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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
164 /* equivalent to gf128mul_table_be[b >> 63] (see crypto/gf128mul.c): */
165 u64 _tt = gf128mul_table_be[a >> 56];
166
167 r->a = cpu_to_le64((a << 8) | (b >> 56));
168 r->b = cpu_to_le64((b << 8) ^ _tt);
169 }
170 EXPORT_SYMBOL(gf128mul_x8_ble);
171
172 void gf128mul_lle(be128 *r, const be128 *b)
173 {
174 be128 p[8];
175 int i;
176
177 p[0] = *r;
178 for (i = 0; i < 7; ++i)
179 gf128mul_x_lle(&p[i + 1], &p[i]);
180
181 memset(r, 0, sizeof(*r));
182 for (i = 0;;) {
183 u8 ch = ((u8 *)b)[15 - i];
184
185 if (ch & 0x80)
186 be128_xor(r, r, &p[0]);
187 if (ch & 0x40)
188 be128_xor(r, r, &p[1]);
189 if (ch & 0x20)
190 be128_xor(r, r, &p[2]);
191 if (ch & 0x10)
192 be128_xor(r, r, &p[3]);
193 if (ch & 0x08)
194 be128_xor(r, r, &p[4]);
195 if (ch & 0x04)
196 be128_xor(r, r, &p[5]);
197 if (ch & 0x02)
198 be128_xor(r, r, &p[6]);
199 if (ch & 0x01)
200 be128_xor(r, r, &p[7]);
201
202 if (++i >= 16)
203 break;
204
205 gf128mul_x8_lle(r);
206 }
207 }
208 EXPORT_SYMBOL(gf128mul_lle);
209
210 void gf128mul_bbe(be128 *r, const be128 *b)
211 {
212 be128 p[8];
213 int i;
214
215 p[0] = *r;
216 for (i = 0; i < 7; ++i)
217 gf128mul_x_bbe(&p[i + 1], &p[i]);
218
219 memset(r, 0, sizeof(*r));
220 for (i = 0;;) {
221 u8 ch = ((u8 *)b)[i];
222
223 if (ch & 0x80)
224 be128_xor(r, r, &p[7]);
225 if (ch & 0x40)
226 be128_xor(r, r, &p[6]);
227 if (ch & 0x20)
228 be128_xor(r, r, &p[5]);
229 if (ch & 0x10)
230 be128_xor(r, r, &p[4]);
231 if (ch & 0x08)
232 be128_xor(r, r, &p[3]);
233 if (ch & 0x04)
234 be128_xor(r, r, &p[2]);
235 if (ch & 0x02)
236 be128_xor(r, r, &p[1]);
237 if (ch & 0x01)
238 be128_xor(r, r, &p[0]);
239
240 if (++i >= 16)
241 break;
242
243 gf128mul_x8_bbe(r);
244 }
245 }
246 EXPORT_SYMBOL(gf128mul_bbe);
247
248 /* This version uses 64k bytes of table space.
249 A 16 byte buffer has to be multiplied by a 16 byte key
250 value in GF(2^128). If we consider a GF(2^128) value in
251 the buffer's lowest byte, we can construct a table of
252 the 256 16 byte values that result from the 256 values
253 of this byte. This requires 4096 bytes. But we also
254 need tables for each of the 16 higher bytes in the
255 buffer as well, which makes 64 kbytes in total.
256 */
257 /* additional explanation
258 * t[0][BYTE] contains g*BYTE
259 * t[1][BYTE] contains g*x^8*BYTE
260 * ..
