1 /*-
2 * Copyright (c) 2014 The FreeBSD Foundation
3 * All rights reserved.
4 *
5 * This software was developed by John-Mark Gurney under
6 * the sponsorship of the FreeBSD Foundation and
7 * Rubicon Communications, LLC (Netgate).
8 * Redistribution and use in source and binary forms, with or without
9 * modification, are permitted provided that the following conditions
10 * are met:
11 * 1. Redistributions of source code must retain the above copyright
12 * notice, this list of conditions and the following disclaimer.
13 * 2. Redistributions in binary form must reproduce the above copyright
14 * notice, this list of conditions and the following disclaimer in the
15 * documentation and/or other materials provided with the distribution.
16 *
17 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
18 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
19 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
20 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
21 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
22 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
23 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
24 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
25 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
26 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
27 * SUCH DAMAGE.
28 *
29 * $FreeBSD$
30 *
31 */
32
33 #include "gfmult.h"
34
35 #define REV_POLY_REDUCT 0xe1 /* 0x87 bit reversed */
36
37 /* reverse the bits of a nibble */
38 static const uint8_t nib_rev[] = {
39 0x0, 0x8, 0x4, 0xc, 0x2, 0xa, 0x6, 0xe,
40 0x1, 0x9, 0x5, 0xd, 0x3, 0xb, 0x7, 0xf,
41 };
42
43 /* calculate v * 2 */
44 static inline struct gf128
45 gf128_mulalpha(struct gf128 v)
46 {
47 uint64_t mask;
48
49 mask = !!(v.v[1] & 1);
50 mask = ~(mask - 1);
51 v.v[1] = (v.v[1] >> 1) | ((v.v[0] & 1) << 63);
52 v.v[0] = (v.v[0] >> 1) ^ ((mask & REV_POLY_REDUCT) << 56);
53
54 return v;
55 }
56
57 /*
58 * Generate a table for 0-16 * h. Store the results in the table w/ indexes
59 * bit reversed, and the words striped across the values.
60 */
61 void
62 gf128_genmultable(struct gf128 h, struct gf128table *t)
63 {
64 struct gf128 tbl[16];
65 int i;
66
67 tbl[0] = MAKE_GF128(0, 0);
68 tbl[1] = h;
69
70 for (i = 2; i < 16; i += 2) {
71 tbl[i] = gf128_mulalpha(tbl[i / 2]);
72 tbl[i + 1] = gf128_add(tbl[i], h);
73 }
74
75 for (i = 0; i < 16; i++) {
76 t->a[nib_rev[i]] = tbl[i].v[0] >> 32;
77 t->b[nib_rev[i]] = tbl[i].v[0];
78 t->c[nib_rev[i]] = tbl[i].v[1] >> 32;
79 t->d[nib_rev[i]] = tbl[i].v[1];
80 }
81 }
82
83 /*
84 * Generate tables containing h, h^2, h^3 and h^4, starting at 0.
85 */
86 void
87 gf128_genmultable4(struct gf128 h, struct gf128table4 *t)
88 {
89 struct gf128 h2, h3, h4;
90
91 gf128_genmultable(h, &t->tbls[0]);
92
93 h2 = gf128_mul(h, &t->tbls[0]);
94
95 gf128_genmultable(h2, &t->tbls[1]);
96
97 h3 = gf128_mul(h, &t->tbls[1]);
98 gf128_genmultable(h3, &t->tbls[2]);
99
100 h4 = gf128_mul(h2, &t->tbls[1]);
101 gf128_genmultable(h4, &t->tbls[3]);
102 }
103
104 /*
105 * Read a row from the table.
106 */
107 static inline struct gf128
108 readrow(struct gf128table *tbl, unsigned bits)
109 {
110 struct gf128 r;
111
112 bits = bits % 16;
113
114 r.v[0] = ((uint64_t)tbl->a[bits] << 32) | tbl->b[bits];
115 r.v[1] = ((uint64_t)tbl->c[bits] << 32) | tbl->d[bits];
116
117 return r;
118 }
119
120 /*
121 * These are the reduction values. Since we are dealing with bit reversed
122 * version, the values need to be bit reversed, AND the indexes are also
123 * bit reversed to make lookups quicker.
124 */
125 static uint16_t reduction[] = {
126 0x0000, 0x1c20, 0x3840, 0x2460, 0x7080, 0x6ca0, 0x48c0, 0x54e0,
127 0xe100, 0xfd20, 0xd940, 0xc560, 0x9180, 0x8da0, 0xa9c0, 0xb5e0,
128 };
129
130 /*
131 * Calculate:
132 * (x*2^4 + word[3,0]*h) *
133 * 2^4 + word[7,4]*h) *
134 * ...
