Free Electrons

Embedded Linux Experts

  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
/* gf128mul.c - GF(2^128) multiplication functions
 *
 * Copyright (c) 2003, Dr Brian Gladman, Worcester, UK.
 * Copyright (c) 2006, Rik Snel <rsnel@cube.dyndns.org>
 *
 * Based on Dr Brian Gladman's (GPL'd) work published at
 * http://gladman.plushost.co.uk/oldsite/cryptography_technology/index.php
 * See the original copyright notice below.
 *
 * This program is free software; you can redistribute it and/or modify it
 * under the terms of the GNU General Public License as published by the Free
 * Software Foundation; either version 2 of the License, or (at your option)
 * any later version.
 */

/*
 ---------------------------------------------------------------------------
 Copyright (c) 2003, Dr Brian Gladman, Worcester, UK.   All rights reserved.

 LICENSE TERMS

 The free distribution and use of this software in both source and binary
 form is allowed (with or without changes) provided that:

   1. distributions of this source code include the above copyright
      notice, this list of conditions and the following disclaimer;

   2. distributions in binary form include the above copyright
      notice, this list of conditions and the following disclaimer
      in the documentation and/or other associated materials;

   3. the copyright holder's name is not used to endorse products
      built using this software without specific written permission.

 ALTERNATIVELY, provided that this notice is retained in full, this product
 may be distributed under the terms of the GNU General Public License (GPL),
 in which case the provisions of the GPL apply INSTEAD OF those given above.

 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 31/01/2006

 This file provides fast multiplication in GF(2^128) as required by several
 cryptographic authentication modes
*/

#include <crypto/gf128mul.h>
#include <linux/kernel.h>
#include <linux/module.h>
#include <linux/slab.h>

#define gf128mul_dat(q) { \
	q(0x00), q(0x01), q(0x02), q(0x03), q(0x04), q(0x05), q(0x06), q(0x07),\
	q(0x08), q(0x09), q(0x0a), q(0x0b), q(0x0c), q(0x0d), q(0x0e), q(0x0f),\
	q(0x10), q(0x11), q(0x12), q(0x13), q(0x14), q(0x15), q(0x16), q(0x17),\
	q(0x18), q(0x19), q(0x1a), q(0x1b), q(0x1c), q(0x1d), q(0x1e), q(0x1f),\
	q(0x20), q(0x21), q(0x22), q(0x23), q(0x24), q(0x25), q(0x26), q(0x27),\
	q(0x28), q(0x29), q(0x2a), q(0x2b), q(0x2c), q(0x2d), q(0x2e), q(0x2f),\
	q(0x30), q(0x31), q(0x32), q(0x33), q(0x34), q(0x35), q(0x36), q(0x37),\
	q(0x38), q(0x39), q(0x3a), q(0x3b), q(0x3c), q(0x3d), q(0x3e), q(0x3f),\
	q(0x40), q(0x41), q(0x42), q(0x43), q(0x44), q(0x45), q(0x46), q(0x47),\
	q(0x48), q(0x49), q(0x4a), q(0x4b), q(0x4c), q(0x4d), q(0x4e), q(0x4f),\
	q(0x50), q(0x51), q(0x52), q(0x53), q(0x54), q(0x55), q(0x56), q(0x57),\
	q(0x58), q(0x59), q(0x5a), q(0x5b), q(0x5c), q(0x5d), q(0x5e), q(0x5f),\
	q(0x60), q(0x61), q(0x62), q(0x63), q(0x64), q(0x65), q(0x66), q(0x67),\
	q(0x68), q(0x69), q(0x6a), q(0x6b), q(0x6c), q(0x6d), q(0x6e), q(0x6f),\
	q(0x70), q(0x71), q(0x72), q(0x73), q(0x74), q(0x75), q(0x76), q(0x77),\
	q(0x78), q(0x79), q(0x7a), q(0x7b), q(0x7c), q(0x7d), q(0x7e), q(0x7f),\
	q(0x80), q(0x81), q(0x82), q(0x83), q(0x84), q(0x85), q(0x86), q(0x87),\
	q(0x88), q(0x89), q(0x8a), q(0x8b), q(0x8c), q(0x8d), q(0x8e), q(0x8f),\
	q(0x90), q(0x91), q(0x92), q(0x93), q(0x94), q(0x95), q(0x96), q(0x97),\
	q(0x98), q(0x99), q(0x9a), q(0x9b), q(0x9c), q(0x9d), q(0x9e), q(0x9f),\
	q(0xa0), q(0xa1), q(0xa2), q(0xa3), q(0xa4), q(0xa5), q(0xa6), q(0xa7),\
	q(0xa8), q(0xa9), q(0xaa), q(0xab), q(0xac), q(0xad), q(0xae), q(0xaf),\
	q(0xb0), q(0xb1), q(0xb2), q(0xb3), q(0xb4), q(0xb5), q(0xb6), q(0xb7),\
	q(0xb8), q(0xb9), q(0xba), q(0xbb), q(0xbc), q(0xbd), q(0xbe), q(0xbf),\
	q(0xc0), q(0xc1), q(0xc2), q(0xc3), q(0xc4), q(0xc5), q(0xc6), q(0xc7),\
	q(0xc8), q(0xc9), q(0xca), q(0xcb), q(0xcc), q(0xcd), q(0xce), q(0xcf),\
	q(0xd0), q(0xd1), q(0xd2), q(0xd3), q(0xd4), q(0xd5), q(0xd6), q(0xd7),\
	q(0xd8), q(0xd9), q(0xda), q(0xdb), q(0xdc), q(0xdd), q(0xde), q(0xdf),\
	q(0xe0), q(0xe1), q(0xe2), q(0xe3), q(0xe4), q(0xe5), q(0xe6), q(0xe7),\
	q(0xe8), q(0xe9), q(0xea), q(0xeb), q(0xec), q(0xed), q(0xee), q(0xef),\
	q(0xf0), q(0xf1), q(0xf2), q(0xf3), q(0xf4), q(0xf5), q(0xf6), q(0xf7),\
	q(0xf8), q(0xf9), q(0xfa), q(0xfb), q(0xfc), q(0xfd), q(0xfe), q(0xff) \
}

