1 | /* gf128mul.h - 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://fp.gladman.plus.com/cryptography_technology/index.htm |
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 | Copyright (c) 2003, Dr Brian Gladman, Worcester, UK. All rights reserved. |
18 | |
19 | LICENSE TERMS |
20 | |
21 | The free distribution and use of this software in both source and binary |
22 | form is allowed (with or without changes) provided that: |
23 | |
24 | 1. distributions of this source code include the above copyright |
25 | notice, this list of conditions and the following disclaimer; |
26 | |
27 | 2. distributions in binary form include the above copyright |
28 | notice, this list of conditions and the following disclaimer |
29 | in the documentation and/or other associated materials; |
30 | |
31 | 3. the copyright holder's name is not used to endorse products |
32 | built using this software without specific written permission. |
33 | |
34 | ALTERNATIVELY, provided that this notice is retained in full, this product |
35 | may be distributed under the terms of the GNU General Public License (GPL), |
36 | in which case the provisions of the GPL apply INSTEAD OF those given above. |
37 | |
38 | DISCLAIMER |
39 | |
40 | This software is provided 'as is' with no explicit or implied warranties |
41 | in respect of its properties, including, but not limited to, correctness |
42 | and/or fitness for purpose. |
43 | --------------------------------------------------------------------------- |
44 | Issue Date: 31/01/2006 |
45 | |
46 | An implementation of field multiplication in Galois Field GF(2^128) |
47 | */ |
48 | |
49 | #ifndef _CRYPTO_GF128MUL_H |
50 | #define _CRYPTO_GF128MUL_H |
51 | |
52 | #include <asm/byteorder.h> |
53 | #include <crypto/b128ops.h> |
54 | #include <linux/slab.h> |
55 | |
56 | /* Comment by Rik: |
57 | * |
58 | * For some background on GF(2^128) see for example: |
59 | * http://csrc.nist.gov/groups/ST/toolkit/BCM/documents/proposedmodes/gcm/gcm-revised-spec.pdf |
60 | * |
61 | * The elements of GF(2^128) := GF(2)[X]/(X^128-X^7-X^2-X^1-1) can |
62 | * be mapped to computer memory in a variety of ways. Let's examine |
63 | * three common cases. |
64 | * |
65 | * Take a look at the 16 binary octets below in memory order. The msb's |
66 | * are left and the lsb's are right. char b[16] is an array and b[0] is |
67 | * the first octet. |
68 | * |
69 | * 10000000 00000000 00000000 00000000 .... 00000000 00000000 00000000 |
70 | * b[0] b[1] b[2] b[3] b[13] b[14] b[15] |
71 | * |
72 | * Every bit is a coefficient of some power of X. We can store the bits |
73 | * in every byte in little-endian order and the bytes themselves also in |
74 | * little endian order. I will call this lle (little-little-endian). |
75 | * The above buffer represents the polynomial 1, and X^7+X^2+X^1+1 looks |
76 | * like 11100001 00000000 .... 00000000 = { 0xE1, 0x00, }. |
77 | * This format was originally implemented in gf128mul and is used |
78 | * in GCM (Galois/Counter mode) and in ABL (Arbitrary Block Length). |
79 | * |
80 | * Another convention says: store the bits in bigendian order and the |
81 | * bytes also. This is bbe (big-big-endian). Now the buffer above |
82 | * represents X^127. X^7+X^2+X^1+1 looks like 00000000 .... 10000111, |
83 | * b[15] = 0x87 and the rest is 0. LRW uses this convention and bbe |
84 | * is partly implemented. |
85 | * |
