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1 /* reveng.c
2 * Greg Cook, 9/Apr/2015
3 */
4
5 /* CRC RevEng, an arbitrary-precision CRC calculator and algorithm finder
6 * Copyright (C) 2010, 2011, 2012, 2013, 2014, 2015 Gregory Cook
7 *
8 * This file is part of CRC RevEng.
9 *
10 * CRC RevEng is free software: you can redistribute it and/or modify
11 * it under the terms of the GNU General Public License as published by
12 * the Free Software Foundation, either version 3 of the License, or
13 * (at your option) any later version.
14 *
15 * CRC RevEng is distributed in the hope that it will be useful,
16 * but WITHOUT ANY WARRANTY; without even the implied warranty of
17 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
18 * GNU General Public License for more details.
19 *
20 * You should have received a copy of the GNU General Public License
21 * along with CRC RevEng. If not, see <http://www.gnu.org/licenses/>.
22 */
23
24 /* 2013-09-16: calini(), calout() work on shortest argument
25 * 2013-06-11: added sequence number to uprog() calls
26 * 2013-02-08: added polynomial range search
27 * 2013-01-18: refactored model checking to pshres(); renamed chkres()
28 * 2012-05-24: efficiently build Init contribution string
29 * 2012-05-24: removed broken search for crossed-endian algorithms
30 * 2012-05-23: rewrote engini() after Ewing; removed modini()
31 * 2011-01-17: fixed ANSI C warnings
32 * 2011-01-08: fixed calini(), modini() caters for crossed-endian algos
33 * 2011-01-04: renamed functions, added calini(), factored pshres();
34 * rewrote engini() and implemented quick Init search
35 * 2011-01-01: reveng() initialises terminating entry, addparms()
36 * initialises all fields
37 * 2010-12-26: renamed CRC RevEng. right results, rejects polys faster
38 * 2010-12-24: completed, first tests (unsuccessful)
39 * 2010-12-21: completed modulate(), partial sketch of reveng()
40 * 2010-12-19: started reveng
41 */
42
43 /* reveng() can in theory be modified to search for polynomials shorter
44 * than the full width as well, but this imposes a heavy time burden on
45 * the full width search, which is the primary use case, as well as
46 * complicating the search range function introduced in version 1.1.0.
47 * It is more effective to search for each shorter width directly.
48 */
49
50 #include <stdlib.h>
51
52 #define FILE void
53 #include "reveng.h"
54
55 static poly_t *modpol(const poly_t init, int rflags, int args, const poly_t *argpolys);
56 static void engini(int *resc, model_t **result, const poly_t divisor, int flags, int args, const poly_t *argpolys);
57 static void calout(int *resc, model_t **result, const poly_t divisor, const poly_t init, int flags, int args, const poly_t *argpolys);
58 static void calini(int *resc, model_t **result, const poly_t divisor, int flags, const poly_t xorout, int args, const poly_t *argpolys);
59 static void chkres(int *resc, model_t **result, const poly_t divisor, const poly_t init, int flags, const poly_t xorout, int args, const poly_t *argpolys);
60
61 static const poly_t pzero = PZERO;
62
63 model_t *
64 reveng(const model_t *guess, const poly_t qpoly, int rflags, int args, const poly_t *argpolys) {
65 /* Complete the parameters of a model by calculation or brute search. */
66 poly_t *pworks, *wptr, rem, gpoly;
67 model_t *result = NULL, *rptr;
68 int resc = 0;
69 unsigned long spin = 0, seq = 0;
70
71 if(~rflags & R_HAVEP) {
72 /* The poly is not known.
73 * Produce a list of differences between the arguments.
74 */
75 pworks = modpol(guess->init, rflags, args, argpolys);
76 if(!pworks || !plen(*pworks)) {
77 free(pworks);
78 goto requit;
79 }
80 /* Initialise the guessed poly to the starting value. */
81 gpoly = pclone(guess->spoly);
82 /* Clear the least significant term, to be set in the
83 * loop. qpoly does not need fixing as it is only
84 * compared with odd polys.