261 * t[15][BYTE] contains g*x^120*BYTE */
262 struct gf128mul_64k *gf128mul_init_64k_bbe(const be128 *g)
263 {
264 struct gf128mul_64k *t;
265 int i, j, k;
266
267 t = kzalloc(sizeof(*t), GFP_KERNEL);
268 if (!t)
269 goto out;
270
271 for (i = 0; i < 16; i++) {
272 t->t[i] = kzalloc(sizeof(*t->t[i]), GFP_KERNEL);
273 if (!t->t[i]) {
274 gf128mul_free_64k(t);
275 t = NULL;
276 goto out;
277 }
278 }
279
280 t->t[0]->t[1] = *g;
281 for (j = 1; j <= 64; j <<= 1)
282 gf128mul_x_bbe(&t->t[0]->t[j + j], &t->t[0]->t[j]);
283
284 for (i = 0;;) {
285 for (j = 2; j < 256; j += j)
286 for (k = 1; k < j; ++k)
287 be128_xor(&t->t[i]->t[j + k],
288 &t->t[i]->t[j], &t->t[i]->t[k]);
289
290 if (++i >= 16)
291 break;
292
293 for (j = 128; j > 0; j >>= 1) {
294 t->t[i]->t[j] = t->t[i - 1]->t[j];
295 gf128mul_x8_bbe(&t->t[i]->t[j]);
296 }
297 }
298
299 out:
300 return t;
301 }
302 EXPORT_SYMBOL(gf128mul_init_64k_bbe);
303
304 void gf128mul_free_64k(struct gf128mul_64k *t)
305 {
306 int i;
307
308 for (i = 0; i < 16; i++)
309 kzfree(t->t[i]);
310 kzfree(t);
311 }
312 EXPORT_SYMBOL(gf128mul_free_64k);
313
314 void gf128mul_64k_bbe(be128 *a, const struct gf128mul_64k *t)
315 {
316 u8 *ap = (u8 *)a;
317 be128 r[1];
318 int i;
319
320 *r = t->t[0]->t[ap[15]];
321 for (i = 1; i < 16; ++i)
322 be128_xor(r, r, &t->t[i]->t[ap[15 - i]]);
323 *a = *r;
324 }
325 EXPORT_SYMBOL(gf128mul_64k_bbe);
326
327 /* This version uses 4k bytes of table space.
328 A 16 byte buffer has to be multiplied by a 16 byte key
329 value in GF(2^128). If we consider a GF(2^128) value in a
330 single byte, we can construct a table of the 256 16 byte
331 values that result from the 256 values of this byte.
332 This requires 4096 bytes. If we take the highest byte in
333 the buffer and use this table to get the result, we then
334 have to multiply by x^120 to get the final value. For the
335 next highest byte the result has to be multiplied by x^112
336 and so on. But we can do this by accumulating the result
337 in an accumulator starting with the result for the top
338 byte. We repeatedly multiply the accumulator value by
339 x^8 and then add in (i.e. xor) the 16 bytes of the next
340 lower byte in the buffer, stopping when we reach the
341 lowest byte. This requires a 4096 byte table.
342 */
343 struct gf128mul_4k *gf128mul_init_4k_lle(const be128 *g)
344 {
345 struct gf128mul_4k *t;
346 int j, k;
347
348 t = kzalloc(sizeof(*t), GFP_KERNEL);
349 if (!t)
350 goto out;
351
352 t->t[128] = *g;
353 for (j = 64; j > 0; j >>= 1)
354 gf128mul_x_lle(&t->t[j], &t->t[j+j]);
355
356 for (j = 2; j < 256; j += j)
357 for (k = 1; k < j; ++k)
358 be128_xor(&t->t[j + k], &t->t[j], &t->t[k]);
359
360 out:
361 return t;
362 }
363 EXPORT_SYMBOL(gf128mul_init_4k_lle);
364
365 struct gf128mul_4k *gf128mul_init_4k_bbe(const be128 *g)
366 {
367 struct gf128mul_4k *t;
368 int j, k;
369
370 t = kzalloc(sizeof(*t), GFP_KERNEL);
371 if (!t)
372 goto out;
373
374 t->t[1] = *g;
375 for (j = 1; j <= 64; j <<= 1)
376 gf128mul_x_bbe(&t->t[j + j], &t->t[j]);
377
378 for (j = 2; j < 256; j += j)
379 for (k = 1; k < j; ++k)
380 be128_xor(&t->t[j + k], &t->t[j], &t->t[k]);
381
382 out:
383 return t;
384 }
385 EXPORT_SYMBOL(gf128mul_init_4k_bbe);
386
387 void gf128mul_4k_lle(be128 *a, const struct gf128mul_4k *t)
388 {
389 u8 *ap = (u8 *)a;
390 be128 r[1];
391 int i = 15;
392
393 *r = t->t[ap[15]];
394 while (i--) {
395 gf128mul_x8_lle(r);
396 be128_xor(r, r, &t->t[ap[i]]);
397 }
398 *a = *r;
399 }
400 EXPORT_SYMBOL(gf128mul_4k_lle);
401
402 void gf128mul_4k_bbe(be128 *a, const struct gf128mul_4k *t)
403 {
404 u8 *ap = (u8 *)a;
405 be128 r[1];
406 int i = 0;
407
408 *r = t->t[ap[0]];
409 while (++i < 16) {
410 gf128mul_x8_bbe(r);
411 be128_xor(r, r, &t->t[ap[i]]);
412 }
413 *a = *r;
414 }
415 EXPORT_SYMBOL(gf128mul_4k_bbe);
416
417 MODULE_LICENSE("GPL");
418 MODULE_DESCRIPTION("Functions for multiplying elements of GF(2^128)");