/* This function returns a new context for Barrett based operations on the modulus M. This context needs to be released using _gcry_mpi_barrett_free. If COPY is true M will be transferred to the context and the user may change M. If COPY is false, M may not be changed until gcry_mpi_barrett_free has been called. */ mpi_barrett_t _gcry_mpi_barrett_init (gcry_mpi_t m, int copy) { mpi_barrett_t ctx; gcry_mpi_t tmp; mpi_normalize (m); ctx = xcalloc (1, sizeof *ctx); if (copy) { ctx->m = mpi_copy (m); ctx->m_copied = 1; } else ctx->m = m; ctx->k = mpi_get_nlimbs (m); tmp = mpi_alloc (ctx->k + 1); /* Barrett precalculation: y = floor(b^(2k) / m). */ mpi_set_ui (tmp, 1); mpi_lshift_limbs (tmp, 2 * ctx->k); mpi_fdiv_q (tmp, tmp, m); ctx->y = tmp; ctx->r1 = mpi_alloc ( 2 * ctx->k + 1 ); ctx->r2 = mpi_alloc ( 2 * ctx->k + 1 ); return ctx; }
static void do_div(void) { if( stackidx < 2 ) { fputs("stack underflow\n", stderr); return; } mpi_fdiv_q( stack[stackidx-2], stack[stackidx-2], stack[stackidx-1] ); stackidx--; }
/**************** * Barrett precalculation: y = floor(b^(2k) / m) */ static gcry_mpi_t init_barrett( gcry_mpi_t m, int *k, gcry_mpi_t *r1, gcry_mpi_t *r2 ) { gcry_mpi_t tmp; mpi_normalize( m ); *k = mpi_get_nlimbs( m ); tmp = mpi_alloc( *k + 1 ); mpi_set_ui( tmp, 1 ); mpi_lshift_limbs( tmp, 2 * *k ); mpi_fdiv_q( tmp, tmp, m ); *r1 = mpi_alloc( 2* *k + 1 ); *r2 = mpi_alloc( 2* *k + 1 ); return tmp; }
/* Find a generator for PRIME where the factorization of (prime-1) is in the NULL terminated array FACTORS. Return the generator as a newly allocated MPI in R_G. If START_G is not NULL, use this as s atart for the search. Returns 0 on success.*/ gcry_error_t gcry_prime_group_generator (gcry_mpi_t *r_g, gcry_mpi_t prime, gcry_mpi_t *factors, gcry_mpi_t start_g) { gcry_mpi_t tmp = gcry_mpi_new (0); gcry_mpi_t b = gcry_mpi_new (0); gcry_mpi_t pmin1 = gcry_mpi_new (0); gcry_mpi_t g = start_g? gcry_mpi_copy (start_g) : gcry_mpi_set_ui (NULL, 3); int first = 1; int i, n; if (!factors || !r_g || !prime) return gpg_error (GPG_ERR_INV_ARG); *r_g = NULL; for (n=0; factors[n]; n++) ; if (n < 2) return gpg_error (GPG_ERR_INV_ARG); /* Extra sanity check - usually disabled. */ /* mpi_set (tmp, factors[0]); */ /* for(i = 1; i < n; i++) */ /* mpi_mul (tmp, tmp, factors[i]); */ /* mpi_add_ui (tmp, tmp, 1); */ /* if (mpi_cmp (prime, tmp)) */ /* return gpg_error (GPG_ERR_INV_ARG); */ gcry_mpi_sub_ui (pmin1, prime, 1); do { if (first) first = 0; else gcry_mpi_add_ui (g, g, 1); if (DBG_CIPHER) { log_debug ("checking g:"); gcry_mpi_dump (g); log_debug ("\n"); } else progress('^'); for (i = 0; i < n; i++) { mpi_fdiv_q (tmp, pmin1, factors[i]); gcry_mpi_powm (b, g, tmp, prime); if (! mpi_cmp_ui (b, 1)) break; } if (DBG_CIPHER) progress('\n'); } while (i < n); gcry_mpi_release (tmp); gcry_mpi_release (b); gcry_mpi_release (pmin1); *r_g = g; return 0; }