85 */
86 if(plen(gpoly))
87 pshift(&gpoly, gpoly, 0UL, 0UL, plen(gpoly) - 1UL, 1UL);
88
89 while(piter(&gpoly) && (~rflags & R_HAVEQ || pcmp(&gpoly, &qpoly) < 0)) {
90 /* For each possible poly of this size, try
91 * dividing all the differences in the list.
92 */
93 if(!(spin++ & R_SPMASK)) {
94 uprog(gpoly, guess->flags, seq++);
95 }
96 for(wptr = pworks; plen(*wptr); ++wptr) {
97 /* straight divide message by poly, don't multiply by x^n */
98 rem = pcrc(*wptr, gpoly, pzero, pzero, 0);
99 if(ptst(rem)) {
100 pfree(&rem);
101 break;
102 } else
103 pfree(&rem);
104 }
105 /* If gpoly divides all the differences, it is a
106 * candidate. Search for an Init value for this
107 * poly or if Init is known, log the result.
108 */
109 if(!plen(*wptr)) {
110 /* gpoly is a candidate poly */
111 if(rflags & R_HAVEI && rflags & R_HAVEX)
112 chkres(&resc, &result, gpoly, guess->init, guess->flags, guess->xorout, args, argpolys);
113 else if(rflags & R_HAVEI)
114 calout(&resc, &result, gpoly, guess->init, guess->flags, args, argpolys);
115 else if(rflags & R_HAVEX)
116 calini(&resc, &result, gpoly, guess->flags, guess->xorout, args, argpolys);
117 else
118 engini(&resc, &result, gpoly, guess->flags, args, argpolys);
119 }
120 if(!piter(&gpoly))
121 break;
122 }
123 /* Finished with gpoly and the differences list, free them.
124 */
125 pfree(&gpoly);
126 for(wptr = pworks; plen(*wptr); ++wptr)
127 pfree(wptr);
128 free(pworks);
129 }
130 else if(rflags & R_HAVEI && rflags & R_HAVEX)
131 /* All parameters are known! Submit the result if we get here */
132 chkres(&resc, &result, guess->spoly, guess->init, guess->flags, guess->xorout, args, argpolys);
133 else if(rflags & R_HAVEI)
134 /* Poly and Init are known, calculate XorOut */
135 calout(&resc, &result, guess->spoly, guess->init, guess->flags, args, argpolys);
136 else if(rflags & R_HAVEX)
137 /* Poly and XorOut are known, calculate Init */
138 calini(&resc, &result, guess->spoly, guess->flags, guess->xorout, args, argpolys);
139 else
140 /* Poly is known but not Init; search for Init. */
141 engini(&resc, &result, guess->spoly, guess->flags, args, argpolys);
142
143 requit:
144 if(!(result = realloc(result, ++resc * sizeof(model_t))))
145 uerror("cannot reallocate result array");
146 rptr = result + resc - 1;
147 rptr->spoly = pzero;
148 rptr->init = pzero;
149 rptr->flags = 0;
150 rptr->xorout = pzero;
151 rptr->check = pzero;
152 rptr->name = NULL;
153
154 return(result);
155 }
156
157 static poly_t *
158 modpol(const poly_t init, int rflags, int args, const poly_t *argpolys) {
159 /* Produce, in ascending length order, a list of differences
160 * between the arguments in the list by summing pairs of arguments.
161 * If R_HAVEI is not set in rflags, only pairs of equal length are
162 * summed.
163 * Otherwise, sums of right-aligned pairs are also returned, with
164 * the supplied init poly added to the leftmost terms of each
165 * poly of the pair.
