2 * Copyright (c) 2014 The FreeBSD Foundation
4 * This software was developed by John-Mark Gurney under
5 * the sponsorship of the FreeBSD Foundation and
6 * Rubicon Communications, LLC (Netgate).
7 * Redistribution and use in source and binary forms, with or without
8 * modification, are permitted provided that the following conditions
10 * 1. Redistributions of source code must retain the above copyright
11 * notice, this list of conditions and the following disclaimer.
12 * 2. Redistributions in binary form must reproduce the above copyright
13 * notice, this list of conditions and the following disclaimer in the
14 * documentation and/or other materials provided with the distribution.
16 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
17 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
18 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
19 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
20 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
21 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
22 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
23 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
24 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
25 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
34 #define REV_POLY_REDUCT 0xe1 /* 0x87 bit reversed */
36 /* reverse the bits of a nibble */
37 static const uint8_t nib_rev[] = {
38 0x0, 0x8, 0x4, 0xc, 0x2, 0xa, 0x6, 0xe,
39 0x1, 0x9, 0x5, 0xd, 0x3, 0xb, 0x7, 0xf,
43 static inline struct gf128
44 gf128_mulalpha(struct gf128 v)
48 mask = !!(v.v[1] & 1);
50 v.v[1] = (v.v[1] >> 1) | ((v.v[0] & 1) << 63);
51 v.v[0] = (v.v[0] >> 1) ^ ((mask & REV_POLY_REDUCT) << 56);
57 * Generate a table for 0-16 * h. Store the results in the table w/ indexes
58 * bit reversed, and the words striped across the values.
61 gf128_genmultable(struct gf128 h, struct gf128table *t)
66 tbl[0] = MAKE_GF128(0, 0);
69 for (i = 2; i < 16; i += 2) {
70 tbl[i] = gf128_mulalpha(tbl[i / 2]);
71 tbl[i + 1] = gf128_add(tbl[i], h);
74 for (i = 0; i < 16; i++) {
75 t->a[nib_rev[i]] = tbl[i].v[0] >> 32;
76 t->b[nib_rev[i]] = tbl[i].v[0];
77 t->c[nib_rev[i]] = tbl[i].v[1] >> 32;
78 t->d[nib_rev[i]] = tbl[i].v[1];
83 * Generate tables containing h, h^2, h^3 and h^4, starting at 0.
86 gf128_genmultable4(struct gf128 h, struct gf128table4 *t)
88 struct gf128 h2, h3, h4;
90 gf128_genmultable(h, &t->tbls[0]);
92 h2 = gf128_mul(h, &t->tbls[0]);
94 gf128_genmultable(h2, &t->tbls[1]);
96 h3 = gf128_mul(h, &t->tbls[1]);
97 gf128_genmultable(h3, &t->tbls[2]);
99 h4 = gf128_mul(h2, &t->tbls[1]);
100 gf128_genmultable(h4, &t->tbls[3]);
104 * Read a row from the table.
106 static inline struct gf128
107 readrow(struct gf128table *tbl, unsigned bits)
113 r.v[0] = ((uint64_t)tbl->a[bits] << 32) | tbl->b[bits];
114 r.v[1] = ((uint64_t)tbl->c[bits] << 32) | tbl->d[bits];
120 * These are the reduction values. Since we are dealing with bit reversed
121 * version, the values need to be bit reversed, AND the indexes are also
122 * bit reversed to make lookups quicker.
124 static uint16_t reduction[] = {
125 0x0000, 0x1c20, 0x3840, 0x2460, 0x7080, 0x6ca0, 0x48c0, 0x54e0,
126 0xe100, 0xfd20, 0xd940, 0xc560, 0x9180, 0x8da0, 0xa9c0, 0xb5e0,
131 * (x*2^4 + word[3,0]*h) *
132 * 2^4 + word[7,4]*h) *
134 * 2^4 + word[63,60]*h
137 gfmultword(uint64_t word, struct gf128 x, struct gf128table *tbl)
144 for (i = 0; i < 64; i += 4) {
148 row = readrow(tbl, bits);
151 redbits = x.v[1] % 16;
152 x.v[1] = (x.v[1] >> 4) | (x.v[0] % 16) << 60;
154 x.v[0] ^= (uint64_t)reduction[redbits] << (64 - 16);
158 x = gf128_add(x, row);
166 * (x*2^4 + worda[3,0]*h^4+wordb[3,0]*h^3+...+wordd[3,0]*h) *
168 * 2^4 + worda[63,60]*h^4+ ... + wordd[63,60]*h
170 * Passing/returning struct is .5% faster than passing in via pointer on
174 gfmultword4(uint64_t worda, uint64_t wordb, uint64_t wordc, uint64_t wordd,
175 struct gf128 x, struct gf128table4 *tbl)
177 struct gf128 rowa, rowb, rowc, rowd;
178 unsigned bitsa, bitsb, bitsc, bitsd;
183 * XXX - nibble reverse words to save a shift? probably not as
184 * nibble reverse would take 20 ops (5 * 4) verse 16
187 for (i = 0; i < 64; i += 4) {
194 rowa = readrow(&tbl->tbls[3], bitsa);
195 rowb = readrow(&tbl->tbls[2], bitsb);
196 rowc = readrow(&tbl->tbls[1], bitsc);
197 rowd = readrow(&tbl->tbls[0], bitsd);
200 redbits = x.v[1] % 16;
201 x.v[1] = (x.v[1] >> 4) | (x.v[0] % 16) << 60;
203 x.v[0] ^= (uint64_t)reduction[redbits] << (64 - 16);
210 x = gf128_add(x, gf128_add(rowa, gf128_add(rowb,
211 gf128_add(rowc, rowd))));
218 gf128_mul(struct gf128 v, struct gf128table *tbl)
222 ret = MAKE_GF128(0, 0);
224 ret = gfmultword(v.v[1], ret, tbl);
225 ret = gfmultword(v.v[0], ret, tbl);
231 * Calculate a*h^4 + b*h^3 + c*h^2 + d*h, or:
232 * (((a*h+b)*h+c)*h+d)*h
235 gf128_mul4(struct gf128 a, struct gf128 b, struct gf128 c, struct gf128 d,
236 struct gf128table4 *tbl)
240 tmp = MAKE_GF128(0, 0);
242 tmp = gfmultword4(a.v[1], b.v[1], c.v[1], d.v[1], tmp, tbl);
243 tmp = gfmultword4(a.v[0], b.v[0], c.v[0], d.v[0], tmp, tbl);
249 * a = data[0..15] + r
254 * Calculate a*h^4 + b*h^3 + c*h^2 + d*h, or:
255 * (((a*h+b)*h+c)*h+d)*h
258 gf128_mul4b(struct gf128 r, const uint8_t *v, struct gf128table4 *tbl)
260 struct gf128 a, b, c, d;
263 tmp = MAKE_GF128(0, 0);
265 a = gf128_add(r, gf128_read(&v[0*16]));
266 b = gf128_read(&v[1*16]);
267 c = gf128_read(&v[2*16]);
268 d = gf128_read(&v[3*16]);
270 tmp = gfmultword4(a.v[1], b.v[1], c.v[1], d.v[1], tmp, tbl);
271 tmp = gfmultword4(a.v[0], b.v[0], c.v[0], d.v[0], tmp, tbl);