proxmark3/client/reveng/reveng.c

/* reveng.c
 * Greg Cook, 27/Jun/2016
 */

/* CRC RevEng: arbitrary-precision CRC calculator and algorithm finder
 * Copyright (C) 2010, 2011, 2012, 2013, 2014, 2015, 2016  Gregory Cook
 *
 * This file is part of CRC RevEng.
 *
 * CRC RevEng is free software: you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 *
 * CRC RevEng is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with CRC RevEng.  If not, see <https://www.gnu.org/licenses/>.
 */

/* 2013-09-16: calini(), calout() work on shortest argument
 * 2013-06-11: added sequence number to uprog() calls
 * 2013-02-08: added polynomial range search
 * 2013-01-18: refactored model checking to pshres(); renamed chkres()
 * 2012-05-24: efficiently build Init contribution string
 * 2012-05-24: removed broken search for crossed-endian algorithms
 * 2012-05-23: rewrote engini() after Ewing; removed modini()
 * 2011-01-17: fixed ANSI C warnings
 * 2011-01-08: fixed calini(), modini() caters for crossed-endian algos
 * 2011-01-04: renamed functions, added calini(), factored pshres();
 *	       rewrote engini() and implemented quick Init search
 * 2011-01-01: reveng() initialises terminating entry, addparms()
 *	       initialises all fields
 * 2010-12-26: renamed CRC RevEng. right results, rejects polys faster
 * 2010-12-24: completed, first tests (unsuccessful)
 * 2010-12-21: completed modulate(), partial sketch of reveng()
 * 2010-12-19: started reveng
 */

/* reveng() can in theory be modified to search for polynomials shorter
 * than the full width as well, but this imposes a heavy time burden on
 * the full width search, which is the primary use case, as well as
 * complicating the search range function introduced in version 1.1.0.
 * It is more effective to search for each shorter width directly.
 */

#include <stdlib.h>

#define FILE void
#include "reveng.h"

static poly_t *modpol(const poly_t init, int rflags, int args, const poly_t *argpolys);
static void engini(int *resc, model_t **result, const poly_t divisor, int flags, int args, const poly_t *argpolys);
static void calout(int *resc, model_t **result, const poly_t divisor, const poly_t init, int flags, int args, const poly_t *argpolys);
static void calini(int *resc, model_t **result, const poly_t divisor, int flags, const poly_t xorout, int args, const poly_t *argpolys);
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);

static const poly_t pzero = PZERO;

model_t *
reveng(const model_t *guess, const poly_t qpoly, int rflags, int args, const poly_t *argpolys) {
	/* Complete the parameters of a model by calculation or brute search. */
	poly_t *pworks, *wptr, rem, gpoly;
	model_t *result = NULL, *rptr;
	int resc = 0;
	unsigned long spin = 0, seq = 0;

	if(~rflags & R_HAVEP) {
		/* The poly is not known.
		 * Produce a list of differences between the arguments.
		 */
		pworks = modpol(guess->init, rflags, args, argpolys);
		if(!pworks || !plen(*pworks)) {
			free(pworks);
			goto requit;
		}
		/* Initialise the guessed poly to the starting value. */
		gpoly = pclone(guess->spoly);
		/* Clear the least significant term, to be set in the
		 * loop. qpoly does not need fixing as it is only
		 * compared with odd polys.
		 */
		if(plen(gpoly))
			pshift(&gpoly, gpoly, 0UL, 0UL, plen(gpoly) - 1UL, 1UL);