/**************** * We do not need to use the strongest RNG because we gain no extra * security from it - The prime number is public and we could also * offer the factors for those who are willing to check that it is * indeed a strong prime. With ALL_FACTORS set to true all afcors of * prime-1 are returned in FACTORS. * * mode 0: Standard * 1: Make sure that at least one factor is of size qbits. */ static gcry_err_code_t prime_generate_internal (int mode, gcry_mpi_t *prime_generated, unsigned int pbits, unsigned int qbits, gcry_mpi_t g, gcry_mpi_t **ret_factors, gcry_random_level_t randomlevel, unsigned int flags, int all_factors, gcry_prime_check_func_t cb_func, void *cb_arg) { gcry_err_code_t err = 0; gcry_mpi_t *factors_new = NULL; /* Factors to return to the caller. */ gcry_mpi_t *factors = NULL; /* Current factors. */ gcry_mpi_t *pool = NULL; /* Pool of primes. */ unsigned char *perms = NULL; /* Permutations of POOL. */ gcry_mpi_t q_factor = NULL; /* Used if QBITS is non-zero. */ unsigned int fbits = 0; /* Length of prime factors. */ unsigned int n = 0; /* Number of factors. */ unsigned int m = 0; /* Number of primes in pool. */ gcry_mpi_t q = NULL; /* First prime factor. */ gcry_mpi_t prime = NULL; /* Prime candidate. */ unsigned int nprime = 0; /* Bits of PRIME. */ unsigned int req_qbits; /* The original QBITS value. */ gcry_mpi_t val_2; /* For check_prime(). */ unsigned int is_secret = (flags & GCRY_PRIME_FLAG_SECRET); unsigned int count1 = 0, count2 = 0; unsigned int i = 0, j = 0; if (pbits < 48) return GPG_ERR_INV_ARG; /* If QBITS is not given, assume a reasonable value. */ if (!qbits) qbits = pbits / 3; req_qbits = qbits; /* Find number of needed prime factors. */ for (n = 1; (pbits - qbits - 1) / n >= qbits; n++) ; n--; val_2 = mpi_alloc_set_ui (2); if ((! n) || ((mode == 1) && (n < 2))) { err = GPG_ERR_INV_ARG; goto leave; } if (mode == 1) { n--; fbits = (pbits - 2 * req_qbits -1) / n; qbits = pbits - req_qbits - n * fbits; } else { fbits = (pbits - req_qbits -1) / n; qbits = pbits - n * fbits; } if (DBG_CIPHER) log_debug ("gen prime: pbits=%u qbits=%u fbits=%u/%u n=%d\n", pbits, req_qbits, qbits, fbits, n); prime = gcry_mpi_new (pbits); /* Generate first prime factor. */ q = gen_prime (qbits, is_secret, randomlevel, NULL, NULL); if (mode == 1) q_factor = gen_prime (req_qbits, is_secret, randomlevel, NULL, NULL); /* Allocate an array to hold the factors + 2 for later usage. */ factors = gcry_calloc (n + 2, sizeof (*factors)); if (!factors) { err = gpg_err_code_from_errno (errno); goto leave; } /* Make a pool of 3n+5 primes (this is an arbitrary value). */ m = n * 3 + 5; if (mode == 1) /* Need some more (for e.g. DSA). */ m += 5; if (m < 25) m = 25; pool = gcry_calloc (m , sizeof (*pool)); if (! pool) { err = gpg_err_code_from_errno (errno); goto leave; } /* Permutate over the pool of primes. */ do { next_try: if (! perms) { /* Allocate new