xref: /openssl/crypto/bn/bn_prime.c (revision d2f6e66d)
1 /*
2  * Copyright 1995-2021 The OpenSSL Project Authors. All Rights Reserved.
3  *
4  * Licensed under the Apache License 2.0 (the "License").  You may not use
5  * this file except in compliance with the License.  You can obtain a copy
6  * in the file LICENSE in the source distribution or at
7  * https://www.openssl.org/source/license.html
8  */
9 
10 #include <stdio.h>
11 #include <time.h>
12 #include "internal/cryptlib.h"
13 #include "bn_local.h"
14 
15 /*
16  * The quick sieve algorithm approach to weeding out primes is Philip
17  * Zimmermann's, as implemented in PGP.  I have had a read of his comments
18  * and implemented my own version.
19  */
20 #include "bn_prime.h"
21 
22 static int probable_prime(BIGNUM *rnd, int bits, int safe, prime_t *mods,
23                           BN_CTX *ctx);
24 static int probable_prime_dh(BIGNUM *rnd, int bits, int safe, prime_t *mods,
25                              const BIGNUM *add, const BIGNUM *rem,
26                              BN_CTX *ctx);
27 static int bn_is_prime_int(const BIGNUM *w, int checks, BN_CTX *ctx,
28                            int do_trial_division, BN_GENCB *cb);
29 
30 #define square(x) ((BN_ULONG)(x) * (BN_ULONG)(x))
31 
32 #if BN_BITS2 == 64
33 # define BN_DEF(lo, hi) (BN_ULONG)hi<<32|lo
34 #else
35 # define BN_DEF(lo, hi) lo, hi
36 #endif
37 
38 /*
39  * See SP800 89 5.3.3 (Step f)
40  * The product of the set of primes ranging from 3 to 751
41  * Generated using process in test/bn_internal_test.c test_bn_small_factors().
42  * This includes 751 (which is not currently included in SP 800-89).
43  */
44 static const BN_ULONG small_prime_factors[] = {
45     BN_DEF(0x3ef4e3e1, 0xc4309333), BN_DEF(0xcd2d655f, 0x71161eb6),
46     BN_DEF(0x0bf94862, 0x95e2238c), BN_DEF(0x24f7912b, 0x3eb233d3),
47     BN_DEF(0xbf26c483, 0x6b55514b), BN_DEF(0x5a144871, 0x0a84d817),
48     BN_DEF(0x9b82210a, 0x77d12fee), BN_DEF(0x97f050b3, 0xdb5b93c2),
49     BN_DEF(0x4d6c026b, 0x4acad6b9), BN_DEF(0x54aec893, 0xeb7751f3),
50     BN_DEF(0x36bc85c4, 0xdba53368), BN_DEF(0x7f5ec78e, 0xd85a1b28),
51     BN_DEF(0x6b322244, 0x2eb072d8), BN_DEF(0x5e2b3aea, 0xbba51112),
52     BN_DEF(0x0e2486bf, 0x36ed1a6c), BN_DEF(0xec0c5727, 0x5f270460),
53     (BN_ULONG)0x000017b1
54 };
55 
56 #define BN_SMALL_PRIME_FACTORS_TOP OSSL_NELEM(small_prime_factors)
57 static const BIGNUM _bignum_small_prime_factors = {
58     (BN_ULONG *)small_prime_factors,
59     BN_SMALL_PRIME_FACTORS_TOP,
60     BN_SMALL_PRIME_FACTORS_TOP,
61     0,
62     BN_FLG_STATIC_DATA
63 };
64 
ossl_bn_get0_small_factors(void)65 const BIGNUM *ossl_bn_get0_small_factors(void)
66 {
67     return &_bignum_small_prime_factors;
68 }
69 
70 /*
71  * Calculate the number of trial divisions that gives the best speed in
72  * combination with Miller-Rabin prime test, based on the sized of the prime.
73  */
calc_trial_divisions(int bits)74 static int calc_trial_divisions(int bits)
75 {
76     if (bits <= 512)
77         return 64;
78     else if (bits <= 1024)
79         return 128;
80     else if (bits <= 2048)
81         return 384;
82     else if (bits <= 4096)
83         return 1024;
84     return NUMPRIMES;
85 }
86 
87 /*
88  * Use a minimum of 64 rounds of Miller-Rabin, which should give a false
89  * positive rate of 2^-128. If the size of the prime is larger than 2048
90  * the user probably wants a higher security level than 128, so switch
91  * to 128 rounds giving a false positive rate of 2^-256.