/*
 * Given a value i in 0..255 as the byte overflow when a field element
 * in GF(2^128) is multiplied by x^8, the following macro returns the
 * 16-bit value that must be XOR-ed into the low-degree end of the
 * product to reduce it modulo the polynomial x^128 + x^7 + x^2 + x + 1.
 *
 * There are two versions of the macro, and hence two tables: one for
 * the "be" convention where the highest-order bit is the coefficient of
 * the highest-degree polynomial term, and one for the "le" convention
 * where the highest-order bit is the coefficient of the lowest-degree
 * polynomial term.  In both cases the values are stored in CPU byte
 * endianness such that the coefficients are ordered consistently across
 * bytes, i.e. in the "be" table bits 15..0 of the stored value
 * correspond to the coefficients of x^15..x^0, and in the "le" table
 * bits 15..0 correspond to the coefficients of x^0..x^15.
 *
 * Therefore, provided that the appropriate byte endianness conversions
 * are done by the multiplication functions (and these must be in place
 * anyway to support both little endian and big endian CPUs), the "be"
 * table can be used for multiplications of both "bbe" and "ble"
 * elements, and the "le" table can be used for multiplications of both
 * "lle" and "lbe" elements.
 */

#define xda_be(i) ( \
	(i & 0x80 ? 0x4380 : 0) ^ (i & 0x40 ? 0x21c0 : 0) ^ \
	(i & 0x20 ? 0x10e0 : 0) ^ (i & 0x10 ? 0x0870 : 0) ^ \
	(i & 0x08 ? 0x0438 : 0) ^ (i & 0x04 ? 0x021c : 0) ^ \
	(i & 0x02 ? 0x010e : 0) ^ (i & 0x01 ? 0x0087 : 0) \
)

#define xda_le(i) ( \
	(i & 0x80 ? 0xe100 : 0) ^ (i & 0x40 ? 0x7080 : 0) ^ \
	(i & 0x20 ? 0x3840 : 0) ^ (i & 0x10 ? 0x1c20 : 0) ^ \
	(i & 0x08 ? 0x0e10 : 0) ^ (i & 0x04 ? 0x0708 : 0) ^ \
	(i & 0x02 ? 0x0384 : 0) ^ (i & 0x01 ? 0x01c2 : 0) \
)

static const u16 gf128mul_table_le[256] = gf128mul_dat(xda_le);
static const u16 gf128mul_table_be[256] = gf128mul_dat(xda_be);

