gf_mul_64k(gf_t a, const gf_t64k_t t, gf_t r)
{ int i;
uint_8t *ap = (uint_8t*)a;
#ifdef CHANGE_GF_REPRESENTATION
convert_representation(a, a, CONVERT);
#endif
memset(r, 0, GF_BYTE_LEN);
for(i = 15; i >= 0; --i)
{
xor_64k(i,ap,t,r);
}
move_block_aligned(a, r);
#ifdef CHANGE_GF_REPRESENTATION
convert_representation(a, a, CONVERT);
#endif
}
#endif
#endif
#if defined( TABLES_8K )
/* This version uses 8k bytes of table space on the stack.
An input field value in a[] has to be multiplied by a
key value in g[]. To do this a[] is split up into 32
smaller field values each 4-bits in length. For the
16 values of each of these smaller field values we can
precompute the result of mulltiplying g[] by the field
value in question. So for each of 32 nibbles we have a
table of 16 field values, each of 16 bytes - 8k bytes
in total.
*/
void init_8k_table(gf_t g, gf_t8k_t t)
{ int i = 0, j, k;
/* do the high 4-bit nibble first - t[1][16] - and note
that the unit multiplier sits at 0x80 - t[1][8] in
the table. Then multiplies by x go at 4, 2, 1
*/
#ifdef CHANGE_GF_REPRESENTATION
convert_representation(t[1][8], g, CONVERT);
#else
memcpy(t[1][8], g, GF_BYTE_LEN);
#endif
memset(t[0][0], 0, GF_BYTE_LEN);
memset(t[1][0], 0, GF_BYTE_LEN);
for(j = 4; j > 0; j >>= 1)
gf_mulx1_lb(t[1][j], t[1][j + j]);
/* now do the low nibble: g * {x^4} = x * g * {x^3} */
gf_mulx1_lb(t[0][8], t[1][1]);
for(j = 4; j > 0; j >>= 1)
gf_mulx1_lb(t[0][j], t[0][j + j]);
for( ; ; )
{
for(j = 2; j < 16; j += j)
for(k = 1; k < j; ++k)
xor_block_aligned(t[i][j + k], t[i][j], t[i][k]);
if(++i == 2 * GF_BYTE_LEN)
return;
if(i > 1)
{
memset(t[i][0], 0, GF_BYTE_LEN);
for(j = 8; j > 0; j >>= 1)
{
memcpy(t[i][j], t[i - 2][j], GF_BYTE_LEN);
gf_mulx8_lb(t[i][j]);
}
}
}
}
#define xor_8k(i,ap,t,r) \
xor_block_aligned(r, r, t[i + i][ap[i] & 15]); \
xor_block_aligned(r, r, t[i + i + 1][ap[i] >> 4])
#if defined( UNROLL_LOOPS )
void gf_mul_8k(gf_t a, const gf_t8k_t t, gf_t r)
{ uint_8t *ap = (uint_8t*)a;
#ifdef CHANGE_GF_REPRESENTATION
convert_representation(a, a, CONVERT);
#endif
memset(r, 0, GF_BYTE_LEN);
xor_8k(15, ap, t, r); xor_8k(14, ap, t, r);
xor_8k(13, ap, t, r); xor_8k(12, ap, t, r);
xor_8k(11, ap, t, r); xor_8k(10, ap, t, r);
xor_8k( 9, ap, t, r); xor_8k( 8, ap, t, r);
xor_8k( 7, ap, t, r); xor_8k( 6, ap, t, r);
xor_8k( 5, ap, t, r); xor_8k( 4, ap, t, r);
xor_8k( 3, ap, t, r); xor_8k( 2, ap, t, r);
xor_8k( 1, ap, t, r); xor_8k( 0, ap, t, r);
move_block_aligned(a, r);
#ifdef CHANGE_GF_REPRESENTATION
convert_representation(a, a, CONVERT);
#endif
}
#else
void gf_mul_8k(gf_t a, const gf_t8k_t t, gf_t r)
{ int i;
uint_8t *ap = (uint_8t*)a;
#ifdef CHANGE_GF_REPRESENTATION
convert_representation(a, a, CONVERT);
#endif
memset(r, 0, GF_BYTE_LEN);
for(i = 15; i >= 0; --i)
{
xor_8k(i,ap,t,r);
}
memcpy(a, r, GF_BYTE_LEN);
#ifdef CHANGE_GF_REPRESENTATION
convert_representation(a, a, CONVERT);
#endif
}
#endif
#endif
#if defined( TABLES_4K )
/* This version uses 4k bytes of table space on the stack.
A 16 byte buffer has to be multiplied by a 16 byte key
value in GF(128). If we consider a GF(128) value in a
single byte, we can construct a table of the 256 16 byte
values that result from the 256 values of this byte.
This requires 4096 bytes. If we take the highest byte in
the buffer and use this table to get the result, we then
have to multiply by x^120 to get the final value. For the
next highest byte the result has to be multiplied by x^112
and so on. But we can do this by accumulating the result
in an accumulator starting with the result for the top
byte. We repeatedly multiply the accumulator value by
x^8 and then add in (i.e. xor) the 16 bytes of the next
lower byte in the buffer, stopping when we reach the
lowest byte. This requires a 4096 byte table.