92  * Returns the number of rounds.
93  */
bn_mr_min_checks(int bits)94 static int bn_mr_min_checks(int bits)
95 {
96     if (bits > 2048)
97         return 128;
98     return 64;
99 }
100 
BN_GENCB_call(BN_GENCB * cb,int a,int b)101 int BN_GENCB_call(BN_GENCB *cb, int a, int b)
102 {
103     /* No callback means continue */
104     if (!cb)
105         return 1;
106     switch (cb->ver) {
107     case 1:
108         /* Deprecated-style callbacks */
109         if (!cb->cb.cb_1)
110             return 1;
111         cb->cb.cb_1(a, b, cb->arg);
112         return 1;
113     case 2:
114         /* New-style callbacks */
115         return cb->cb.cb_2(a, b, cb);
116     default:
117         break;
118     }
119     /* Unrecognised callback type */
120     return 0;
121 }
122 
BN_generate_prime_ex2(BIGNUM * ret,int bits,int safe,const BIGNUM * add,const BIGNUM * rem,BN_GENCB * cb,BN_CTX * ctx)123 int BN_generate_prime_ex2(BIGNUM *ret, int bits, int safe,
124                           const BIGNUM *add, const BIGNUM *rem, BN_GENCB *cb,
125                           BN_CTX *ctx)
126 {
127     BIGNUM *t;
128     int found = 0;
129     int i, j, c1 = 0;
130     prime_t *mods = NULL;
131     int checks = bn_mr_min_checks(bits);
132 
133     if (bits < 2) {
134         /* There are no prime numbers this small. */
135         ERR_raise(ERR_LIB_BN, BN_R_BITS_TOO_SMALL);
136         return 0;
137     } else if (add == NULL && safe && bits < 6 && bits != 3) {
138         /*
139          * The smallest safe prime (7) is three bits.
140          * But the following two safe primes with less than 6 bits (11, 23)
141          * are unreachable for BN_rand with BN_RAND_TOP_TWO.
142          */
143         ERR_raise(ERR_LIB_BN, BN_R_BITS_TOO_SMALL);
144         return 0;
145     }
146 
147     mods = OPENSSL_zalloc(sizeof(*mods) * NUMPRIMES);
148     if (mods == NULL)
149         return 0;
150 
151     BN_CTX_start(ctx);
152     t = BN_CTX_get(ctx);
153     if (t == NULL)
154         goto err;
155  loop:
156     /* make a random number and set the top and bottom bits */
157     if (add == NULL) {
158         if (!probable_prime(ret, bits, safe, mods, ctx))
159             goto err;
160     } else {
161         if (!probable_prime_dh(ret, bits, safe, mods, add, rem, ctx))
162             goto err;
163     }
164 
165     if (!BN_GENCB_call(cb, 0, c1++))
166         /* aborted */
167         goto err;
168 
169     if (!safe) {
170         i = bn_is_prime_int(ret, checks, ctx, 0, cb);
171         if (i == -1)
172             goto err;
173         if (i == 0)
174             goto loop;
175     } else {
176         /*
177          * for "safe prime" generation, check that (p-1)/2 is prime. Since a
178          * prime is odd, We just need to divide by 2
179          */
180         if (!BN_rshift1(t, ret))
181             goto err;
182 
183         for (i = 0; i < checks; i++) {
184             j = bn_is_prime_int(ret, 1, ctx, 0, cb);
185             if (j == -1)
186                 goto err;
187             if (j == 0)
188                 goto loop;
189 
190             j = bn_is_prime_int(t, 1, ctx, 0, cb);
191             if (j == -1)
192                 goto err;
193             if (j == 0)
194                 goto loop;
195 
196             if (!BN_GENCB_call(cb, 2, c1 - 1))
197                 goto err;
198             /* We have a safe prime test pass */
199         }
200     }
201     /* we have a prime :-) */
202     found = 1;
203  err:
204     OPENSSL_free(mods);
205     BN_CTX_end(ctx);
206     bn_check_top(ret);
207     return found;
208 }
209 
210 #ifndef FIPS_MODULE
BN_generate_prime_ex(BIGNUM * ret,int bits,int safe,const BIGNUM * add,const BIGNUM * rem,BN_GENCB * cb)211 int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe,
212                          const BIGNUM *add, const BIGNUM *rem, BN_GENCB *cb)
213 {
214     BN_CTX *ctx = BN_CTX_new();
215     int retval;
216 
217     if (ctx == NULL)
218         return 0;
219 
