/* $OpenBSD: rnd.c,v 1.141 2012/06/24 18:25:12 matthew Exp $ */ /* * Copyright (c) 2011 Theo de Raadt. * Copyright (c) 2008 Damien Miller. * Copyright (c) 1996, 1997, 2000-2002 Michael Shalayeff. * Copyright Theodore Ts'o, 1994, 1995, 1996, 1997, 1998, 1999. * All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * 1. Redistributions of source code must retain the above copyright * notice, and the entire permission notice in its entirety, * including the disclaimer of warranties. * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in the * documentation and/or other materials provided with the distribution. * 3. The name of the author may not be used to endorse or promote * products derived from this software without specific prior * written permission. * * ALTERNATIVELY, this product may be distributed under the terms of * the GNU Public License, in which case the provisions of the GPL are * required INSTEAD OF the above restrictions. (This clause is * necessary due to a potential bad interaction between the GPL and * the restrictions contained in a BSD-style copyright.) * * THIS SOFTWARE IS PROVIDED ``AS IS'' AND ANY EXPRESS OR IMPLIED * WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE * DISCLAIMED. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, * INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR * SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED * OF THE POSSIBILITY OF SUCH DAMAGE. */ /* * Computers are very predictable devices. Hence it is extremely hard * to produce truly random numbers on a computer --- as opposed to * pseudo-random numbers, which can be easily generated by using an * algorithm. Unfortunately, it is very easy for attackers to guess * the sequence of pseudo-random number generators, and for some * applications this is not acceptable. Instead, we must try to * gather "environmental noise" from the computer's environment, which * must be hard for outside attackers to observe and use to * generate random numbers. In a Unix environment, this is best done * from inside the kernel. * * Sources of randomness from the environment include inter-keyboard * timings, inter-interrupt timings from some interrupts, and other * events which are both (a) non-deterministic and (b) hard for an * outside observer to measure. Randomness from these sources is * added to the "rnd states" queue; this is used as much of the * source material which is mixed on occasion using a CRC-like function * into the "entropy pool". This is not cryptographically strong, but * it is adequate assuming the randomness is not chosen maliciously, * and it very fast because the interrupt-time event is only to add * a small random token to the "rnd states" queue. * * When random bytes are desired, they are obtained by pulling from * the entropy pool and running a MD5 hash. The MD5 hash avoids * exposing the internal state of the entropy pool. Even if it is * possible to analyze MD5 in some clever way, as long as the amount * of data returned from the generator is less than the inherent * entropy in the pool, the output data is totally unpredictable. For * this reason, the routine decreases its internal estimate of how many * bits of "true randomness" are contained in the entropy pool as it * outputs random numbers. * * If this estimate goes to zero, the MD5 hash will continue to generate * output since there is no true risk because the MD5 output is not * exported outside this subsystem. It is next used as input to seed a * RC4 stream cipher. Attempts are made to follow best practice * regarding this stream cipher - the first chunk of output is discarded * and the cipher is re-seeded from time to time. This design provides * very high amounts of output data from a