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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 */
163void gf128mul_lle(be128 *a, const be128 *b);
164
165void 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
176static 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
182static 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(b, 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
195static 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(a, 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 */
208static 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(a, 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
222struct gf128mul_4k {
223 be128 t[256];
224};
225
226struct gf128mul_4k *gf128mul_init_4k_lle(const be128 *g);
227struct gf128mul_4k *gf128mul_init_4k_bbe(const be128 *g);
228void gf128mul_4k_lle(be128 *a, const struct gf128mul_4k *t);
229void gf128mul_4k_bbe(be128 *a, const struct gf128mul_4k *t);
230void gf128mul_x8_ble(le128 *r, const le128 *x);
231static inline void gf128mul_free_4k(struct gf128mul_4k *t)
232{
233 kzfree(t);
234}
235
236
237/* 64k table optimization, implemented for bbe */
238
239struct 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 */
248struct gf128mul_64k *gf128mul_init_64k_bbe(const be128 *g);
249void gf128mul_free_64k(struct gf128mul_64k *t);
250void gf128mul_64k_bbe(be128 *a, const struct gf128mul_64k *t);
251
252#endif /* _CRYPTO_GF128MUL_H */
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(128)
47*/
48
49#ifndef _CRYPTO_GF128MUL_H
50#define _CRYPTO_GF128MUL_H
51
52#include <crypto/b128ops.h>
53#include <linux/slab.h>
54
55/* Comment by Rik:
56 *
57 * For some background on GF(2^128) see for example:
58 * http://csrc.nist.gov/groups/ST/toolkit/BCM/documents/proposedmodes/gcm/gcm-revised-spec.pdf
59 *
60 * The elements of GF(2^128) := GF(2)[X]/(X^128-X^7-X^2-X^1-1) can
61 * be mapped to computer memory in a variety of ways. Let's examine
62 * three common cases.
63 *
64 * Take a look at the 16 binary octets below in memory order. The msb's
65 * are left and the lsb's are right. char b[16] is an array and b[0] is
66 * the first octet.
67 *
68 * 80000000 00000000 00000000 00000000 .... 00000000 00000000 00000000
69 * b[0] b[1] b[2] b[3] b[13] b[14] b[15]
70 *
71 * Every bit is a coefficient of some power of X. We can store the bits
72 * in every byte in little-endian order and the bytes themselves also in
73 * little endian order. I will call this lle (little-little-endian).
74 * The above buffer represents the polynomial 1, and X^7+X^2+X^1+1 looks
75 * like 11100001 00000000 .... 00000000 = { 0xE1, 0x00, }.
76 * This format was originally implemented in gf128mul and is used
77 * in GCM (Galois/Counter mode) and in ABL (Arbitrary Block Length).
78 *
79 * Another convention says: store the bits in bigendian order and the
80 * bytes also. This is bbe (big-big-endian). Now the buffer above
81 * represents X^127. X^7+X^2+X^1+1 looks like 00000000 .... 10000111,
82 * b[15] = 0x87 and the rest is 0. LRW uses this convention and bbe
83 * is partly implemented.
84 *
85 * Both of the above formats are easy to implement on big-endian
86 * machines.
87 *
88 * EME (which is patent encumbered) uses the ble format (bits are stored
89 * in big endian order and the bytes in little endian). The above buffer
90 * represents X^7 in this case and the primitive polynomial is b[0] = 0x87.
91 *
92 * The common machine word-size is smaller than 128 bits, so to make
93 * an efficient implementation we must split into machine word sizes.
94 * This file uses one 32bit for the moment. Machine endianness comes into
95 * play. The lle format in relation to machine endianness is discussed
96 * below by the original author of gf128mul Dr Brian Gladman.
97 *
98 * Let's look at the bbe and ble format on a little endian machine.