86 | * Both of the above formats are easy to implement on big-endian |
87 | * machines. |
88 | * |
89 | * XTS and EME (the latter of which is patent encumbered) use the ble |
90 | * format (bits are stored in big endian order and the bytes in little |
91 | * endian). The above buffer represents X^7 in this case and the |
92 | * primitive polynomial is b[0] = 0x87. |
93 | * |
94 | * The common machine word-size is smaller than 128 bits, so to make |
95 | * an efficient implementation we must split into machine word sizes. |
96 | * This implementation uses 64-bit words for the moment. Machine |
97 | * endianness comes into play. The lle format in relation to machine |
98 | * endianness is discussed below by the original author of gf128mul Dr |
99 | * Brian Gladman. |
100 | * |
101 | * Let's look at the bbe and ble format on a little endian machine. |
102 | * |
103 | * bbe on a little endian machine u32 x[4]: |
104 | * |
105 | * MS x[0] LS MS x[1] LS |
106 | * ms ls ms ls ms ls ms ls ms ls ms ls ms ls ms ls |
107 | * 103..96 111.104 119.112 127.120 71...64 79...72 87...80 95...88 |
108 | * |
109 | * MS x[2] LS MS x[3] LS |
110 | * ms ls ms ls ms ls ms ls ms ls ms ls ms ls ms ls |
111 | * 39...32 47...40 55...48 63...56 07...00 15...08 23...16 31...24 |
112 | * |
113 | * ble on a little endian machine |
114 | * |
115 | * MS x[0] LS MS x[1] LS |
116 | * ms ls ms ls ms ls ms ls ms ls ms ls ms ls ms ls |
117 | * 31...24 23...16 15...08 07...00 63...56 55...48 47...40 39...32 |
118 | * |
119 | * MS x[2] LS MS x[3] LS |
120 | * ms ls ms ls ms ls ms ls ms ls ms ls ms ls ms ls |
121 | * 95...88 87...80 79...72 71...64 127.120 199.112 111.104 103..96 |
122 | * |
123 | * Multiplications in GF(2^128) are mostly bit-shifts, so you see why |
124 | * ble (and lbe also) are easier to implement on a little-endian |
125 | * machine than on a big-endian machine. The converse holds for bbe |
126 | * and lle. |
127 | * |
128 | * Note: to have good alignment, it seems to me that it is sufficient |
129 | * to keep elements of GF(2^128) in type u64[2]. On 32-bit wordsize |
130 | * machines this will automatically aligned to wordsize and on a 64-bit |
131 | * machine also. |
132 | */ |
133 | /* Multiply a GF(2^128) field element by x. Field elements are |
134 | held in arrays of bytes in which field bits 8n..8n + 7 are held in |
135 | byte[n], with lower indexed bits placed in the more numerically |
136 | significant bit positions within bytes. |
137 | |
138 | On little endian machines the bit indexes translate into the bit |
139 | positions within four 32-bit words in the following way |
140 | |
141 | MS x[0] LS MS x[1] LS |
142 | ms ls ms ls ms ls ms ls ms ls ms ls ms ls ms ls |
143 | 24...31 16...23 08...15 00...07 56...63 48...55 40...47 32...39 |
144 | |
145 | MS x[2] LS MS x[3] LS |
146 | ms ls ms ls ms ls ms ls ms ls ms ls ms ls ms ls |
147 | 88...95 80...87 72...79 64...71 120.127 112.119 104.111 96..103 |
148 | |
149 | On big endian machines the bit indexes translate into the bit |
150 | positions within four 32-bit words in the following way |
151 | |
152 | MS x[0] LS MS x[1] LS |
153 | ms ls ms ls ms ls ms ls ms ls ms ls ms ls ms ls |
154 | 00...07 08...15 16...23 24...31 32...39 40...47 48...55 56...63 |
155 | |
156 | MS x[2] LS MS x[3] LS |
157 | ms ls ms ls ms ls ms ls ms ls ms ls ms ls ms ls |
158 | 64...71 72...79 80...87 88...95 96..103 104.111 112.119 120.127 |
159 | */ |
160 | |