/*
 * The following functions multiply a field element by x^8 in
 * the polynomial field representation.  They use 64-bit word operations
 * to gain speed but compensate for machine endianness and hence work
 * correctly on both styles of machine.
 */

static void gf128mul_x8_lle(be128 *x)
{
	u64 a = be64_to_cpu(x->a);
	u64 b = be64_to_cpu(x->b);
	u64 _tt = gf128mul_table_le[b & 0xff];

	x->b = cpu_to_be64((b >> 8) | (a << 56));
	x->a = cpu_to_be64((a >> 8) ^ (_tt << 48));
}

static void gf128mul_x8_bbe(be128 *x)
{
	u64 a = be64_to_cpu(x->a);
	u64 b = be64_to_cpu(x->b);
	u64 _tt = gf128mul_table_be[a >> 56];

	x->a = cpu_to_be64((a << 8) | (b >> 56));
	x->b = cpu_to_be64((b << 8) ^ _tt);
}

void gf128mul_lle(be128 *r, const be128 *b)
{
	be128 p[8];
	int i;

	p[0] = *r;
	for (i = 0; i < 7; ++i)
		gf128mul_x_lle(&p[i + 1], &p[i]);

	memset(r, 0, sizeof(*r));
	for (i = 0;;) {
		u8 ch = ((u8 *)b)[15 - i];

		if (ch & 0x80)
			be128_xor(r, r, &p[0]);
		if (ch & 0x40)
			be128_xor(r, r, &p[1]);
		if (ch & 0x20)
			be128_xor(r, r, &p[2]);
		if (ch & 0x10)
			be128_xor(r, r, &p[3]);
		if (ch & 0x08)
			be128_xor(r, r, &p[4]);
		if (ch & 0x04)
			be128_xor(r, r, &p[5]);
		if (ch & 0x02)
			be128_xor(r, r, &p[6]);
		if (ch & 0x01)
			be128_xor(r, r, &p[7]);

		if (++i >= 16)
			break;

		gf128mul_x8_lle(r);
	}
}
EXPORT_SYMBOL(gf128mul_lle);

void gf128mul_bbe(be128 *r, const be128 *b)
{
	be128 p[8];
	int i;

	p[0] = *r;
	for (i = 0; i < 7; ++i)
		gf128mul_x_bbe(&p[i + 1], &p[i]);

	memset(r, 0, sizeof(*r));
	for (i = 0;;) {
		u8 ch = ((u8 *)b)[i];

		if (ch & 0x80)
			be128_xor(r, r, &p[7]);
		if (ch & 0x40)
			be128_xor(r, r, &p[6]);
		if (ch & 0x20)
			be128_xor(r, r, &p[5]);
		if (ch & 0x10)
			be128_xor(r, r, &p[4]);
		if (ch & 0x08)
			be128_xor(r, r, &p[3]);
		if (ch & 0x04)
			be128_xor(r, r, &p[2]);
		if (ch & 0x02)
			be128_xor(r, r, &p[1]);
		if (ch & 0x01)
			be128_xor(r, r, &p[0]);

		if (++i >= 16)
			break;

		gf128mul_x8_bbe(r);
	}
}
EXPORT_SYMBOL(gf128mul_bbe);

/*      This version uses 64k bytes of table space.
    A 16 byte buffer has to be multiplied by a 16 byte key
    value in GF(2^128).  If we consider a GF(2^128) value in
    the buffer's lowest 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. But we also
    need tables for each of the 16 higher bytes in the
    buffer as well, which makes 64 kbytes in total.
*/
/* additional explanation
 * t[0][BYTE] contains g*BYTE
 * t[1][BYTE] contains g*x^8*BYTE
 *  ..
 * t[15][BYTE] contains g*x^120*BYTE */
struct gf128mul_64k *gf128mul_init_64k_bbe(const be128 *g)
{
	struct gf128mul_64k *t;
	int i, j, k;

	t = kzalloc(sizeof(*t), GFP_KERNEL);
	if (!t)
		goto out;