potentially small entropy * base, at high enough speeds to encourage use of random numbers in * nearly any situation. * * The output of this single RC4 engine is then shared amongst many * consumers in the kernel and userland via a few interfaces: * arc4random_buf(), arc4random(), arc4random_uniform(), randomread() * for the set of /dev/random nodes, and the sysctl kern.arandom. * * Acknowledgements: * ================= * * Ideas for constructing this random number generator were derived * from Pretty Good Privacy's random number generator, and from private * discussions with Phil Karn. Colin Plumb provided a faster random * number generator, which speeds up the mixing function of the entropy * pool, taken from PGPfone. Dale Worley has also contributed many * useful ideas and suggestions to improve this driver. * * Any flaws in the design are solely my responsibility, and should * not be attributed to the Phil, Colin, or any of the authors of PGP. * * Further background information on this topic may be obtained from * RFC 1750, "Randomness Recommendations for Security", by Donald * Eastlake, Steve Crocker, and Jeff Schiller. * * Using a RC4 stream cipher as 2nd stage after the MD5 output * is the result of work by David Mazieres. */ #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include /* * For the purposes of better mixing, we use the CRC-32 polynomial as * well to make a twisted Generalized Feedback Shift Register * * (See M. Matsumoto & Y. Kurita, 1992. Twisted GFSR generators. ACM * Transactions on Modeling and Computer Simulation 2(3):179-194. * Also see M. Matsumoto & Y. Kurita, 1994. Twisted GFSR generators * II. ACM Transactions on Mdeling and Computer Simulation 4:254-266) * * Thanks to Colin Plumb for suggesting this. * * We have not analyzed the resultant polynomial to prove it primitive; * in fact it almost certainly isn't. Nonetheless, the irreducible factors * of a random large-degree polynomial over GF(2) are more than large enough * that periodicity is not a concern. * * The input hash is much less sensitive than the output hash. All * we want from it is to be a good non-cryptographic hash - * i.e. to not produce collisions when fed "random" data of the sort * we expect to see. As long as the pool state differs for different * inputs, we have preserved the input entropy and done a good job. * The fact that an intelligent attacker can construct inputs that * will produce controlled alterations to the pool's state is not * important because we don't consider such inputs to contribute any * randomness. The only property we need with respect to them is that * the attacker can't increase his/her knowledge of the pool's state. * Since all additions are reversible (knowing the final state and the * input, you can reconstruct the initial state), if an attacker has * any uncertainty about the initial state, he/she can only shuffle * that uncertainty about, but never cause any collisions (which would * decrease the uncertainty). * * The chosen system lets the state of the pool be (essentially) the input * modulo the generator polynomial. Now, for random primitive polynomials, * this is a universal class of hash functions, meaning that the chance * of a collision is limited by the attacker's knowledge of the generator * polynomial, so if it is chosen at random, an attacker can never force * a collision. Here, we use a fixed polynomial, but we *can* assume that * ###--> it is unknown to the processes generating the input entropy. <-### * Because of this important property, this is a good, collision-resistant * hash; hash collisions will occur no more often than chance. */ /* * Stirring polynomials over GF(2) for various pool sizes. Used in * add_entropy_words() below. * * The