1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
|
/*
* ecgen, tool for generating Elliptic curve domain parameters
* Copyright (C) 2017 J08nY
*/
#include "exhaustive.h"
#include "anomalous.h"
#include "ansi.h"
#include "check.h"
#include "gen/curve.h"
#include "gen/equation.h"
#include "gen/field.h"
#include "gen/gens.h"
#include "gen/order.h"
#include "gen/point.h"
#include "gen/seed.h"
#include "io/output.h"
#include "util/memory.h"
#include "util/timeout.h"
void exhaustive_clear(exhaustive_t *setup) {
if (setup->validators) {
for (size_t i = 0; i < OFFSET_END; ++i) {
check_free(&setup->validators[i]);
}
}
if (setup->argss) {
for (size_t i = 0; i < OFFSET_END; ++i) {
arg_free(&setup->argss[i]);
}
}
}
static void exhaustive_ginit(gen_f *generators) {
if (cfg->seed_algo) {
switch (cfg->seed_algo) {
case SEED_ANSI: {
// setup ANSI X9.62 generators
if (cfg->seed) {
generators[OFFSET_SEED] = &ansi_gen_seed_argument;
} else {
if (cfg->random) {
generators[OFFSET_SEED] = &ansi_gen_seed_random;
} else {
generators[OFFSET_SEED] = &ansi_gen_seed_input;
}
}
generators[OFFSET_A] = &gen_skip;
generators[OFFSET_B] = &ansi_gen_equation;
}
case SEED_BRAINPOOL:
break;
case SEED_BRAINPOOL_RFC:
break;
case SEED_FIPS:
break;
default:
break;
}
if (cfg->prime) {
generators[OFFSET_ORDER] = &order_gen_prime;
} else if (cfg->cofactor) {
generators[OFFSET_ORDER] = &order_gen_smallfact;
} else {
generators[OFFSET_ORDER] = &order_gen_any;
}
} else {
// setup normal generators
generators[OFFSET_SEED] = &gen_skip;
if (cfg->anomalous) {
generators[OFFSET_A] = &gen_skip;
generators[OFFSET_B] = &anomalous_gen_equation;
} else if (cfg->random) {
generators[OFFSET_A] = &a_gen_random;
generators[OFFSET_B] = &b_gen_random;
} else {
generators[OFFSET_A] = &a_gen_input;
generators[OFFSET_B] = &b_gen_input;
}
if (cfg->koblitz) {
switch (cfg->koblitz_value) {
case 0:
generators[OFFSET_A] = &a_gen_zero;
break;
case 1:
generators[OFFSET_A] = &a_gen_one;
break;
default:
break;
}
generators[OFFSET_B] = &b_gen_one;
}
if (cfg->prime) {
generators[OFFSET_ORDER] = &order_gen_prime;
} else if (cfg->cofactor) {
generators[OFFSET_ORDER] = &order_gen_smallfact;
} else if (cfg->anomalous) {
generators[OFFSET_ORDER] = &anomalous_gen_order;
} else {
generators[OFFSET_ORDER] = &order_gen_any;
}
}
// setup common generators
generators[OFFSET_CURVE] = &curve_gen_any;
if (cfg->unique) {
generators[OFFSET_GENERATORS] = &gens_gen_one;
} else {
generators[OFFSET_GENERATORS] = &gens_gen_any;
}
if (cfg->anomalous) {
generators[OFFSET_FIELD] = &anomalous_gen_field;
} else if (cfg->random) {
generators[OFFSET_FIELD] = &field_gen_random;
} else {
generators[OFFSET_FIELD] = &field_gen_input;
}
switch (cfg->points.type) {
case POINTS_RANDOM:
if (cfg->points.amount) {
generators[OFFSET_POINTS] = &points_gen_random;
} else {
generators[OFFSET_POINTS] = &point_gen_random;
}
break;
case POINTS_PRIME:
generators[OFFSET_POINTS] = &points_gen_prime;
break;
case POINTS_NONPRIME:
generators[OFFSET_POINTS] = &points_gen_nonprime;
break;
case POINTS_ALL:
generators[OFFSET_POINTS] = &points_gen_allgroups;
break;
case POINTS_NONE:
generators[OFFSET_POINTS] = &gen_skip;
break;
}
}
static void exhaustive_cinit(check_t **validators) {
check_t *curve_check = check_new(curve_check_nonzero, NULL);
validators[OFFSET_CURVE] = curve_check;
}
static void exhaustive_ainit(arg_t **argss) {
if (cfg->anomalous) {
arg_t *field_arg = arg_new();
arg_t *eq_arg = arg_new();
size_t *i = try_calloc(sizeof(size_t));
*i = 3;
field_arg->args = i;
field_arg->nargs = 1;
eq_arg->args = i;
eq_arg->nargs = 1;
eq_arg->allocd = i;
argss[OFFSET_FIELD] = field_arg;
argss[OFFSET_B] = eq_arg;
}
if (cfg->points.type == POINTS_RANDOM) {
arg_t *points_arg = arg_new();
points_arg->args = &cfg->points.amount;
points_arg->nargs = 1;
argss[OFFSET_POINTS] = points_arg;
}
if (cfg->cofactor) {
arg_t *order_arg = arg_new();
arg_t *gens_arg = arg_new();
