1 /* gf128mul.c - GF(2^128) multiplication functions
3 * Copyright (c) 2003, Dr Brian Gladman, Worcester, UK.
4 * Copyright (c) 2006, Rik Snel <rsnel@cube.dyndns.org>
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.
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)
17 ---------------------------------------------------------------------------
18 Copyright (c) 2003, Dr Brian Gladman, Worcester, UK. All rights reserved.
22 The free distribution and use of this software in both source and binary
23 form is allowed (with or without changes) provided that:
25 1. distributions of this source code include the above copyright
26 notice, this list of conditions and the following disclaimer;
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;
32 3. the copyright holder's name is not used to endorse products
33 built using this software without specific written permission.
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.
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 ---------------------------------------------------------------------------
47 This file provides fast multiplication in GF(2^128) as required by several
48 cryptographic authentication modes
51 #include <crypto/gf128mul.h>
52 #include <linux/kernel.h>
53 #include <linux/module.h>
54 #include <linux/slab.h>
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) \
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.
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.
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.
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) \
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) \
129 static const u16 gf128mul_table_le
[256] = gf128mul_dat(xda_le
);
130 static const u16 gf128mul_table_be
[256] = gf128mul_dat(xda_be
);
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.
139 static void gf128mul_x8_lle(be128
*x
)
141 u64 a
= be64_to_cpu(x
->a
);
142 u64 b
= be64_to_cpu(x
->b
);
143 u64 _tt
= gf128mul_table_le
[b
& 0xff];
145 x
->b
= cpu_to_be64((b
>> 8) | (a
<< 56));
146 x
->a
= cpu_to_be64((a
>> 8) ^ (_tt
<< 48));
149 static void gf128mul_x8_bbe(be128
*x
)
151 u64 a
= be64_to_cpu(x
->a
);
152 u64 b
= be64_to_cpu(x
->b
);
153 u64 _tt
= gf128mul_table_be
[a
>> 56];
155 x
->a
= cpu_to_be64((a
<< 8) | (b
>> 56));
156 x
->b
= cpu_to_be64((b
<< 8) ^ _tt
);
159 void gf128mul_x8_ble(le128
*r
, const le128
*x
)
161 u64 a
= le64_to_cpu(x
->a
);
162 u64 b
= le64_to_cpu(x
->b
);
163 u64 _tt
= gf128mul_table_be
[a
>> 56];
165 r
->a
= cpu_to_le64((a
<< 8) | (b
>> 56));
166 r
->b
= cpu_to_le64((b
<< 8) ^ _tt
);
168 EXPORT_SYMBOL(gf128mul_x8_ble
);
170 void gf128mul_lle(be128
*r
, const be128
*b
)
176 for (i
= 0; i
< 7; ++i
)
177 gf128mul_x_lle(&p
[i
+ 1], &p
[i
]);
179 memset(r
, 0, sizeof(*r
));
181 u8 ch
= ((u8
*)b
)[15 - i
];
184 be128_xor(r
, r
, &p
[0]);
186 be128_xor(r
, r
, &p
[1]);
188 be128_xor(r
, r
, &p
[2]);
190 be128_xor(r
, r
, &p
[3]);
192 be128_xor(r
, r
, &p
[4]);
194 be128_xor(r
, r
, &p
[5]);
196 be128_xor(r
, r
, &p
[6]);
198 be128_xor(r
, r
, &p
[7]);
206 EXPORT_SYMBOL(gf128mul_lle
);
208 void gf128mul_bbe(be128
*r
, const be128
*b
)
214 for (i
= 0; i
< 7; ++i
)
215 gf128mul_x_bbe(&p
[i
+ 1], &p
[i
]);
217 memset(r
, 0, sizeof(*r
));
219 u8 ch
= ((u8
*)b
)[i
];
222 be128_xor(r
, r
, &p
[7]);
224 be128_xor(r
, r
, &p
[6]);
226 be128_xor(r
, r
, &p
[5]);
228 be128_xor(r
, r
, &p
[4]);
230 be128_xor(r
, r
, &p
[3]);
232 be128_xor(r
, r
, &p
[2]);
234 be128_xor(r
, r
, &p
[1]);
236 be128_xor(r
, r
, &p
[0]);
244 EXPORT_SYMBOL(gf128mul_bbe
);
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.
255 /* additional explanation
256 * t[0][BYTE] contains g*BYTE
257 * t[1][BYTE] contains g*x^8*BYTE
259 * t[15][BYTE] contains g*x^120*BYTE */
260 struct gf128mul_64k
*gf128mul_init_64k_bbe(const be128
*g
)
262 struct gf128mul_64k
*t
;
265 t
= kzalloc(sizeof(*t
), GFP_KERNEL
);
269 for (i
= 0; i
< 16; i
++) {
270 t
->t
[i
] = kzalloc(sizeof(*t
->t
[i
]), GFP_KERNEL
);
272 gf128mul_free_64k(t
);
279 for (j
= 1; j
<= 64; j
<<= 1)
280 gf128mul_x_bbe(&t
->t
[0]->t
[j
+ j
], &t
->t
[0]->t
[j
]);
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
]);
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
]);
300 EXPORT_SYMBOL(gf128mul_init_64k_bbe
);
302 void gf128mul_free_64k(struct gf128mul_64k
*t
)
306 for (i
= 0; i
< 16; i
++)
310 EXPORT_SYMBOL(gf128mul_free_64k
);
312 void gf128mul_64k_bbe(be128
*a
, const struct gf128mul_64k
*t
)
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
]]);
323 EXPORT_SYMBOL(gf128mul_64k_bbe
);
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.
341 struct gf128mul_4k
*gf128mul_init_4k_lle(const be128
*g
)
343 struct gf128mul_4k
*t
;
346 t
= kzalloc(sizeof(*t
), GFP_KERNEL
);
351 for (j
= 64; j
> 0; j
>>= 1)
352 gf128mul_x_lle(&t
->t
[j
], &t
->t
[j
+j
]);
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
]);
361 EXPORT_SYMBOL(gf128mul_init_4k_lle
);
363 struct gf128mul_4k
*gf128mul_init_4k_bbe(const be128
*g
)
365 struct gf128mul_4k
*t
;
368 t
= kzalloc(sizeof(*t
), GFP_KERNEL
);
373 for (j
= 1; j
<= 64; j
<<= 1)
374 gf128mul_x_bbe(&t
->t
[j
+ j
], &t
->t
[j
]);
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
]);
383 EXPORT_SYMBOL(gf128mul_init_4k_bbe
);
385 void gf128mul_4k_lle(be128
*a
, const struct gf128mul_4k
*t
)
394 be128_xor(r
, r
, &t
->t
[ap
[i
]]);
398 EXPORT_SYMBOL(gf128mul_4k_lle
);
400 void gf128mul_4k_bbe(be128
*a
, const struct gf128mul_4k
*t
)
409 be128_xor(r
, r
, &t
->t
[ap
[i
]]);
413 EXPORT_SYMBOL(gf128mul_4k_bbe
);
415 MODULE_LICENSE("GPL");
416 MODULE_DESCRIPTION("Functions for multiplying elements of GF(2^128)");