135 * 2^4 + word[63,60]*h
136 */
137 static struct gf128
138 gfmultword(uint64_t word, struct gf128 x, struct gf128table *tbl)
139 {
140 struct gf128 row;
141 unsigned bits;
142 unsigned redbits;
143 int i;
144
145 for (i = 0; i < 64; i += 4) {
146 bits = word % 16;
147
148 /* fetch row */
149 row = readrow(tbl, bits);
150
151 /* x * 2^4 */
152 redbits = x.v[1] % 16;
153 x.v[1] = (x.v[1] >> 4) | (x.v[0] % 16) << 60;
154 x.v[0] >>= 4;
155 x.v[0] ^= (uint64_t)reduction[redbits] << (64 - 16);
156
157 word >>= 4;
158
159 x = gf128_add(x, row);
160 }
161
162 return x;
163 }
164
165 /*
166 * Calculate
167 * (x*2^4 + worda[3,0]*h^4+wordb[3,0]*h^3+...+wordd[3,0]*h) *
168 * ...
169 * 2^4 + worda[63,60]*h^4+ ... + wordd[63,60]*h
170 *
171 * Passing/returning struct is .5% faster than passing in via pointer on
172 * amd64.
173 */
174 static struct gf128
175 gfmultword4(uint64_t worda, uint64_t wordb, uint64_t wordc, uint64_t wordd,
176 struct gf128 x, struct gf128table4 *tbl)
177 {
178 struct gf128 rowa, rowb, rowc, rowd;
179 unsigned bitsa, bitsb, bitsc, bitsd;
180 unsigned redbits;
181 int i;
182
183 /*
184 * XXX - nibble reverse words to save a shift? probably not as
185 * nibble reverse would take 20 ops (5 * 4) verse 16
186 */
187
188 for (i = 0; i < 64; i += 4) {
189 bitsa = worda % 16;
190 bitsb = wordb % 16;
191 bitsc = wordc % 16;
192 bitsd = wordd % 16;
193
194 /* fetch row */
195 rowa = readrow(&tbl->tbls[3], bitsa);
196 rowb = readrow(&tbl->tbls[2], bitsb);
197 rowc = readrow(&tbl->tbls[1], bitsc);
198 rowd = readrow(&tbl->tbls[0], bitsd);
199
200 /* x * 2^4 */
201 redbits = x.v[1] % 16;
202 x.v[1] = (x.v[1] >> 4) | (x.v[0] % 16) << 60;
203 x.v[0] >>= 4;
204 x.v[0] ^= (uint64_t)reduction[redbits] << (64 - 16);
205
206 worda >>= 4;
207 wordb >>= 4;
208 wordc >>= 4;
209 wordd >>= 4;
210
211 x = gf128_add(x, gf128_add(rowa, gf128_add(rowb,
212 gf128_add(rowc, rowd))));
213 }
214
215 return x;
216 }
217
218 struct gf128
219 gf128_mul(struct gf128 v, struct gf128table *tbl)
220 {
221 struct gf128 ret;
222
223 ret = MAKE_GF128(0, 0);
224
225 ret = gfmultword(v.v[1], ret, tbl);
226 ret = gfmultword(v.v[0], ret, tbl);
227
228 return ret;
229 }
230
231 /*
232 * Calculate a*h^4 + b*h^3 + c*h^2 + d*h, or:
233 * (((a*h+b)*h+c)*h+d)*h
234 */
235 struct gf128
236 gf128_mul4(struct gf128 a, struct gf128 b, struct gf128 c, struct gf128 d,
237 struct gf128table4 *tbl)
238 {
239 struct gf128 tmp;
240
241 tmp = MAKE_GF128(0, 0);
242
243 tmp = gfmultword4(a.v[1], b.v[1], c.v[1], d.v[1], tmp, tbl);
244 tmp = gfmultword4(a.v[0], b.v[0], c.v[0], d.v[0], tmp, tbl);
245
246 return tmp;
247 }
248
249 /*
250 * a = data[0..15] + r
251 * b = data[16..31]
252 * c = data[32..47]
253 * d = data[48..63]
254 *
255 * Calculate a*h^4 + b*h^3 + c*h^2 + d*h, or:
256 * (((a*h+b)*h+c)*h+d)*h
257 */
258 struct gf128
259 gf128_mul4b(struct gf128 r, const uint8_t *v, struct gf128table4 *tbl)
260 {
261 struct gf128 a, b, c, d;
262 struct gf128 tmp;
263
264 tmp = MAKE_GF128(0, 0);
265
266 a = gf128_add(r, gf128_read(&v[0*16]));
267 b = gf128_read(&v[1*16]);
268 c = gf128_read(&v[2*16]);
269 d = gf128_read(&v[3*16]);
270
271 tmp = gfmultword4(a.v[1], b.v[1], c.v[1], d.v[1], tmp, tbl);
272 tmp = gfmultword4(a.v[0], b.v[0], c.v[0], d.v[0], tmp, tbl);
273
274 return tmp;
275 }
Cache object: 2f41d2e29643deec705faf0cd7c9b703
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