polynomial terms are chosen to be evenly spaced (minimum RMS * distance from evenly spaced; except for the last tap, which is 1 to * get the twisting happening as fast as possible. * * The reultant polynomial is: * 2^POOLWORDS + 2^POOL_TAP1 + 2^POOL_TAP2 + 2^POOL_TAP3 + 2^POOL_TAP4 + 1 */ #define POOLWORDS 2048 #define POOLBYTES (POOLWORDS*4) #define POOLMASK (POOLWORDS - 1) #define POOL_TAP1 1638 #define POOL_TAP2 1231 #define POOL_TAP3 819 #define POOL_TAP4 411 struct mutex entropylock = MUTEX_INITIALIZER(IPL_HIGH); /* * Raw entropy collection from device drivers; at interrupt context or not. * add_*_randomness() provide data which is put into the entropy queue. * Almost completely under the entropylock. */ struct timer_rand_state { /* There is one of these per entropy source */ u_int last_time; u_int last_delta; u_int last_delta2; u_int dont_count_entropy : 1; u_int max_entropy : 1; } rnd_states[RND_SRC_NUM]; #define QEVLEN (1024 / sizeof(struct rand_event)) #define QEVSLOW (QEVLEN * 3 / 4) /* yet another 0.75 for 60-minutes hour /-; */ #define QEVSBITS 10 struct rand_event { struct timer_rand_state *re_state; u_int re_nbits; u_int re_time; u_int re_val; } rnd_event_space[QEVLEN]; struct rand_event *rnd_event_head = rnd_event_space; struct rand_event *rnd_event_tail = rnd_event_space; struct timeout rnd_timeout; struct rndstats rndstats; u_int32_t entropy_pool[POOLWORDS]; u_int entropy_add_ptr; u_char entropy_input_rotate; void dequeue_randomness(void *); void add_entropy_words(const u_int32_t *, u_int); void extract_entropy(u_int8_t *, int); int filt_randomread(struct knote *, long); void filt_randomdetach(struct knote *); int filt_randomwrite(struct knote *, long); struct filterops randomread_filtops = { 1, NULL, filt_randomdetach, filt_randomread }; struct filterops randomwrite_filtops = { 1, NULL, filt_randomdetach, filt_randomwrite }; static __inline struct rand_event * rnd_get(void) { struct rand_event *p = rnd_event_tail; if (p == rnd_event_head) return NULL; if (p + 1 >= &rnd_event_space[QEVLEN]) rnd_event_tail = rnd_event_space; else rnd_event_tail++; return p; } static __inline struct rand_event * rnd_put(void) { struct rand_event *p = rnd_event_head + 1; if (p >= &rnd_event_space[QEVLEN]) p = rnd_event_space; if (p == rnd_event_tail) return NULL; return rnd_event_head = p; } static __inline int rnd_qlen(void) { int len = rnd_event_head - rnd_event_tail; return (len < 0)? -len : len; } /* * This function adds entropy to the entropy pool by using timing * delays. It uses the timer_rand_state structure to make an estimate * of how many bits of entropy this call has added to the pool. * * The number "val" is also added to the pool - it should somehow describe * the type of event which just happened. Currently the values of 0-255 * are for keyboard scan codes, 256 and upwards - for interrupts. * On the i386, this is assumed to be at most 16 bits, and the high bits * are used for a high-resolution timer. */ void enqueue_randomness(int state, int val) { int delta, delta2, delta3; struct timer_rand_state *p; struct rand_event *rep; struct timespec ts; u_int time, nbits; #ifdef DIAGNOSTIC if (state < 0 || state >= RND_SRC_NUM) return; #endif if (timeout_initialized(&rnd_timeout)) nanotime(&ts); p = &rnd_states[state]; val += state << 13; time = (ts.tv_nsec >> 10) + (ts.tv_sec << 20); nbits = 0; /* * Calculate the number of bits of randomness that we probably * added. We take into account the first and second order * deltas in order to make our estimate. */ if (!p->dont_count_entropy) { delta = time - p->last_time; delta2 = delta - p->last_delta; delta3 = delta2 - p->last_delta2; if (delta < 0) delta = -delta; if (delta2 < 0) delta2 = -delta2; if (delta3 < 