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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
129static const u16 gf128mul_table_le[256] = gf128mul_dat(xda_le);
130static 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
139static 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
149static 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
159void 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}
168EXPORT_SYMBOL(gf128mul_x8_ble);
169
170void 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}
206EXPORT_SYMBOL(gf128mul_lle);
207
208void 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}
244EXPORT_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 */
260struct 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
297out:
298 return t;
299}
300EXPORT_SYMBOL(gf128mul_init_64k_bbe);
301
302void 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}
310EXPORT_SYMBOL(gf128mul_free_64k);
311
312void 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}
323EXPORT_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*/
341struct 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
358out:
359 return t;
360}
361EXPORT_SYMBOL(gf128mul_init_4k_lle);
362
363struct 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
380out:
381 return t;
382}
383EXPORT_SYMBOL(gf128mul_init_4k_bbe);
384
385void 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}
398EXPORT_SYMBOL(gf128mul_4k_lle);
399
400void 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}
413EXPORT_SYMBOL(gf128mul_4k_bbe);
414
415MODULE_LICENSE("GPL");
416MODULE_DESCRIPTION("Functions for multiplying elements of GF(2^128)");