220     retval = BN_generate_prime_ex2(ret, bits, safe, add, rem, cb, ctx);
221 
222     BN_CTX_free(ctx);
223     return retval;
224 }
225 #endif
226 
227 #ifndef OPENSSL_NO_DEPRECATED_3_0
BN_is_prime_ex(const BIGNUM * a,int checks,BN_CTX * ctx_passed,BN_GENCB * cb)228 int BN_is_prime_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed,
229                    BN_GENCB *cb)
230 {
231     return ossl_bn_check_prime(a, checks, ctx_passed, 0, cb);
232 }
233 
BN_is_prime_fasttest_ex(const BIGNUM * w,int checks,BN_CTX * ctx,int do_trial_division,BN_GENCB * cb)234 int BN_is_prime_fasttest_ex(const BIGNUM *w, int checks, BN_CTX *ctx,
235                             int do_trial_division, BN_GENCB *cb)
236 {
237     return ossl_bn_check_prime(w, checks, ctx, do_trial_division, cb);
238 }
239 #endif
240 
241 /* Wrapper around bn_is_prime_int that sets the minimum number of checks */
ossl_bn_check_prime(const BIGNUM * w,int checks,BN_CTX * ctx,int do_trial_division,BN_GENCB * cb)242 int ossl_bn_check_prime(const BIGNUM *w, int checks, BN_CTX *ctx,
243                         int do_trial_division, BN_GENCB *cb)
244 {
245     int min_checks = bn_mr_min_checks(BN_num_bits(w));
246 
247     if (checks < min_checks)
248         checks = min_checks;
249 
250     return bn_is_prime_int(w, checks, ctx, do_trial_division, cb);
251 }
252 
253 /*
254  * Use this only for key generation.
255  * It always uses trial division. The number of checks
256  * (MR rounds) passed in is used without being clamped to a minimum value.
257  */
ossl_bn_check_generated_prime(const BIGNUM * w,int checks,BN_CTX * ctx,BN_GENCB * cb)258 int ossl_bn_check_generated_prime(const BIGNUM *w, int checks, BN_CTX *ctx,
259                                   BN_GENCB *cb)
260 {
261     return bn_is_prime_int(w, checks, ctx, 1, cb);
262 }
263 
BN_check_prime(const BIGNUM * p,BN_CTX * ctx,BN_GENCB * cb)264 int BN_check_prime(const BIGNUM *p, BN_CTX *ctx, BN_GENCB *cb)
265 {
266     return ossl_bn_check_prime(p, 0, ctx, 1, cb);
267 }
268 
269 /*
270  * Tests that |w| is probably prime
271  * See FIPS 186-4 C.3.1 Miller Rabin Probabilistic Primality Test.
272  *
273  * Returns 0 when composite, 1 when probable prime, -1 on error.
274  */
bn_is_prime_int(const BIGNUM * w,int checks,BN_CTX * ctx,int do_trial_division,BN_GENCB * cb)275 static int bn_is_prime_int(const BIGNUM *w, int checks, BN_CTX *ctx,
276                            int do_trial_division, BN_GENCB *cb)
277 {
278     int i, status, ret = -1;
279 #ifndef FIPS_MODULE
280     BN_CTX *ctxlocal = NULL;
281 #else
282 
283     if (ctx == NULL)
284         return -1;
285 #endif
286 
287     /* w must be bigger than 1 */
288     if (BN_cmp(w, BN_value_one()) <= 0)
289         return 0;
290 
291     /* w must be odd */
292     if (BN_is_odd(w)) {
293         /* Take care of the really small prime 3 */
294         if (BN_is_word(w, 3))
295             return 1;
296     } else {
297         /* 2 is the only even prime */
298         return BN_is_word(w, 2);
299     }
300 
301     /* first look for small factors */
302     if (do_trial_division) {
303         int trial_divisions = calc_trial_divisions(BN_num_bits(w));
304 
305         for (i = 1; i < trial_divisions; i++) {
306             BN_ULONG mod = BN_mod_word(w, primes[i]);
307             if (mod == (BN_ULONG)-1)
308                 return -1;
309             if (mod == 0)
310                 return BN_is_word(w, primes[i]);
311         }
312         if (!BN_GENCB_call(cb, 1, -1))
313             return -1;
314     }
315 #ifndef FIPS_MODULE
316     if (ctx == NULL && (ctxlocal = ctx = BN_CTX_new()) == NULL)
317         goto err;
318 #endif
319 
320     if (!ossl_bn_miller_rabin_is_prime(w, checks, ctx, cb, 0, &status)) {
321         ret = -1;
322         goto err;
323     }
324     ret = (status == BN_PRIMETEST_PROBABLY_PRIME);
325 err:
326 #ifndef FIPS_MODULE
327     BN_CTX_free(ctxlocal);
328 #endif
329     return ret;
330 }
331 
332 /*
333  * Refer to FIPS 186-4 C.3.2 Enhanced Miller-Rabin Probabilistic Primality Test.