		while(piter(&gpoly) && (~rflags & R_HAVEQ || pcmp(&gpoly, &qpoly) < 0)) {
			/* For each possible poly of this size, try
			 * dividing all the differences in the list.
			 */
			if(!(spin++ & R_SPMASK)) {
				uprog(gpoly, guess->flags, seq++);
			}
			for(wptr = pworks; plen(*wptr); ++wptr) {
				/* straight divide message by poly, don't multiply by x^n */
				rem = pcrc(*wptr, gpoly, pzero, pzero, 0);
				if(ptst(rem)) {
					pfree(&rem);
					break;
				} else
					pfree(&rem);
			}
			/* If gpoly divides all the differences, it is a
			 * candidate.  Search for an Init value for this
			 * poly or if Init is known, log the result.
			 */
			if(!plen(*wptr)) {
				/* gpoly is a candidate poly */
				if(rflags & R_HAVEI && rflags & R_HAVEX)
					chkres(&resc, &result, gpoly, guess->init, guess->flags, guess->xorout, args, argpolys);
				else if(rflags & R_HAVEI)
					calout(&resc, &result, gpoly, guess->init, guess->flags, args, argpolys);
				else if(rflags & R_HAVEX)
					calini(&resc, &result, gpoly, guess->flags, guess->xorout, args, argpolys);
				else
					engini(&resc, &result, gpoly, guess->flags, args, argpolys);
			}
			if(!piter(&gpoly))
				break;
		}
		/* Finished with gpoly and the differences list, free them.
		 */
		pfree(&gpoly);
		for(wptr = pworks; plen(*wptr); ++wptr)
			pfree(wptr);
		free(pworks);
	}
	else if(rflags & R_HAVEI && rflags & R_HAVEX)
		/* All parameters are known!  Submit the result if we get here */
		chkres(&resc, &result, guess->spoly, guess->init, guess->flags, guess->xorout, args, argpolys);
	else if(rflags & R_HAVEI)
		/* Poly and Init are known, calculate XorOut */
		calout(&resc, &result, guess->spoly, guess->init, guess->flags, args, argpolys);
	else if(rflags & R_HAVEX)
		/* Poly and XorOut are known, calculate Init */
		calini(&resc, &result, guess->spoly, guess->flags, guess->xorout, args, argpolys);
	else
		/* Poly is known but not Init; search for Init. */
		engini(&resc, &result, guess->spoly, guess->flags, args, argpolys);

requit:
	if(!(result = realloc(result, ++resc * sizeof(model_t)))) {
		uerror("cannot reallocate result array");
		return NULL;
	}
	rptr = result + resc - 1;
	rptr->spoly  = pzero;
	rptr->init   = pzero;
	rptr->flags  = 0;
	rptr->xorout = pzero;
	rptr->check  = pzero;
	rptr->name   = NULL;

	return(result);
}

static poly_t *
modpol(const poly_t init, int rflags, int args, const poly_t *argpolys) {
	/* Produce, in ascending length order, a list of differences
	 * between the arguments in the list by summing pairs of arguments.
	 * If R_HAVEI is not set in rflags, only pairs of equal length are
	 * summed.
	 * Otherwise, sums of right-aligned pairs are also returned, with
	 * the supplied init poly added to the leftmost terms of each
	 * poly of the pair.
	 */
	poly_t work, swap, *result, *rptr, *iptr;
	const poly_t *aptr, *bptr, *eptr = argpolys + args;
	unsigned long alen, blen;

	if(args < 2) return(NULL);

	if(!(result = malloc(((((args - 1) * args) >> 1) + 1) * sizeof(poly_t))))
		uerror("cannot allocate memory for codeword table");

	rptr = result;

	for(aptr = argpolys; aptr < eptr; ++aptr) {
		alen = plen(*aptr);
		for(bptr = aptr + 1; bptr < eptr; ++bptr) {
			blen = plen(*bptr);
			if(alen == blen) {
				work = pclone(*aptr);
				psum(&work, *bptr, 0UL);
			} else if(rflags & R_HAVEI && alen < blen) {
				work = pclone(*bptr);
				psum(&work, *aptr, blen - alen);
				psum(&work, init, 0UL);
				psum(&work, init, blen - alen);
			} else if(rflags & R_HAVEI /* && alen > blen */) {
				work = pclone(*aptr);
				psum(&work, *bptr, alen - blen);
				psum(&work, init, 0UL);
				psum(&work, init, alen - blen);
			} else
				work = pzero;

			if(plen(work))
				pnorm(&work);
			if((blen = plen(work))) {
				/* insert work into result[] in ascending order of length */
				for(iptr = result; iptr < rptr; ++iptr) {
					if(plen(work) < plen(*iptr)) {
						swap = *iptr;
						*iptr = work;
						work = swap;
					}
					else if(plen(*iptr) == blen && !pcmp(&work, iptr)) {
						pfree(&work);
						work = *--rptr;
						break;
					}
				}
				*rptr++ = work;
			}
		}
	}
	*rptr = pzero;
	return(result);
}

static void
engini(int *resc, model_t **result, const poly_t divisor, int flags, int args, const poly_t *argpolys) {
	/* Search for init values implied by the arguments.
	 * Method from: Ewing, Gregory C. (March 2010).
	 * "Reverse-Engineering a CRC Algorithm". Christchurch:
	 * University of Canterbury.
	 * <http://www.cosc.canterbury.ac.nz/greg.ewing/essays/
	 * CRC-Reverse-Engineering.html>
	 */
	poly_t apoly = PZERO, bpoly, pone = PZERO, *mat, *jptr;
	const poly_t *aptr, *bptr, *iptr;
	unsigned long alen, blen, dlen, ilen, i, j;
	int cy;

	dlen = plen(divisor);