*/
void init_4k_table(gf_t g, gf_t4k_t t)
{ int j, k;
#ifdef CHANGE_GF_REPRESENTATION
convert_representation(t[128], g, CONVERT);
#else
memcpy(t[128], g, GF_BYTE_LEN);
#endif
memset(t[0], 0, GF_BYTE_LEN);
for(j = 64; j > 0; j >>= 1)
gf_mulx1_lb(t[j], t[j + j]);
for(j = 2; j < 256; j += j)
for(k = 1; k < j; ++k)
xor_block_aligned(t[j + k], t[j], t[k]);
}
#define xor_4k(i,ap,t,r) gf_mulx8_lb(r); xor_block_aligned(r, r, t[ap[i]])
#if defined( UNROLL_LOOPS )
void gf_mul_4k(gf_t a, const gf_t4k_t t, gf_t r)
{ uint_8t *ap = (uint_8t*)a;
#ifdef CHANGE_GF_REPRESENTATION
convert_representation(a, a, CONVERT);
#endif
memset(r, 0, GF_BYTE_LEN);
xor_4k(15, ap, t, r); xor_4k(14, ap, t, r);
xor_4k(13, ap, t, r); xor_4k(12, ap, t, r);
xor_4k(11, ap, t, r); xor_4k(10, ap, t, r);
xor_4k( 9, ap, t, r); xor_4k( 8, ap, t, r);
xor_4k( 7, ap, t, r); xor_4k( 6, ap, t, r);
xor_4k( 5, ap, t, r); xor_4k( 4, ap, t, r);
xor_4k( 3, ap, t, r); xor_4k( 2, ap, t, r);
xor_4k( 1, ap, t, r); xor_4k( 0, ap, t, r);
move_block_aligned(a, r);
#ifdef CHANGE_GF_REPRESENTATION
convert_representation(a, a, CONVERT);
#endif
}
#else
void gf_mul_4k(gf_t a, const gf_t4k_t t, gf_t r)
{ int i = 15;
uint_8t *ap = (uint_8t*)a;
#ifdef CHANGE_GF_REPRESENTATION
convert_representation(a, a, CONVERT);
#endif
memset(r, 0, GF_BYTE_LEN);
for(i = 15; i >=0; --i)
{
xor_4k(i, ap, t, r);
}
move_block_aligned(a, r);
#ifdef CHANGE_GF_REPRESENTATION
convert_representation(a, a, CONVERT);
#endif
}
#endif
#endif
#if defined( TABLES_256 )
/* This version uses 256 bytes of table space on the stack.
A 16 byte buffer has to be multiplied by a 16 byte key
value in GF(128). If we consider a GF(128) value in a
single 4-bit nibble, we can construct a table of the 16
16 byte values that result from the 16 values of this
byte. This requires 256 bytes. If we take the highest
4-bit nibble in the buffer and use this table to get the
result, we then have to multiply by x^124 to get the
final value. For the next highest byte the result has to
be multiplied by x^120 and so on. But we can do this by
accumulating the result in an accumulator starting with
the result for the top nibble. We repeatedly multiply
the accumulator value by x^4 and then add in (i.e. xor)
the 16 bytes of the next lower nibble in the buffer,
stopping when we reach the lowest nibblebyte. This uses
a 256 byte table.
*/
void init_256_table(gf_t g, gf_t256_t t)
{ int j, k;
#ifdef CHANGE_GF_REPRESENTATION
convert_representation(t[8], g, CONVERT);
#else
memcpy(t[8], g, GF_BYTE_LEN);
#endif
memset(t[0], 0, GF_BYTE_LEN);
for(j = 4; j > 0; j >>= 1)
gf_mulx1_lb(t[j], t[j + j]);
for(j = 2; j < 16; j += j)
for(k = 1; k < j; ++k)
xor_block_aligned(t[j + k], t[j], t[k]);
}
#define xor_256(i,ap,t,r) \
gf_mulx4_lb(r); xor_block_aligned(r, r, t[ap[i] & 15]); \
gf_mulx4_lb(r); xor_block_aligned(r, r, t[ap[i] >> 4])
#if defined( UNROLL_LOOPS )
void gf_mul_256(gf_t a, const gf_t256_t t, gf_t r)
{ uint_8t *ap = (uint_8t*)a;
#ifdef CHANGE_GF_REPRESENTATION
convert_representation(a, a, CONVERT);
#endif
memset(r, 0, GF_BYTE_LEN);
xor_256(15, ap, t, r); xor_256(14, ap, t, r);
xor_256(13, ap, t, r); xor_256(12, ap, t, r);
xor_256(11, ap, t, r); xor_256(10, ap, t, r);
xor_256( 9, ap, t, r); xor_256( 8, ap, t, r);
xor_256( 7, ap, t, r); xor_256( 6, ap, t, r);
xor_256( 5, ap, t, r); xor_256( 4, ap, t, r);
xor_256( 3, ap, t, r); xor_256( 2, ap, t, r);
xor_256( 1, ap, t, r); xor_256( 0, ap, t, r);
move_block_aligned(a, r);
#ifdef CHANGE_GF_REPRESENTATION
convert_representation(a, a, CONVERT);
#endif
}
#else
void gf_mul_256(gf_t a, const gf_t256_t t, gf_t r)
{ int i;
uint_8t *ap = (uint_8t*)a;
#ifdef CHANGE_GF_REPRESENTATION
convert_representation(a, a, CONVERT);
#endif
memset(r, 0, GF_BYTE_LEN);
for(i = 15; i >= 0; --i)
{
xor_256(i, ap, t, r);
}
move_block_aligned(a, r);
#ifdef CHANGE_GF_REPRESENTATION
convert_representation(a, a, CONVERT);
#endif
}
#endif
#endif