	for (i = 0; i < 16; i++) {
		t->t[i] = kzalloc(sizeof(*t->t[i]), GFP_KERNEL);
		if (!t->t[i]) {
			gf128mul_free_64k(t);
			t = NULL;
			goto out;
		}
	}

	t->t[0]->t[1] = *g;
	for (j = 1; j <= 64; j <<= 1)
		gf128mul_x_bbe(&t->t[0]->t[j + j], &t->t[0]->t[j]);

	for (i = 0;;) {
		for (j = 2; j < 256; j += j)
			for (k = 1; k < j; ++k)
				be128_xor(&t->t[i]->t[j + k],
					  &t->t[i]->t[j], &t->t[i]->t[k]);

		if (++i >= 16)
			break;

		for (j = 128; j > 0; j >>= 1) {
			t->t[i]->t[j] = t->t[i - 1]->t[j];
			gf128mul_x8_bbe(&t->t[i]->t[j]);
		}
	}

out:
	return t;
}
EXPORT_SYMBOL(gf128mul_init_64k_bbe);

void gf128mul_free_64k(struct gf128mul_64k *t)
{
	int i;

	for (i = 0; i < 16; i++)
		kzfree(t->t[i]);
	kzfree(t);
}
EXPORT_SYMBOL(gf128mul_free_64k);

void gf128mul_64k_bbe(be128 *a, const struct gf128mul_64k *t)
{
	u8 *ap = (u8 *)a;
	be128 r[1];
	int i;

	*r = t->t[0]->t[ap[15]];
	for (i = 1; i < 16; ++i)
		be128_xor(r, r, &t->t[i]->t[ap[15 - i]]);
	*a = *r;
}
EXPORT_SYMBOL(gf128mul_64k_bbe);

/*      This version uses 4k bytes of table space.
    A 16 byte buffer has to be multiplied by a 16 byte key
    value in GF(2^128).  If we consider a GF(2^128) 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.
*/
struct gf128mul_4k *gf128mul_init_4k_lle(const be128 *g)
{
	struct gf128mul_4k *t;
	int j, k;

	t = kzalloc(sizeof(*t), GFP_KERNEL);
	if (!t)
		goto out;

	t->t[128] = *g;
	for (j = 64; j > 0; j >>= 1)
		gf128mul_x_lle(&t->t[j], &t->t[j+j]);

	for (j = 2; j < 256; j += j)
		for (k = 1; k < j; ++k)
			be128_xor(&t->t[j + k], &t->t[j], &t->t[k]);

out:
	return t;
}
EXPORT_SYMBOL(gf128mul_init_4k_lle);

struct gf128mul_4k *gf128mul_init_4k_bbe(const be128 *g)
{
	struct gf128mul_4k *t;
	int j, k;

	t = kzalloc(sizeof(*t), GFP_KERNEL);
	if (!t)
		goto out;

	t->t[1] = *g;
	for (j = 1; j <= 64; j <<= 1)
		gf128mul_x_bbe(&t->t[j + j], &t->t[j]);

	for (j = 2; j < 256; j += j)
		for (k = 1; k < j; ++k)
			be128_xor(&t->t[j + k], &t->t[j], &t->t[k]);

out:
	return t;
}
EXPORT_SYMBOL(gf128mul_init_4k_bbe);

void gf128mul_4k_lle(be128 *a, const struct gf128mul_4k *t)
{
	u8 *ap = (u8 *)a;
	be128 r[1];
	int i = 15;

	*r = t->t[ap[15]];
	while (i--) {
		gf128mul_x8_lle(r);
		be128_xor(r, r, &t->t[ap[i]]);
	}
	*a = *r;
}
EXPORT_SYMBOL(gf128mul_4k_lle);

void gf128mul_4k_bbe(be128 *a, const struct gf128mul_4k *t)
{
	u8 *ap = (u8 *)a;
	be128 r[1];
	int i = 0;

	*r = t->t[ap[0]];
	while (++i < 16) {
		gf128mul_x8_bbe(r);
		be128_xor(r, r, &t->t[ap[i]]);
	}
	*a = *r;
}
EXPORT_SYMBOL(gf128mul_4k_bbe);

MODULE_LICENSE("GPL");
MODULE_DESCRIPTION("Functions for multiplying elements of GF(2^128)");