	/* Allocate the CRC matrix */
	if(!(mat = (poly_t *) malloc((dlen << 1) * sizeof(poly_t))))
		uerror("cannot allocate memory for CRC matrix");

	/* Find arguments of the two shortest lengths */
	alen = blen = plen(*(aptr = bptr = iptr = argpolys));
	for(++iptr; iptr < argpolys + args; ++iptr) {
		ilen = plen(*iptr);
		if(ilen < alen) {
			bptr = aptr; blen = alen;
			aptr = iptr; alen = ilen;
		} else if(ilen > alen && (aptr == bptr || ilen < blen)) {
			bptr = iptr; blen = ilen;
		}
	}
	if(aptr == bptr) {
		/* if no arguments are suitable, calculate Init with an
		 * assumed XorOut of 0.  Create a padded XorOut
		 */
		palloc(&apoly, dlen);
		calini(resc, result, divisor, flags, apoly, args, argpolys);
		pfree(&apoly);
		free(mat);
		return;
	}

	/* Find the potential contribution of the bottom bit of Init */
	palloc(&pone, 1UL);
	piter(&pone);
	if(blen < (dlen << 1)) {
		palloc(&apoly, dlen); /* >= 1 */
		psum(&apoly, pone, (dlen << 1) - 1UL - blen); /* >= 0 */
		psum(&apoly, pone, (dlen << 1) - 1UL - alen); /* >= 1 */
	} else {
		palloc(&apoly, blen - dlen + 1UL); /* > dlen */
		psum(&apoly, pone, 0UL);
		psum(&apoly, pone, blen - alen); /* >= 1 */
	}
	if(plen(apoly) > dlen) {
		mat[dlen] = pcrc(apoly, divisor, pzero, pzero, 0);
		pfree(&apoly);
	} else {
		mat[dlen] = apoly;
	}

	/* Find the actual contribution of Init */
	apoly = pcrc(*aptr, divisor, pzero, pzero, 0);
	bpoly = pcrc(*bptr, divisor, pzero, apoly, 0);

	/* Populate the matrix */
	palloc(&apoly, 1UL);
	for(jptr=mat; jptr<mat+dlen; ++jptr)
		*jptr = pzero;
	for(iptr = jptr++; jptr < mat + (dlen << 1); iptr = jptr++)
		*jptr = pcrc(apoly, divisor, *iptr, pzero, P_MULXN);
	pfree(&apoly);

	/* Transpose the matrix, augment with the Init contribution
	 * and convert to row echelon form
	 */
	for(i=0UL; i<dlen; ++i) {
		apoly = pzero;
		iptr = mat + (dlen << 1);
		for(j=0UL; j<dlen; ++j)
			ppaste(&apoly, *--iptr, i, j, j + 1UL, dlen + 1UL);
		if(ptst(apoly))
			ppaste(&apoly, bpoly, i, dlen, dlen + 1UL, dlen + 1UL);
		j = pfirst(apoly);
		while(j < dlen && !pident(mat[j], pzero)) {
			psum(&apoly, mat[j], 0UL); /* pfirst(apoly) > j */
			j = pfirst(apoly);
		}
		if(j < dlen)
			mat[j] = apoly; /* pident(mat[j], pzero) || pfirst(mat[j]) == j */
		else
			pfree(&apoly);
	}
	palloc(&bpoly, dlen + 1UL);
	psum(&bpoly, pone, dlen);

	/* Iterate through all solutions */
	do {
		/* Solve the matrix by Gaussian elimination.
		 * The parity of the result, masked by each row, should be even.
		 */
		cy = 1;
		apoly = pclone(bpoly);
		jptr = mat + dlen;
		for(i=0UL; i<dlen; ++i) {
			/* Compute next bit of Init */
			if(pmpar(apoly, *--jptr))
				psum(&apoly, pone, dlen - 1UL - i);
			/* Toggle each zero row with carry, for next iteration */
			if(cy) {
			       if(pident(*jptr, pzero)) {
				       /* 0 to 1, no carry */
				       *jptr = bpoly;
				       cy = 0;
			       } else if(pident(*jptr, bpoly)) {
				       /* 1 to 0, carry forward */
				       *jptr = pzero;
			       }
			}
		}

		/* Trim the augment mask bit */
		praloc(&apoly, dlen);