0) delta3 = -delta3; if (delta > delta2) delta = delta2; if (delta > delta3) delta = delta3; delta3 = delta >>= 1; /* * delta &= 0xfff; * we don't do it since our time sheet is different from linux */ if (delta & 0xffff0000) { nbits = 16; delta >>= 16; } if (delta & 0xff00) { nbits += 8; delta >>= 8; } if (delta & 0xf0) { nbits += 4; delta >>= 4; } if (delta & 0xc) { nbits += 2; delta >>= 2; } if (delta & 2) { nbits += 1; delta >>= 1; } if (delta & 1) nbits++; } else if (p->max_entropy) nbits = 8 * sizeof(val) - 1; /* given the multi-order delta logic above, this should never happen */ if (nbits >= 32) return; mtx_enter(&entropylock); if (!p->dont_count_entropy) { /* * the logic is to drop low-entropy entries, * in hope for dequeuing to be more randomfull */ if (rnd_qlen() > QEVSLOW && nbits < QEVSBITS) { rndstats.rnd_drople++; goto done; } p->last_time = time; p->last_delta = delta3; p->last_delta2 = delta2; } if ((rep = rnd_put()) == NULL) { rndstats.rnd_drops++; goto done; } rep->re_state = p; rep->re_nbits = nbits; rep->re_time = ts.tv_nsec ^ (ts.tv_sec << 20); rep->re_val = val; rndstats.rnd_enqs++; rndstats.rnd_ed[nbits]++; rndstats.rnd_sc[state]++; rndstats.rnd_sb[state] += nbits; if (rnd_qlen() > QEVSLOW/2 && timeout_initialized(&rnd_timeout) && timeout_pending(&rnd_timeout)) timeout_add(&rnd_timeout, 1); done: mtx_leave(&entropylock); } /* * This function adds a byte into the entropy pool. It does not * update the entropy estimate. The caller must do this if appropriate. * * The pool is stirred with a polynomial of degree POOLWORDS over GF(2); * see POOL_TAP[1-4] above * * Rotate the input word by a changing number of bits, to help assure * that all bits in the entropy get toggled. Otherwise, if the pool * is consistently feed small numbers (such as keyboard scan codes) * then the upper bits of the entropy pool will frequently remain * untouched. */ void add_entropy_words(const u_int32_t *buf, u_int n) { /* derived from IEEE 802.3 CRC-32 */ static const u_int32_t twist_table[8] = { 0x00000000, 0x3b6e20c8, 0x76dc4190, 0x4db26158, 0xedb88320, 0xd6d6a3e8, 0x9b64c2b0, 0xa00ae278 }; for (; n--; buf++) { u_int32_t w = (*buf << entropy_input_rotate) | (*buf >> (32 - entropy_input_rotate)); u_int i = entropy_add_ptr = (entropy_add_ptr - 1) & POOLMASK; /* * Normally, we add 7 bits of rotation to the pool. * At the beginning of the pool, add an extra 7 bits * rotation, so that successive passes spread the * input bits across the pool evenly. */ entropy_input_rotate = (entropy_input_rotate + (i ? 7 : 14)) & 31; /* XOR pool contents corresponding to polynomial terms */ w ^= entropy_pool[(i + POOL_TAP1) & POOLMASK] ^ entropy_pool[(i + POOL_TAP2) & POOLMASK] ^ entropy_pool[(i + POOL_TAP3) & POOLMASK] ^ entropy_pool[(i + POOL_TAP4) & POOLMASK] ^ entropy_pool[(i + 1) & POOLMASK] ^ entropy_pool[i]; /* + 2^POOLWORDS */ entropy_pool[i] = (w >> 3) ^ twist_table[w & 7]; } } /* * Pulls entropy out of the queue and throws merges it into the pool * with the CRC. */ /* ARGSUSED */ void dequeue_randomness(void *v) { struct rand_event *rep; u_int32_t buf[2]; u_int nbits; mtx_enter(&entropylock); if (timeout_initialized(&rnd_timeout)) timeout_del(&rnd_timeout); rndstats.rnd_deqs++; while ((rep = rnd_get())) { buf[0] = rep->re_time; buf[1] = rep->re_val; nbits = rep->re_nbits; mtx_leave(&entropylock); add_entropy_words(buf, 2); mtx_enter(&entropylock); rndstats.rnd_total += nbits; } mtx_leave(&entropylock); } /* * Grabs a chunk from the entropy_pool[] and slams it through MD5 when * requested. */ void extract_entropy(u_int8_t *buf, int nbytes) { static u_int32_t extract_pool[POOLWORDS]; u_char buffer[16]; MD5_CTX tmp; u_int i; add_timer_randomness(nbytes); while (nbytes) { i = MIN(nbytes, sizeof(buffer)); /* * INTENTIONALLY not protected by entropylock. Races * during bcopy() result in acceptable input data; races * during MD5Update() would create nasty data dependencies. */ bcopy(entropy_pool, extract_pool, sizeof(extract_pool)); /* Hash the pool to get the output */ MD5Init(&tmp); MD5Update(&tmp, (u_int8_t *)extract_pool, sizeof(extract_pool)); MD5Final(buffer, &tmp); /* Copy data to destination buffer */ bcopy(buffer, buf, i); nbytes -= i; buf += i; /* Modify pool so next hash will produce different results */ add_timer_randomness(nbytes); dequeue_randomness(NULL); } /* Wipe data from memory */ explicit_bzero(extract_pool, sizeof(extract_pool)); explicit_bzero(&tmp, sizeof(tmp)); explicit_bzero(buffer, sizeof(buffer)); } /* * Bytes of key material for each rc4 instance. */ #define ARC4_KEY_BYTES 64 /* * Throw away a multiple of the first N words of output, as suggested * in the paper "Weaknesses in the Key Scheduling Algorithm of RC4" * by Fluher, Mantin, and Shamir. (N = 256 in our case.) If the start * of a new RC stream is an event that a consumer could spot, we drop * the strictly recommended amount (ceil(n/log e) = 6). If consumers * only see random sub-streams, we cheat and do less computation. */ #define ARC4_STATE 256 #define ARC4_DISCARD_SAFE 6 #define ARC4_DISCARD_CHEAP 4 /* * Start with an unstable state so that rc4_getbytes() can * operate (poorly) before rc4_keysetup(). */ struct rc4_ctx arc4random_state = { 0, 0, { 1, 2, 3, 4, 5, 6 } }; struct mutex rndlock = MUTEX_INITIALIZER(IPL_HIGH); struct timeout arc4_timeout; void arc4_reinit(void *v); /* timeout to start reinit */ void arc4_init(void *, void *); /* actually do the reinit */ /* Return one word of randomness from an RC4 generator */ u_int32_t arc4random(void) { u_int32_t ret; mtx_enter(&rndlock); rc4_getbytes(&arc4random_state, (u_char *)&ret, sizeof(ret)); rndstats.arc4_reads += sizeof(ret); mtx_leave(&rndlock); return ret; } /* * Fill a buffer of arbitrary length with RC4-derived randomness. */ void arc4random_buf(void *buf, size_t n) { mtx_enter(&rndlock); rc4_getbytes(&arc4random_state, (u_char *)buf, n); rndstats.arc4_reads += n; mtx_leave(&rndlock); } /* * Calculate a uniformly distributed random number less than upper_bound * avoiding "modulo bias". * * Uniformity is achieved by generating new random numbers until the one * returned is outside the range [0, 2**32 % upper_bound). This * guarantees the selected random number will be inside * [2**32 % upper_bound, 2**32) which maps back to [0, upper_bound) * after reduction modulo upper_bound. */ u_int32_t arc4random_uniform(u_int32_t upper_bound) { u_int32_t r, min; if (upper_bound < 2) return 0; /* 2**32 % x == (2**32 - x) % x */ min = -upper_bound % upper_bound; /* * This could theoretically loop forever but each retry has * p > 0.5 (worst case, usually far better) of selecting a * number inside the range we need, so it should rarely need * to re-roll. */ for (;;) { r = arc4random(); if (r >= min) break; } return r % upper_bound; } /* ARGSUSED */ void arc4_init(void *v, void *w) { struct rc4_ctx new_ctx; struct timespec ts; u_int8_t buf[ARC4_KEY_BYTES], *p; int i; /* * Use MD5 PRNG data and a system timespec; early in the boot * process this is the best we can do -- some architectures do * not collect entropy very well during this time, but may have * clock information which is better than nothing. */ extract_entropy((u_int8_t *)buf, sizeof buf); if (timeout_initialized(&rnd_timeout)) nanotime(&ts); for (p = (u_int8_t *)&ts, i = 0; i < sizeof(ts); i++) buf[i] ^= p[i]; /* Carry over some state from the previous PRNG instance */ mtx_enter(&rndlock); if (rndstats.arc4_nstirs > 