166 */
167 poly_t work, swap, *result, *rptr, *iptr;
168 const poly_t *aptr, *bptr, *eptr = argpolys + args;
169 unsigned long alen, blen;
170
171 if(args < 2) return(NULL);
172
173 if(!(result = malloc(((((args - 1) * args) >> 1) + 1) * sizeof(poly_t))))
174 uerror("cannot allocate memory for codeword table");
175
176 rptr = result;
177
178 for(aptr = argpolys; aptr < eptr; ++aptr) {
179 alen = plen(*aptr);
180 for(bptr = aptr + 1; bptr < eptr; ++bptr) {
181 blen = plen(*bptr);
182 if(alen == blen) {
183 work = pclone(*aptr);
184 psum(&work, *bptr, 0UL);
185 } else if(rflags & R_HAVEI && alen < blen) {
186 work = pclone(*bptr);
187 psum(&work, *aptr, blen - alen);
188 psum(&work, init, 0UL);
189 psum(&work, init, blen - alen);
190 } else if(rflags & R_HAVEI /* && alen > blen */) {
191 work = pclone(*aptr);
192 psum(&work, *bptr, alen - blen);
193 psum(&work, init, 0UL);
194 psum(&work, init, alen - blen);
195 } else
196 work = pzero;
197
198 if(plen(work))
199 pnorm(&work);
200 if((blen = plen(work))) {
201 /* insert work into result[] in ascending order of length */
202 for(iptr = result; iptr < rptr; ++iptr) {
203 if(plen(work) < plen(*iptr)) {
204 swap = *iptr;
205 *iptr = work;
206 work = swap;
207 }
208 else if(plen(*iptr) == blen && !pcmp(&work, iptr)) {
209 pfree(&work);
210 work = *--rptr;
211 break;
212 }
213 }
214 *rptr++ = work;
215 }
216 }
217 }
218 *rptr = pzero;
219 return(result);
220 }
221
222 static void
223 engini(int *resc, model_t **result, const poly_t divisor, int flags, int args, const poly_t *argpolys) {
224 /* Search for init values implied by the arguments.
225 * Method from: Ewing, Gregory C. (March 2010).
226 * "Reverse-Engineering a CRC Algorithm". Christchurch:
227 * University of Canterbury.
228 * <http://www.cosc.canterbury.ac.nz/greg.ewing/essays/
229 * CRC-Reverse-Engineering.html>
230 */
231 poly_t apoly = PZERO, bpoly, pone = PZERO, *mat, *jptr;
232 const poly_t *aptr, *bptr, *iptr;
233 unsigned long alen, blen, dlen, ilen, i, j;
234 int cy;
235
236 dlen = plen(divisor);
237
238 /* Allocate the CRC matrix */
239 if(!(mat = (poly_t *) malloc((dlen << 1) * sizeof(poly_t))))
240 uerror("cannot allocate memory for CRC matrix");
241
242 /* Find arguments of the two shortest lengths */
243 alen = blen = plen(*(aptr = bptr = iptr = argpolys));
244 for(++iptr; iptr < argpolys + args; ++iptr) {
245 ilen = plen(*iptr);
246 if(ilen < alen) {
247 bptr = aptr; blen = alen;
248 aptr = iptr; alen = ilen;
249 } else if(ilen > alen && (aptr == bptr || ilen < blen)) {
250 bptr = iptr; blen = ilen;
251 }
252 }
253 if(aptr == bptr) {
254 /* if no arguments are suitable, calculate Init with an
255 * assumed XorOut of 0. Create a padded XorOut
256 */
257 palloc(&apoly, dlen);
258 calini(resc, result, divisor, flags, apoly, args, argpolys);
259 pfree(&apoly);
260 return;
261 }
262
263 /* Find the potential contribution of the bottom bit of Init */
264 palloc(&pone, 1UL);
265 piter(&pone);
266 if(blen < (dlen << 1)) {
267 palloc(&apoly, dlen); /* >= 1 */
268 psum(&apoly, pone, (dlen << 1) - 1UL - blen); /* >= 0 */
269 psum(&apoly, pone, (dlen << 1) - 1UL - alen); /* >= 1 */
270 } else {
271 palloc(&apoly, blen - dlen + 1UL); /* > dlen */