order_arg->args = &cfg->cofactor_bound;
order_arg->nargs = 1;
gens_arg->args = &cfg->cofactor_bound;
gens_arg->nargs = 1;
argss[OFFSET_ORDER] = order_arg;
argss[OFFSET_GENERATORS] = gens_arg;
}
}
void exhaustive_uinit(unroll_f *unrolls) {
if (cfg->seed_algo) {
unrolls[OFFSET_SEED] = &seed_unroll;
} else {
unrolls[OFFSET_SEED] = &unroll_skip;
}
unrolls[OFFSET_FIELD] = &unroll_skip;
unrolls[OFFSET_A] = &unroll_skip;
unrolls[OFFSET_B] = &unroll_skip;
unrolls[OFFSET_CURVE] = &curve_unroll;
unrolls[OFFSET_ORDER] = &unroll_skip;
unrolls[OFFSET_GENERATORS] = &gens_unroll;
unrolls[OFFSET_POINTS] = &points_unroll;
}
int exhaustive_gen_retry(curve_t *curve, const exhaustive_t *setup,
offset_e start_offset, offset_e end_offset, int retry) {
if (start_offset == end_offset) {
return 2;
}
if (start_offset > end_offset) {
return 0;
}
gen_f *generators = setup->generators;
check_t **validators = setup->validators;
arg_t **argss = setup->argss;
unroll_f *unrolls = setup->unrolls;
pari_sp stack_tops[OFFSET_END] = {0};
int gen_tries[OFFSET_END] = {0};
int state = start_offset;
while (state < end_offset) {
stack_tops[state] = avma;
arg_t *arg = argss ? argss[state] : NULL;
int diff;
bool timeout = false;
timeout_start(cfg->timeout) {
// This is not the best, but currently the best idea I have.
diff = start_offset - state;
timeout = true;
}
else {
diff = generators[state](curve, arg, (offset_e)state);
}
timeout_stop();
int new_state = state + diff;
if (new_state < start_offset) new_state = start_offset;
if (diff > 0 && validators && validators[state]) {
check_t *validator = validators[state];
for (size_t i = 0; i < validator->nchecks; ++i) {
int new_diff =
validator->checks[i](curve, arg, (offset_e)state);
if (new_diff <= 0) {
diff = new_diff;
break;
}
}
}
if (diff <= 0) {
if (diff == INT_MIN || state + diff < 0) {
fprintf(err, "Error generating a curve. state = %i\n", state);
return 0;
}
// record try
int tried = ++gen_tries[state];
if (retry && tried >= retry) {
if (cfg->verbose) {
fprintf(verbose, "Reached retry limit: %i, state = %i\n",
retry, state);
}
return 0;
}
// unroll
for (int i = state; i > new_state;) {
if (unrolls && unrolls[i]) {
i += unrolls[i](curve, stack_tops[i], stack_tops[i - 1]);
} else {
--i;
}
}
if (timeout) {
verbose_log("#");
} else {
if (diff < 0) {
verbose_log("-");
} else {
verbose_log(".");
}
}
// unroll stack
avma = stack_tops[new_state];
} else {
// we are going forward, reset tries
gen_tries[state] = 0;
verbose_log("+");
}
state = new_state;
}
verbose_log("\n");
return 1;
}
int exhaustive_gen(curve_t *curve, const exhaustive_t *setup,
offset_e start_offset, offset_e end_offset) {
return exhaustive_gen_retry(curve, setup, start_offset, end_offset, 0);
}
static void exhaustive_init(exhaustive_t *setup) {
exhaustive_ginit(setup->generators);
exhaustive_cinit(setup->validators);
exhaustive_ainit(setup->argss);
exhaustive_uinit(setup->unrolls);
anomalous_init();
}
static void exhaustive_quit(exhaustive_t *setup) {
equation_quit();
anomalous_quit();
exhaustive_clear(setup);
}
int exhaustive_do() {
debug_log_start("Starting Exhaustive method");
gen_f generators[OFFSET_END] = {NULL};
check_t *validators[OFFSET_END] = {NULL};
arg_t *argss[OFFSET_END] = {NULL};
unroll_f unrolls[OFFSET_END] = {NULL};
exhaustive_t setup = {.generators = generators,
.validators = validators,
.argss = argss,
.unrolls = unrolls};
exhaustive_init(&setup);
output_o_begin();
for (unsigned long i = 0; i < cfg->count; ++i) {
debug_log_start("Generating new curve");
curve_t *curve = curve_new();
if (!exhaustive_gen(curve, &setup, OFFSET_SEED, OFFSET_END)) {
curve_free(&curve);
return EXIT_FAILURE;
}
debug_log_end("Generated new curve");
output_o(curve);
if (i != cfg->count - 1) {
output_o_separator();
}
curve_free(&curve);
}
output_o_end();
exhaustive_quit(&setup);
debug_log_end("Finished Exhaustive method");
return EXIT_SUCCESS;
}
|