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1 | /* -*-c-*- |
2 | * |
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3 | * $Id: gf-arith.c,v 1.3 2004/03/27 17:54:11 mdw Exp $ |
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4 | * |
5 | * Basic arithmetic on binary polynomials |
6 | * |
7 | * (c) 2004 Straylight/Edgeware |
8 | */ |
9 | |
10 | /*----- Licensing notice --------------------------------------------------* |
11 | * |
12 | * This file is part of Catacomb. |
13 | * |
14 | * Catacomb is free software; you can redistribute it and/or modify |
15 | * it under the terms of the GNU Library General Public License as |
16 | * published by the Free Software Foundation; either version 2 of the |
17 | * License, or (at your option) any later version. |
18 | * |
19 | * Catacomb is distributed in the hope that it will be useful, |
20 | * but WITHOUT ANY WARRANTY; without even the implied warranty of |
21 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
22 | * GNU Library General Public License for more details. |
23 | * |
24 | * You should have received a copy of the GNU Library General Public |
25 | * License along with Catacomb; if not, write to the Free |
26 | * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, |
27 | * MA 02111-1307, USA. |
28 | */ |
29 | |
30 | /*----- Revision history --------------------------------------------------* |
31 | * |
32 | * $Log: gf-arith.c,v $ |
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33 | * Revision 1.3 2004/03/27 17:54:11 mdw |
34 | * Standard curves and curve checking. |
35 | * |
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36 | * Revision 1.2 2004/03/21 22:52:06 mdw |
37 | * Merge and close elliptic curve branch. |
38 | * |
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39 | * Revision 1.1.2.1 2004/03/21 22:39:46 mdw |
40 | * Elliptic curves on binary fields work. |
41 | * |
42 | */ |
43 | |
44 | /*----- Header files ------------------------------------------------------*/ |
45 | |
46 | #include "gf.h" |
47 | |
48 | /*----- Macros ------------------------------------------------------------*/ |
49 | |
50 | #define MAX(x, y) ((x) >= (y) ? (x) : (y)) |
51 | |
52 | /*----- Main code ---------------------------------------------------------*/ |
53 | |
54 | /* --- @gf_add@ --- * |
55 | * |
56 | * Arguments: @mp *d@ = destination |
57 | * @mp *a, *b@ = sources |
58 | * |
59 | * Returns: Result, @a@ added to @b@. |
60 | */ |
61 | |
62 | mp *gf_add(mp *d, mp *a, mp *b) |
63 | { |
64 | MP_DEST(d, MAX(MP_LEN(a), MP_LEN(b)), (a->f | b->f) & MP_BURN); |
65 | gfx_add(d->v, d->vl, a->v, a->vl, b->v, b->vl); |
66 | d->f = (a->f | b->f) & MP_BURN; |
67 | MP_SHRINK(d); |
68 | return (d); |
69 | } |
70 | |
71 | /* --- @gf_mul@ --- * |
72 | * |
73 | * Arguments: @mp *d@ = destination |
74 | * @mp *a, *b@ = sources |
75 | * |
76 | * Returns: Result, @a@ multiplied by @b@. |
77 | */ |
78 | |
79 | mp *gf_mul(mp *d, mp *a, mp *b) |
80 | { |
81 | a = MP_COPY(a); |
82 | b = MP_COPY(b); |
83 | |
84 | if (MP_LEN(a) <= MPK_THRESH || MP_LEN(b) <= GFK_THRESH) { |
85 | MP_DEST(d, MP_LEN(a) + MP_LEN(b), a->f | b->f | MP_UNDEF); |
86 | gfx_mul(d->v, d->vl, a->v, a->vl, b->v, b->vl); |
87 | } else { |
88 | size_t m = MAX(MP_LEN(a), MP_LEN(b)); |
89 | mpw *s; |
90 | MP_DEST(d, 2 * m, a->f | b->f | MP_UNDEF); |
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91 | s = mpalloc(d->a, 3 * m); |