272 psum(&apoly, pone, 0UL);
273 psum(&apoly, pone, blen - alen); /* >= 1 */
274 }
275 if(plen(apoly) > dlen) {
276 mat[dlen] = pcrc(apoly, divisor, pzero, pzero, 0);
277 pfree(&apoly);
278 } else {
279 mat[dlen] = apoly;
280 }
281
282 /* Find the actual contribution of Init */
283 apoly = pcrc(*aptr, divisor, pzero, pzero, 0);
284 bpoly = pcrc(*bptr, divisor, pzero, apoly, 0);
285
286 /* Populate the matrix */
287 palloc(&apoly, 1UL);
288 for(jptr=mat; jptr<mat+dlen; ++jptr)
289 *jptr = pzero;
290 for(iptr = jptr++; jptr < mat + (dlen << 1); iptr = jptr++)
291 *jptr = pcrc(apoly, divisor, *iptr, pzero, P_MULXN);
292 pfree(&apoly);
293
294 /* Transpose the matrix, augment with the Init contribution
295 * and convert to row echelon form
296 */
297 for(i=0UL; i<dlen; ++i) {
298 apoly = pzero;
299 iptr = mat + (dlen << 1);
300 for(j=0UL; j<dlen; ++j)
301 ppaste(&apoly, *--iptr, i, j, j + 1UL, dlen + 1UL);
302 if(ptst(apoly))
303 ppaste(&apoly, bpoly, i, dlen, dlen + 1UL, dlen + 1UL);
304 j = pfirst(apoly);
305 while(j < dlen && !pident(mat[j], pzero)) {
306 psum(&apoly, mat[j], 0UL); /* pfirst(apoly) > j */
307 j = pfirst(apoly);
308 }
309 if(j < dlen)
310 mat[j] = apoly; /* pident(mat[j], pzero) || pfirst(mat[j]) == j */
311 else
312 pfree(&apoly);
313 }
314 palloc(&bpoly, dlen + 1UL);
315 psum(&bpoly, pone, dlen);
316
317 /* Iterate through all solutions */
318 do {
319 /* Solve the matrix by Gaussian elimination.
320 * The parity of the result, masked by each row, should be even.
321 */
322 cy = 1;
323 apoly = pclone(bpoly);
324 jptr = mat + dlen;
325 for(i=0UL; i<dlen; ++i) {
326 /* Compute next bit of Init */
327 if(pmpar(apoly, *--jptr))
328 psum(&apoly, pone, dlen - 1UL - i);
329 /* Toggle each zero row with carry, for next iteration */
330 if(cy) {
331 if(pident(*jptr, pzero)) {
332 /* 0 to 1, no carry */
333 *jptr = bpoly;
334 cy = 0;
335 } else if(pident(*jptr, bpoly)) {
336 /* 1 to 0, carry forward */
337 *jptr = pzero;
338 }
339 }
340 }
341
342 /* Trim the augment mask bit */
343 praloc(&apoly, dlen);
344
345 /* Test the Init value and add to results if correct */
346 calout(resc, result, divisor, apoly, flags, args, argpolys);
347 pfree(&apoly);
348 } while(!cy);
349 pfree(&pone);
350 pfree(&bpoly);
351
352 /* Free the matrix. */
353 for(jptr=mat; jptr < mat + (dlen << 1); ++jptr)
354 pfree(jptr);
355 free(mat);
356 }
357
358 static void
359 calout(int *resc, model_t **result, const poly_t divisor, const poly_t init, int flags, int args, const poly_t *argpolys) {
360 /* Calculate Xorout, check it against all the arguments and
361 * add to results if consistent.
362 */
363 poly_t xorout;
364 const poly_t *aptr, *iptr;
365 unsigned long alen, ilen;
366
367 if(args < 1) return;
368
369 /* find argument of the shortest length */
370 alen = plen(*(aptr = iptr = argpolys));
371 for(++iptr; iptr < argpolys + args; ++iptr) {
372 ilen = plen(*iptr);
373 if(ilen < alen) {
374 aptr = iptr; alen = ilen;
375 }
376 }
377
378 xorout = pcrc(*aptr, divisor, init, pzero, 0);
379 /* On little-endian algorithms, the calculations yield
380 * the reverse of the actual xorout: in the Williams
381 * model, the refout stage intervenes between init and
382 * xorout.