334  * OR C.3.1 Miller-Rabin Probabilistic Primality Test (if enhanced is zero).
335  * The Step numbers listed in the code refer to the enhanced case.
336  *
337  * if enhanced is set, then status returns one of the following:
338  *     BN_PRIMETEST_PROBABLY_PRIME
339  *     BN_PRIMETEST_COMPOSITE_WITH_FACTOR
340  *     BN_PRIMETEST_COMPOSITE_NOT_POWER_OF_PRIME
341  * if enhanced is zero, then status returns either
342  *     BN_PRIMETEST_PROBABLY_PRIME or
343  *     BN_PRIMETEST_COMPOSITE
344  *
345  * returns 0 if there was an error, otherwise it returns 1.
346  */
ossl_bn_miller_rabin_is_prime(const BIGNUM * w,int iterations,BN_CTX * ctx,BN_GENCB * cb,int enhanced,int * status)347 int ossl_bn_miller_rabin_is_prime(const BIGNUM *w, int iterations, BN_CTX *ctx,
348                                   BN_GENCB *cb, int enhanced, int *status)
349 {
350     int i, j, a, ret = 0;
351     BIGNUM *g, *w1, *w3, *x, *m, *z, *b;
352     BN_MONT_CTX *mont = NULL;
353 
354     /* w must be odd */
355     if (!BN_is_odd(w))
356         return 0;
357 
358     BN_CTX_start(ctx);
359     g = BN_CTX_get(ctx);
360     w1 = BN_CTX_get(ctx);
361     w3 = BN_CTX_get(ctx);
362     x = BN_CTX_get(ctx);
363     m = BN_CTX_get(ctx);
364     z = BN_CTX_get(ctx);
365     b = BN_CTX_get(ctx);
366 
367     if (!(b != NULL
368             /* w1 := w - 1 */
369             && BN_copy(w1, w)
370             && BN_sub_word(w1, 1)
371             /* w3 := w - 3 */
372             && BN_copy(w3, w)
373             && BN_sub_word(w3, 3)))
374         goto err;
375 
376     /* check w is larger than 3, otherwise the random b will be too small */
377     if (BN_is_zero(w3) || BN_is_negative(w3))
378         goto err;
379 
380     /* (Step 1) Calculate largest integer 'a' such that 2^a divides w-1 */
381     a = 1;
382     while (!BN_is_bit_set(w1, a))
383         a++;
384     /* (Step 2) m = (w-1) / 2^a */
385     if (!BN_rshift(m, w1, a))
386         goto err;
387 
388     /* Montgomery setup for computations mod a */
389     mont = BN_MONT_CTX_new();
390     if (mont == NULL || !BN_MONT_CTX_set(mont, w, ctx))
391         goto err;
392 
393     if (iterations == 0)
394         iterations = bn_mr_min_checks(BN_num_bits(w));
395 
396     /* (Step 4) */
397     for (i = 0; i < iterations; ++i) {
398         /* (Step 4.1) obtain a Random string of bits b where 1 < b < w-1 */
399         if (!BN_priv_rand_range_ex(b, w3, 0, ctx)
400                 || !BN_add_word(b, 2)) /* 1 < b < w-1 */
401             goto err;
402 
403         if (enhanced) {
404             /* (Step 4.3) */
405             if (!BN_gcd(g, b, w, ctx))
406                 goto err;
407             /* (Step 4.4) */