		/* Test the Init value and add to results if correct */
		calout(resc, result, divisor, apoly, flags, args, argpolys);
		pfree(&apoly);
	} while(!cy);
	pfree(&pone);
	pfree(&bpoly);

	/* Free the matrix. */
	for(jptr=mat; jptr < mat + (dlen << 1); ++jptr)
		pfree(jptr);
	free(mat);
}

static void
calout(int *resc, model_t **result, const poly_t divisor, const poly_t init, int flags, int args, const poly_t *argpolys) {
	/* Calculate Xorout, check it against all the arguments and
	 * add to results if consistent.
	 */
	poly_t xorout;
	const poly_t *aptr, *iptr;
	unsigned long alen, ilen;

	if(args < 1) return;

	/* find argument of the shortest length */
	alen = plen(*(aptr = iptr = argpolys));
	for(++iptr; iptr < argpolys + args; ++iptr) {
		ilen = plen(*iptr);
		if(ilen < alen) {
			aptr = iptr; alen = ilen;
		}
	}

	xorout = pcrc(*aptr, divisor, init, pzero, 0);
	/* On little-endian algorithms, the calculations yield
	 * the reverse of the actual xorout: in the Williams
	 * model, the refout stage intervenes between init and
	 * xorout.
	 */
	if(flags & P_REFOUT)
		prev(&xorout);

	/* Submit the model to the results table.
	 * Could skip the shortest argument but we wish to check our
	 * calculation.
	 */
	chkres(resc, result, divisor, init, flags, xorout, args, argpolys);
	pfree(&xorout);
}

static void
calini(int *resc, model_t **result, const poly_t divisor, int flags, const poly_t xorout, int args, const poly_t *argpolys) {
	/* Calculate Init, check it against all the arguments and add to
	 * results if consistent.
	 */
	poly_t rcpdiv, rxor, arg, init;
	const poly_t *aptr, *iptr;
	unsigned long alen, ilen;

	if(args < 1) return;

	/* find argument of the shortest length */
	alen = plen(*(aptr = iptr = argpolys));
	for(++iptr; iptr < argpolys + args; ++iptr) {
		ilen = plen(*iptr);
		if(ilen < alen) {
			aptr = iptr; alen = ilen;
		}
	}

	rcpdiv = pclone(divisor);
	prcp(&rcpdiv);
	/* If the algorithm is reflected, an ordinary CRC requires the
	 * model's XorOut to be reversed, as XorOut follows the RefOut
	 * stage.  To reverse the CRC calculation we need rxor to be the
	 * mirror image of the forward XorOut.
	 */
	rxor = pclone(xorout);
	if(~flags & P_REFOUT)
		prev(&rxor);
	arg = pclone(*aptr);
	prev(&arg);

	init = pcrc(arg, rcpdiv, rxor, pzero, 0);
	pfree(&arg);
	pfree(&rxor);
	pfree(&rcpdiv);
	prev(&init);

	/* Submit the model to the results table.
	 * Could skip the shortest argument but we wish to check our
	 * calculation.
	 */
	chkres(resc, result, divisor, init, flags, xorout, args, argpolys);
	pfree(&init);
}

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) {
	/* Checks a model against the argument list, and adds to the
	 * external results table if consistent.
	 * Extends the result array and update the external pointer if
	 * necessary.
	 */
	model_t *rptr;
	poly_t xor, crc;
	const poly_t *aptr = argpolys, *const eptr = argpolys + args;

	/* If the algorithm is reflected, an ordinary CRC requires the
	 * model's XorOut to be reversed, as XorOut follows the RefOut
	 * stage.
	 */
	xor = pclone(xorout);
	if(flags & P_REFOUT)
		prev(&xor);

	for(; aptr < eptr; ++aptr) {
		crc = pcrc(*aptr, divisor, init, xor, 0);
		if(ptst(crc)) {
			pfree(&crc);
			break;
		} else {
			pfree(&crc);
		}
	}
	pfree(&xor);
	if(aptr != eptr) return;

	*result = realloc(*result, ++*resc * sizeof(model_t));
	if (!*result) {
		uerror("cannot reallocate result array");
		return;
	}
	
	rptr = *result + *resc - 1;
	rptr->spoly  = pclone(divisor);
	rptr->init   = pclone(init);
	rptr->flags  = flags;
	rptr->xorout = pclone(xorout);
	rptr->name   = NULL;

	/* compute check value for this model */
	mcheck(rptr);

	/* callback to notify new model */
	ufound(rptr);
}