99 *
100 * bbe on a little endian machine u32 x[4]:
101 *
102 * MS x[0] LS MS x[1] LS
103 * ms ls ms ls ms ls ms ls ms ls ms ls ms ls ms ls
104 * 103..96 111.104 119.112 127.120 71...64 79...72 87...80 95...88
105 *
106 * MS x[2] LS MS x[3] LS
107 * ms ls ms ls ms ls ms ls ms ls ms ls ms ls ms ls
108 * 39...32 47...40 55...48 63...56 07...00 15...08 23...16 31...24
109 *
110 * ble on a little endian machine
111 *
112 * MS x[0] LS MS x[1] LS
113 * ms ls ms ls ms ls ms ls ms ls ms ls ms ls ms ls
114 * 31...24 23...16 15...08 07...00 63...56 55...48 47...40 39...32
115 *
116 * MS x[2] LS MS x[3] LS
117 * ms ls ms ls ms ls ms ls ms ls ms ls ms ls ms ls
118 * 95...88 87...80 79...72 71...64 127.120 199.112 111.104 103..96
119 *
120 * Multiplications in GF(2^128) are mostly bit-shifts, so you see why
121 * ble (and lbe also) are easier to implement on a little-endian
122 * machine than on a big-endian machine. The converse holds for bbe
123 * and lle.
124 *
125 * Note: to have good alignment, it seems to me that it is sufficient
126 * to keep elements of GF(2^128) in type u64[2]. On 32-bit wordsize
127 * machines this will automatically aligned to wordsize and on a 64-bit
128 * machine also.
129 */
130/* Multiply a GF128 field element by x. Field elements are held in arrays
131 of bytes in which field bits 8n..8n + 7 are held in byte[n], with lower
132 indexed bits placed in the more numerically significant bit positions
133 within bytes.
134
135 On little endian machines the bit indexes translate into the bit
136 positions within four 32-bit words in the following way
137
138 MS x[0] LS MS x[1] LS
139 ms ls ms ls ms ls ms ls ms ls ms ls ms ls ms ls
140 24...31 16...23 08...15 00...07 56...63 48...55 40...47 32...39
141
142 MS x[2] LS MS x[3] LS
143 ms ls ms ls ms ls ms ls ms ls ms ls ms ls ms ls
144 88...95 80...87 72...79 64...71 120.127 112.119 104.111 96..103
145
146 On big endian machines the bit indexes translate into the bit
147 positions within four 32-bit words in the following way
148
149 MS x[0] LS MS x[1] LS
150 ms ls ms ls ms ls ms ls ms ls ms ls ms ls ms ls
151 00...07 08...15 16...23 24...31 32...39 40...47 48...55 56...63
152
153 MS x[2] LS MS x[3] LS
154 ms ls ms ls ms ls ms ls ms ls ms ls ms ls ms ls
155 64...71 72...79 80...87 88...95 96..103 104.111 112.119 120.127
156*/
157
158/* A slow generic version of gf_mul, implemented for lle and bbe
159 * It multiplies a and b and puts the result in a */
160void gf128mul_lle(be128 *a, const be128 *b);
161
162void gf128mul_bbe(be128 *a, const be128 *b);
163
164/* multiply by x in ble format, needed by XTS */
165void gf128mul_x_ble(be128 *a, const be128 *b);
166
167/* 4k table optimization */
168
169struct gf128mul_4k {
170 be128 t[256];
171};
172
173struct gf128mul_4k *gf128mul_init_4k_lle(const be128 *g);
174struct gf128mul_4k *gf128mul_init_4k_bbe(const be128 *g);
175void gf128mul_4k_lle(be128 *a, struct gf128mul_4k *t);
176void gf128mul_4k_bbe(be128 *a, struct gf128mul_4k *t);
177
178static inline void gf128mul_free_4k(struct gf128mul_4k *t)
179{
180 kfree(t);
181}
182
183
184/* 64k table optimization, implemented for lle and bbe */
185
186struct gf128mul_64k {
187 struct gf128mul_4k *t[16];
188};
189
190/* first initialize with the constant factor with which you
191 * want to multiply and then call gf128_64k_lle with the other
192 * factor in the first argument, the table in the second and a
193 * scratch register in the third. Afterwards *a = *r. */
194struct gf128mul_64k *gf128mul_init_64k_lle(const be128 *g);
195struct gf128mul_64k *gf128mul_init_64k_bbe(const be128 *g);
196void gf128mul_free_64k(struct gf128mul_64k *t);
197void gf128mul_64k_lle(be128 *a, struct gf128mul_64k *t);
198void gf128mul_64k_bbe(be128 *a, struct gf128mul_64k *t);
199
200#endif /* _CRYPTO_GF128MUL_H */