0) rc4_crypt(&arc4random_state, buf, buf, sizeof(buf)); mtx_leave(&rndlock); rc4_keysetup(&new_ctx, buf, sizeof(buf)); rc4_skip(&new_ctx, ARC4_STATE * ARC4_DISCARD_CHEAP); mtx_enter(&rndlock); bcopy(&new_ctx, &arc4random_state, sizeof(new_ctx)); rndstats.rnd_used += sizeof(buf) * 8; rndstats.arc4_nstirs++; mtx_leave(&rndlock); explicit_bzero(buf, sizeof(buf)); explicit_bzero(&new_ctx, sizeof(new_ctx)); } /* * Called by timeout to mark arc4 for stirring, */ void arc4_reinit(void *v) { workq_add_task(NULL, 0, arc4_init, NULL, NULL); /* 10 minutes, per dm@'s suggestion */ timeout_add_sec(&arc4_timeout, 10 * 60); } void random_init(void) { rnd_states[RND_SRC_TIMER].dont_count_entropy = 1; rnd_states[RND_SRC_TRUE].dont_count_entropy = 1; rnd_states[RND_SRC_TRUE].max_entropy = 1; /* * Load some code as input data until we are more alive. * NOTE: We assume there are at 8192 bytes mapped after version, * because we want to pull some "code" in as well. */ rc4_keysetup(&arc4random_state, (u_int8_t *)&version, 8192); } void random_start(void) { if (msgbufp && msgbufp->msg_magic == MSG_MAGIC) add_entropy_words((u_int32_t *)msgbufp->msg_bufc, msgbufp->msg_bufs / sizeof(u_int32_t)); dequeue_randomness(NULL); arc4_init(NULL, NULL); timeout_set(&arc4_timeout, arc4_reinit, NULL); arc4_reinit(NULL); timeout_set(&rnd_timeout, dequeue_randomness, NULL); } int randomopen(dev_t dev, int flag, int mode, struct proc *p) { return 0; } int randomclose(dev_t dev, int flag, int mode, struct proc *p) { return 0; } /* * Maximum number of bytes to serve directly from the main arc4random * pool. Larger requests are served from a discrete arc4 instance keyed * from the main pool. */ #define ARC4_MAIN_MAX_BYTES 2048 int randomread(dev_t dev, struct uio *uio, int ioflag) { u_char lbuf[ARC4_KEY_BYTES]; struct rc4_ctx lctx; size_t total = uio->uio_resid; u_char *buf; int myctx = 0, ret = 0; if (uio->uio_resid == 0) return 0; buf = malloc(POOLBYTES, M_TEMP, M_WAITOK); if (total > ARC4_MAIN_MAX_BYTES) { arc4random_buf(lbuf, sizeof(lbuf)); rc4_keysetup(&lctx, lbuf, sizeof(lbuf)); rc4_skip(&lctx, ARC4_STATE * ARC4_DISCARD_SAFE); explicit_bzero(lbuf, sizeof(lbuf)); myctx = 1; } while (ret == 0 && uio->uio_resid > 0) { int n = min(POOLBYTES, uio->uio_resid); if (myctx) rc4_getbytes(&lctx, buf, n); else arc4random_buf(buf, n); ret = uiomove((caddr_t)buf, n, uio); if (ret == 0 && uio->uio_resid > 0) yield(); } if (myctx) explicit_bzero(&lctx, sizeof(lctx)); explicit_bzero(buf, POOLBYTES); free(buf, M_TEMP); return ret; } int randomwrite(dev_t dev, struct uio *uio, int flags) { int ret = 0, newdata = 0; u_int32_t *buf; if (uio->uio_resid == 0) return 0; buf = malloc(POOLBYTES, M_TEMP, M_WAITOK); while (!ret && uio->uio_resid > 0) { int n = min(POOLBYTES, uio->uio_resid); ret = uiomove(buf, n, uio); if (ret) break; while (n % sizeof(u_int32_t)) ((u_int8_t *)buf)[n++] = 0; add_entropy_words(buf, n / 4); if (ret == 0 && uio->uio_resid > 0) yield(); newdata = 1; } if (newdata) arc4_init(NULL, NULL); explicit_bzero(buf, POOLBYTES); free(buf, M_TEMP); return ret; } int randomkqfilter(dev_t dev, struct knote *kn) { switch (kn->kn_filter) { case EVFILT_READ: kn->kn_fop = &randomread_filtops; break; case EVFILT_WRITE: kn->kn_fop = &randomwrite_filtops; break; default: return (EINVAL); } return (0); } void filt_randomdetach(struct knote *kn) { } int filt_randomread(struct knote *kn, long hint) { kn->kn_data = ARC4_MAIN_MAX_BYTES; return (1); } int filt_randomwrite(struct knote *kn, long hint) { kn->kn_data = POOLBYTES; return (1); } int randomioctl(dev_t dev, u_long cmd, caddr_t data, int flag, struct proc *p) { switch (cmd) { case FIOASYNC: /* No async flag in softc so this is a no-op. */ break; case FIONBIO: /* Handled in the upper FS layer. */ break; default: return ENOTTY; } return 0; }