408             if (!BN_is_one(g)) {
409                 *status = BN_PRIMETEST_COMPOSITE_WITH_FACTOR;
410                 ret = 1;
411                 goto err;
412             }
413         }
414         /* (Step 4.5) z = b^m mod w */
415         if (!BN_mod_exp_mont(z, b, m, w, ctx, mont))
416             goto err;
417         /* (Step 4.6) if (z = 1 or z = w-1) */
418         if (BN_is_one(z) || BN_cmp(z, w1) == 0)
419             goto outer_loop;
420         /* (Step 4.7) for j = 1 to a-1 */
421         for (j = 1; j < a ; ++j) {
422             /* (Step 4.7.1 - 4.7.2) x = z. z = x^2 mod w */
423             if (!BN_copy(x, z) || !BN_mod_mul(z, x, x, w, ctx))
424                 goto err;
425             /* (Step 4.7.3) */
426             if (BN_cmp(z, w1) == 0)
427                 goto outer_loop;
428             /* (Step 4.7.4) */
429             if (BN_is_one(z))
430                 goto composite;
431         }
432         /* At this point z = b^((w-1)/2) mod w */
433         /* (Steps 4.8 - 4.9) x = z, z = x^2 mod w */
434         if (!BN_copy(x, z) || !BN_mod_mul(z, x, x, w, ctx))
435             goto err;
436         /* (Step 4.10) */
437         if (BN_is_one(z))
438             goto composite;
439         /* (Step 4.11) x = b^(w-1) mod w */
440         if (!BN_copy(x, z))
441             goto err;
442 composite:
443         if (enhanced) {
444             /* (Step 4.1.2) g = GCD(x-1, w) */
445             if (!BN_sub_word(x, 1) || !BN_gcd(g, x, w, ctx))
446                 goto err;
447             /* (Steps 4.1.3 - 4.1.4) */
448             if (BN_is_one(g))
449                 *status = BN_PRIMETEST_COMPOSITE_NOT_POWER_OF_PRIME;
450             else
451                 *status = BN_PRIMETEST_COMPOSITE_WITH_FACTOR;
452         } else {
453             *status = BN_PRIMETEST_COMPOSITE;
454         }
455         ret = 1;
456         goto err;
457 outer_loop: ;
458         /* (Step 4.1.5) */
459         if (!BN_GENCB_call(cb, 1, i))
460             goto err;
461     }
462     /* (Step 5) */
463     *status = BN_PRIMETEST_PROBABLY_PRIME;
464     ret = 1;
465 err:
466     BN_clear(g);
467     BN_clear(w1);
468     BN_clear(w3);
469     BN_clear(x);
470     BN_clear(m);
471     BN_clear(z);
472     BN_clear(b);
473     BN_CTX_end(ctx);
474     BN_MONT_CTX_free(mont);
475     return ret;
476 }
477 
478 /*
479  * Generate a random number of |bits| bits that is probably prime by sieving.
480  * If |safe| != 0, it generates a safe prime.
481  * |mods| is a preallocated array that gets reused when called again.
482  *
483  * The probably prime is saved in |rnd|.
484  *
485  * Returns 1 on success and 0 on error.