161 | /* A slow generic version of gf_mul, implemented for lle and bbe |
162 | * It multiplies a and b and puts the result in a */ |
163 | void gf128mul_lle(be128 *a, const be128 *b); |
164 | |
165 | void gf128mul_bbe(be128 *a, const be128 *b); |
166 | |
167 | /* |
168 | * The following functions multiply a field element by x in |
169 | * the polynomial field representation. They use 64-bit word operations |
170 | * to gain speed but compensate for machine endianness and hence work |
171 | * correctly on both styles of machine. |
172 | * |
173 | * They are defined here for performance. |
174 | */ |
175 | |
176 | static inline u64 gf128mul_mask_from_bit(u64 x, int which) |
177 | { |
178 | /* a constant-time version of 'x & ((u64)1 << which) ? (u64)-1 : 0' */ |
179 | return ((s64)(x << (63 - which)) >> 63); |
180 | } |
181 | |
182 | static inline void gf128mul_x_lle(be128 *r, const be128 *x) |
183 | { |
184 | u64 a = be64_to_cpu(x->a); |
185 | u64 b = be64_to_cpu(x->b); |
186 | |
187 | /* equivalent to gf128mul_table_le[(b << 7) & 0xff] << 48 |
188 | * (see crypto/gf128mul.c): */ |
189 | u64 _tt = gf128mul_mask_from_bit(x: b, which: 0) & ((u64)0xe1 << 56); |
190 | |
191 | r->b = cpu_to_be64((b >> 1) | (a << 63)); |
192 | r->a = cpu_to_be64((a >> 1) ^ _tt); |
193 | } |
194 | |
195 | static inline void gf128mul_x_bbe(be128 *r, const be128 *x) |
196 | { |
197 | u64 a = be64_to_cpu(x->a); |
198 | u64 b = be64_to_cpu(x->b); |
199 | |
200 | /* equivalent to gf128mul_table_be[a >> 63] (see crypto/gf128mul.c): */ |
201 | u64 _tt = gf128mul_mask_from_bit(x: a, which: 63) & 0x87; |
202 | |
203 | r->a = cpu_to_be64((a << 1) | (b >> 63)); |
204 | r->b = cpu_to_be64((b << 1) ^ _tt); |
205 | } |
206 | |
207 | /* needed by XTS */ |
208 | static inline void gf128mul_x_ble(le128 *r, const le128 *x) |
209 | { |
210 | u64 a = le64_to_cpu(x->a); |
211 | u64 b = le64_to_cpu(x->b); |
212 | |
213 | /* equivalent to gf128mul_table_be[b >> 63] (see crypto/gf128mul.c): */ |
214 | u64 _tt = gf128mul_mask_from_bit(x: a, which: 63) & 0x87; |
215 | |
216 | r->a = cpu_to_le64((a << 1) | (b >> 63)); |
217 | r->b = cpu_to_le64((b << 1) ^ _tt); |
218 | } |
219 | |
220 | /* 4k table optimization */ |
221 | |
222 | struct gf128mul_4k { |
223 | be128 t[256]; |
224 | }; |
225 | |
226 | struct gf128mul_4k *gf128mul_init_4k_lle(const be128 *g); |
227 | struct gf128mul_4k *gf128mul_init_4k_bbe(const be128 *g); |
228 | void gf128mul_4k_lle(be128 *a, const struct gf128mul_4k *t); |
229 | void gf128mul_4k_bbe(be128 *a, const struct gf128mul_4k *t); |
230 | void gf128mul_x8_ble(le128 *r, const le128 *x); |
231 | static inline void gf128mul_free_4k(struct gf128mul_4k *t) |
232 | { |
233 | kfree_sensitive(objp: t); |
234 | } |
235 | |
236 | |
237 | /* 64k table optimization, implemented for bbe */ |
238 | |
239 | struct gf128mul_64k { |
240 | struct gf128mul_4k *t[16]; |
241 | }; |
242 | |
243 | /* First initialize with the constant factor with which you |
244 | * want to multiply and then call gf128mul_64k_bbe with the other |
245 | * factor in the first argument, and the table in the second. |
246 | * Afterwards, the result is stored in *a. |
247 | */ |
248 | struct gf128mul_64k *gf128mul_init_64k_bbe(const be128 *g); |
249 | void gf128mul_free_64k(struct gf128mul_64k *t); |
250 | void gf128mul_64k_bbe(be128 *a, const struct gf128mul_64k *t); |
251 | |
252 | #endif /* _CRYPTO_GF128MUL_H */ |
253 | |