92 | gfx_kmul(d->v, d->vl, a->v, a->vl, b->v, b->vl, s, s + 3 * m); |
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93 | mpfree(d->a, s); |
94 | } |
95 | |
96 | d->f = (a->f | b->f) & MP_BURN; |
97 | MP_SHRINK(d); |
98 | MP_DROP(a); |
99 | MP_DROP(b); |
100 | return (d); |
101 | } |
102 | |
103 | /* --- @gf_sqr@ --- * |
104 | * |
105 | * Arguments: @mp *d@ = destination |
106 | * @mp *a@ = source |
107 | * |
108 | * Returns: Result, @a@ squared. |
109 | */ |
110 | |
111 | mp *gf_sqr(mp *d, mp *a) |
112 | { |
113 | MP_COPY(a); |
114 | MP_DEST(d, 2 * MP_LEN(a), a->f & MP_BURN); |
115 | gfx_sqr(d->v, d->vl, a->v, a->vl); |
116 | d->f = a->f & MP_BURN; |
117 | MP_SHRINK(d); |
118 | MP_DROP(a); |
119 | return (d); |
120 | } |
121 | |
122 | /* --- @gf_div@ --- * |
123 | * |
124 | * Arguments: @mp **qq, **rr@ = destination, quotient and remainder |
125 | * @mp *a, *b@ = sources |
126 | * |
127 | * Use: Calculates the quotient and remainder when @a@ is divided by |
128 | * @b@. The destinations @*qq@ and @*rr@ must be distinct. |
129 | * Either of @qq@ or @rr@ may be null to indicate that the |
130 | * result is irrelevant. (Discarding both results is silly.) |
131 | * There is a performance advantage if @a == *rr@. |
132 | */ |
133 | |
134 | void gf_div(mp **qq, mp **rr, mp *a, mp *b) |
135 | { |
136 | mp *r = rr ? *rr : MP_NEW; |
137 | mp *q = qq ? *qq : MP_NEW; |
138 | |
139 | /* --- Set the remainder up right --- */ |
140 | |
141 | b = MP_COPY(b); |
142 | a = MP_COPY(a); |
143 | if (r) |
144 | MP_DROP(r); |
145 | r = a; |
146 | MP_DEST(r, MP_LEN(b) + 2, a->f | b->f); |
147 | |
148 | /* --- Fix up the quotient too --- */ |
149 | |
150 | r = MP_COPY(r); |
151 | MP_DEST(q, MP_LEN(r), r->f | MP_UNDEF); |
152 | MP_DROP(r); |
153 | |
154 | /* --- Perform the calculation --- */ |
155 | |
156 | gfx_div(q->v, q->vl, r->v, r->vl, b->v, b->vl); |
157 | |
158 | /* --- Sort out the sign of the results --- * |
159 | * |
160 | * If the signs of the arguments differ, and the remainder is nonzero, I |
161 | * must add one to the absolute value of the quotient and subtract the |
162 | * remainder from @b@. |
163 | */ |
164 | |
165 | q->f = (r->f | b->f) & MP_BURN; |
166 | r->f = (r->f | b->f) & MP_BURN; |
167 | |
168 | /* --- Store the return values --- */ |
169 | |
170 | MP_DROP(b); |
171 | |
172 | if (!qq) |
173 | MP_DROP(q); |
174 | else { |
175 | MP_SHRINK(q); |
176 | *qq = q; |
177 | } |
178 | |
179 | if (!rr) |
180 | MP_DROP(r); |
181 | else { |
182 | MP_SHRINK(r); |
183 | *rr = r; |
184 | } |
185 | } |
186 | |
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187 | /* --- @gf_irreduciblep@ --- * |
188 | * |
189 | * Arguments: @mp *f@ = a polynomial |
190 | * |
191 | * Returns: Nonzero if the polynomial is irreducible; otherwise zero. |
192 | */ |
193 | |
194 | int gf_irreduciblep(mp *f) |
195 | { |
196 | unsigned long m = mp_bits(f) - 1; |
197 | mp *u = MP_TWO; |
198 | mp *v = MP_NEW; |
199 | |
200 | m /= 2; |
201 | while (m) { |
202 | u = gf_sqr(u, u); |
203 | gf_div(0, &u, u, f); |
204 | v = gf_add(v, u, MP_TWO); |
205 | gf_gcd(&v, 0, 0, v, f); |
206 | if (!MP_EQ(v, MP_ONE)) break; |
207 | m--; |
208 | } |
209 | MP_DROP(u); |
210 | MP_DROP(v); |
211 | return (!m); |
212 | } |
213 | |
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214 | /*----- Test rig ----------------------------------------------------------*/ |
215 | |
216 | #ifdef TEST_RIG |