486  */
probable_prime(BIGNUM * rnd,int bits,int safe,prime_t * mods,BN_CTX * ctx)487 static int probable_prime(BIGNUM *rnd, int bits, int safe, prime_t *mods,
488                           BN_CTX *ctx)
489 {
490     int i;
491     BN_ULONG delta;
492     int trial_divisions = calc_trial_divisions(bits);
493     BN_ULONG maxdelta = BN_MASK2 - primes[trial_divisions - 1];
494 
495  again:
496     if (!BN_priv_rand_ex(rnd, bits, BN_RAND_TOP_TWO, BN_RAND_BOTTOM_ODD, 0,
497                          ctx))
498         return 0;
499     if (safe && !BN_set_bit(rnd, 1))
500         return 0;
501     /* we now have a random number 'rnd' to test. */
502     for (i = 1; i < trial_divisions; i++) {
503         BN_ULONG mod = BN_mod_word(rnd, (BN_ULONG)primes[i]);
504         if (mod == (BN_ULONG)-1)
505             return 0;
506         mods[i] = (prime_t) mod;
507     }
508     delta = 0;
509  loop:
510     for (i = 1; i < trial_divisions; i++) {
511         /*
512          * check that rnd is a prime and also that
513          * gcd(rnd-1,primes) == 1 (except for 2)
514          * do the second check only if we are interested in safe primes
515          * in the case that the candidate prime is a single word then
516          * we check only the primes up to sqrt(rnd)
517          */
518         if (bits <= 31 && delta <= 0x7fffffff
519                 && square(primes[i]) > BN_get_word(rnd) + delta)
520             break;
521         if (safe ? (mods[i] + delta) % primes[i] <= 1
522                  : (mods[i] + delta) % primes[i] == 0) {
523             delta += safe ? 4 : 2;
524             if (delta > maxdelta)
525                 goto again;
526             goto loop;
527         }
528     }
529     if (!BN_add_word(rnd, delta))
530         return 0;
531     if (BN_num_bits(rnd) != bits)
532         goto again;
533     bn_check_top(rnd);
534     return 1;
535 }
536 
537 /*
538  * Generate a random number |rnd| of |bits| bits that is probably prime
539  * and satisfies |rnd| % |add| == |rem| by sieving.
540  * If |safe| != 0, it generates a safe prime.
541  * |mods| is a preallocated array that gets reused when called again.
542  *
543  * Returns 1 on success and 0 on error.
544  */
probable_prime_dh(BIGNUM * rnd,int bits,int safe,prime_t * mods,const BIGNUM * add,const BIGNUM * rem,BN_CTX * ctx)545 static int probable_prime_dh(BIGNUM *rnd, int bits, int safe, prime_t *mods,
546                              const BIGNUM *add, const BIGNUM *rem,
547                              BN_CTX *ctx)
548 {
549     int i, ret = 0;
550     BIGNUM *t1;
551     BN_ULONG delta;
552     int trial_divisions = calc_trial_divisions(bits);
553     BN_ULONG maxdelta = BN_MASK2 - primes[trial_divisions - 1];
554 
555     BN_CTX_start(ctx);
556     if ((t1 = BN_CTX_get(ctx)) == NULL)
557         goto err;
558 
559     if (maxdelta > BN_MASK2 - BN_get_word(add))
560         maxdelta = BN_MASK2 - BN_get_word(add);
561 
562  again:
563     if (!BN_rand_ex(rnd, bits, BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ODD, 0, ctx))
564         goto err;
565 
566     /* we need ((rnd-rem) % add) == 0 */
567 
568     if (!BN_mod(t1, rnd, add, ctx))
569         goto err;
570     if (!BN_sub(rnd, rnd, t1))
571         goto err;
572     if (rem == NULL) {
573         if (!BN_add_word(rnd, safe ? 3u : 1u))
574             goto err;
575     } else {
576         if (!BN_add(rnd, rnd, rem))
577             goto err;
578     }
579 
580     if (BN_num_bits(rnd) < bits
581             || BN_get_word(rnd) < (safe ? 5u : 3u)) {
582         if (!BN_add(rnd, rnd, add))
583             goto err;
584     }
585 
586     /* we now have a random number 'rnd' to test. */
587     for (i = 1; i < trial_divisions; i++) {
588         BN_ULONG mod = BN_mod_word(rnd, (BN_ULONG)primes[i]);
589         if (mod == (BN_ULONG)-1)
590             goto err;
591         mods[i] = (prime_t) mod;
592     }
593     delta = 0;
594  loop:
595     for (i = 1; i < trial_divisions; i++) {
596         /* check that rnd is a prime */
597         if (bits <= 31 && delta <= 0x7fffffff
598                 && square(primes[i]) > BN_get_word(rnd) + delta)
599             break;
600         /* rnd mod p == 1 implies q = (rnd-1)/2 is divisible by p */
601         if (safe ? (mods[i] + delta) % primes[i] <= 1
602                  : (mods[i] + delta) % primes[i] == 0) {
603             delta += BN_get_word(add);
604             if (delta > maxdelta)
605                 goto again;
606             goto loop;
607         }
608     }
609     if (!BN_add_word(rnd, delta))
610         goto err;
611     ret = 1;
612 
613  err:
614     BN_CTX_end(ctx);
615     bn_check_top(rnd);
616     return ret;
617 }
618