383 */
384 if(flags & P_REFOUT)
385 prev(&xorout);
386
387 /* Submit the model to the results table.
388 * Could skip the shortest argument but we wish to check our
389 * calculation.
390 */
391 chkres(resc, result, divisor, init, flags, xorout, args, argpolys);
392 pfree(&xorout);
393 }
394
395 static void
396 calini(int *resc, model_t **result, const poly_t divisor, int flags, const poly_t xorout, int args, const poly_t *argpolys) {
397 /* Calculate Init, check it against all the arguments and add to
398 * results if consistent.
399 */
400 poly_t rcpdiv, rxor, arg, init;
401 const poly_t *aptr, *iptr;
402 unsigned long alen, ilen;
403
404 if(args < 1) return;
405
406 /* find argument of the shortest length */
407 alen = plen(*(aptr = iptr = argpolys));
408 for(++iptr; iptr < argpolys + args; ++iptr) {
409 ilen = plen(*iptr);
410 if(ilen < alen) {
411 aptr = iptr; alen = ilen;
412 }
413 }
414
415 rcpdiv = pclone(divisor);
416 prcp(&rcpdiv);
417 /* If the algorithm is reflected, an ordinary CRC requires the
418 * model's XorOut to be reversed, as XorOut follows the RefOut
419 * stage. To reverse the CRC calculation we need rxor to be the
420 * mirror image of the forward XorOut.
421 */
422 rxor = pclone(xorout);
423 if(~flags & P_REFOUT)
424 prev(&rxor);
425 arg = pclone(*aptr);
426 prev(&arg);
427
428 init = pcrc(arg, rcpdiv, rxor, pzero, 0);
429 pfree(&arg);
430 pfree(&rxor);
431 pfree(&rcpdiv);
432 prev(&init);
433
434 /* Submit the model to the results table.
435 * Could skip the shortest argument but we wish to check our
436 * calculation.
437 */
438 chkres(resc, result, divisor, init, flags, xorout, args, argpolys);
439 pfree(&init);
440 }
441
442 static void
443 chkres(int *resc, model_t **result, const poly_t divisor, const poly_t init, int flags, const poly_t xorout, int args, const poly_t *argpolys) {
444 /* Checks a model against the argument list, and adds to the
445 * external results table if consistent.
446 * Extends the result array and update the external pointer if
447 * necessary.
448 */
449 model_t *rptr;
450 poly_t xor, crc;
451 const poly_t *aptr = argpolys, *const eptr = argpolys + args;
452
453 /* If the algorithm is reflected, an ordinary CRC requires the
454 * model's XorOut to be reversed, as XorOut follows the RefOut
455 * stage.
456 */
457 xor = pclone(xorout);
458 if(flags & P_REFOUT)
459 prev(&xor);
460
461 for(; aptr < eptr; ++aptr) {
462 crc = pcrc(*aptr, divisor, init, xor, 0);
463 if(ptst(crc)) {
464 pfree(&crc);
465 break;
466 } else {
467 pfree(&crc);
468 }
469 }
470 pfree(&xor);
471 if(aptr != eptr) return;
472
473 if(!(*result = realloc(*result, ++*resc * sizeof(model_t))))
474 uerror("cannot reallocate result array");
475
476 rptr = *result + *resc - 1;
477 rptr->spoly = pclone(divisor);
478 rptr->init = pclone(init);
479 rptr->flags = flags;
480 rptr->xorout = pclone(xorout);
481 rptr->name = NULL;
482
483 /* compute check value for this model */
484 mcheck(rptr);
485
486 /* callback to notify new model */
487 ufound(rptr);
488 }
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