217 | |
218 | static int verify(const char *op, mp *expect, mp *result, mp *a, mp *b) |
219 | { |
220 | if (!MP_EQ(expect, result)) { |
221 | fprintf(stderr, "\n*** %s failed", op); |
222 | fputs("\n*** a = ", stderr); mp_writefile(a, stderr, 16); |
223 | fputs("\n*** b = ", stderr); mp_writefile(b, stderr, 16); |
224 | fputs("\n*** result = ", stderr); mp_writefile(result, stderr, 16); |
225 | fputs("\n*** expect = ", stderr); mp_writefile(expect, stderr, 16); |
226 | fputc('\n', stderr); |
227 | return (0); |
228 | } |
229 | return (1); |
230 | } |
231 | |
232 | #define RIG(name, op) \ |
233 | static int t##name(dstr *v) \ |
234 | { \ |
235 | mp *a = *(mp **)v[0].buf; \ |
236 | mp *b = *(mp **)v[1].buf; \ |
237 | mp *r = *(mp **)v[2].buf; \ |
238 | mp *c = op(MP_NEW, a, b); \ |
239 | int ok = verify(#name, r, c, a, b); \ |
240 | mp_drop(a); mp_drop(b); mp_drop(c); mp_drop(r); \ |
241 | assert(mparena_count(MPARENA_GLOBAL) == 0); \ |
242 | return (ok); \ |
243 | } |
244 | |
245 | RIG(add, gf_add) |
246 | RIG(mul, gf_mul) |
247 | |
248 | #undef RIG |
249 | |
250 | static int tsqr(dstr *v) |
251 | { |
252 | mp *a = *(mp **)v[0].buf; |
253 | mp *r = *(mp **)v[1].buf; |
254 | mp *c = MP_NEW; |
255 | int ok = 1; |
256 | c = gf_sqr(MP_NEW, a); |
257 | ok &= verify("sqr", r, c, a, MP_ZERO); |
258 | mp_drop(a); mp_drop(r); mp_drop(c); |
259 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
260 | return (ok); |
261 | } |
262 | |
263 | static int tdiv(dstr *v) |
264 | { |
265 | mp *a = *(mp **)v[0].buf; |
266 | mp *b = *(mp **)v[1].buf; |
267 | mp *q = *(mp **)v[2].buf; |
268 | mp *r = *(mp **)v[3].buf; |
269 | mp *c = MP_NEW, *d = MP_NEW; |
270 | int ok = 1; |
271 | gf_div(&c, &d, a, b); |
272 | ok &= verify("div(quotient)", q, c, a, b); |
273 | ok &= verify("div(remainder)", r, d, a, b); |
274 | mp_drop(a); mp_drop(b); mp_drop(c); mp_drop(d); mp_drop(r); mp_drop(q); |
275 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
276 | return (ok); |
277 | } |
278 | |
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279 | static int tirred(dstr *v) |
280 | { |
281 | mp *a = *(mp **)v[0].buf; |
282 | int r = *(int *)v[1].buf; |
283 | int c = gf_irreduciblep(a); |
284 | int ok = 1; |
285 | if (r != c) { |
286 | ok = 0; |
287 | fprintf(stderr, "\n*** irred failed"); |
288 | fputs("\n*** a = ", stderr); mp_writefile(a, stderr, 16); |
289 | fprintf(stderr, "\n*** r = %d\n", r); |
290 | fprintf(stderr, "*** c = %d\n", c); |
291 | } |
292 | mp_drop(a); |
293 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
294 | return (ok); |
295 | } |
296 | |
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297 | static test_chunk tests[] = { |
298 | { "add", tadd, { &type_mp, &type_mp, &type_mp, 0 } }, |
299 | { "mul", tmul, { &type_mp, &type_mp, &type_mp, 0 } }, |
300 | { "sqr", tsqr, { &type_mp, &type_mp, 0 } }, |
301 | { "div", tdiv, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } }, |
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302 | { "irred", tirred, { &type_mp, &type_int, 0 } }, |
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303 | { 0, 0, { 0 } }, |
304 | }; |
305 | |
306 | int main(int argc, char *argv[]) |
307 | { |
308 | sub_init(); |
309 | test_run(argc, argv, tests, SRCDIR "/tests/gf"); |
310 | return (0); |
311 | } |
312 | |
313 | #endif |
314 | |
315 | /*----- That's all, folks -------------------------------------------------*/ |