primes. */ for(i = 0; i < m; i++) { mpi_free (pool[i]); pool[i] = NULL; } /* Init m_out_of_n(). */ perms = gcry_calloc (1, m); if (! perms) { err = gpg_err_code_from_errno (errno); goto leave; } for(i = 0; i < n; i++) { perms[i] = 1; pool[i] = gen_prime (fbits, is_secret, randomlevel, NULL, NULL); factors[i] = pool[i]; } } else { m_out_of_n ((char*)perms, n, m); for (i = j = 0; (i < m) && (j < n); i++) if (perms[i]) { if(! pool[i]) pool[i] = gen_prime (fbits, 0, 1, NULL, NULL); factors[j++] = pool[i]; } if (i == n) { gcry_free (perms); perms = NULL; progress ('!'); goto next_try; /* Allocate new primes. */ } } /* Generate next prime candidate: p = 2 * q [ * q_factor] * factor_0 * factor_1 * ... * factor_n + 1. */ mpi_set (prime, q); mpi_mul_ui (prime, prime, 2); if (mode == 1) mpi_mul (prime, prime, q_factor); for(i = 0; i < n; i++) mpi_mul (prime, prime, factors[i]); mpi_add_ui (prime, prime, 1); nprime = mpi_get_nbits (prime); if (nprime < pbits) { if (++count1 > 20) { count1 = 0; qbits++; progress('>'); mpi_free (q); q = gen_prime (qbits, 0, 0, NULL, NULL); goto next_try; } } else count1 = 0; if (nprime > pbits) { if (++count2 > 20) { count2 = 0; qbits--; progress('<'); mpi_free (q); q = gen_prime (qbits, 0, 0, NULL, NULL); goto next_try; } } else count2 = 0; } while (! ((nprime == pbits) && check_prime (prime, val_2, cb_func, cb_arg))); if (DBG_CIPHER) { progress ('\n'); log_mpidump ("prime : ", prime); log_mpidump ("factor q: ", q); if (mode == 1) log_mpidump ("factor q0: ", q_factor); for (i = 0; i < n; i++) log_mpidump ("factor pi: ", factors[i]); log_debug ("bit sizes: prime=%u, q=%u", mpi_get_nbits (prime), mpi_get_nbits (q)); if (mode == 1) log_debug (", q0=%u", mpi_get_nbits (q_factor)); for (i = 0; i < n; i++) log_debug (", p%d=%u", i, mpi_get_nbits (factors[i])); progress('\n'); } if (ret_factors) { /* Caller wants the factors. */ factors_new = gcry_calloc (n + 4, sizeof (*factors_new)); if (! factors_new) { err = gpg_err_code_from_errno (errno); goto leave; } if (all_factors) { i = 0; factors_new[i++] = gcry_mpi_set_ui (NULL, 2); factors_new[i++] = mpi_copy (q); if (mode == 1) factors_new[i++] = mpi_copy (q_factor); for(j=0; j < n; j++) factors_new[i++] = mpi_copy (factors[j]); } else { i = 0; if (mode == 1) { factors_new[i++] = mpi_copy (q_factor); for (; i <= n; i++) factors_new[i] = mpi_copy (factors[i]); } else for (; i < n; i++ ) factors_new[i] = mpi_copy (factors[i]); } } if (g) { /* Create a generator (start with 3). */ gcry_mpi_t tmp = mpi_alloc (mpi_get_nlimbs (prime)); gcry_mpi_t b = mpi_alloc (mpi_get_nlimbs (prime)); gcry_mpi_t pmin1 = mpi_alloc (mpi_get_nlimbs (prime)); if (mode == 1) err = GPG_ERR_NOT_IMPLEMENTED; else { factors[n] = q; factors[n + 1] = mpi_alloc_set_ui (2); mpi_sub_ui (pmin1, prime, 1); mpi_set_ui (g, 2); do { mpi_add_ui (g, g, 1); if (DBG_CIPHER) { log_debug ("checking g:"); gcry_mpi_dump (g); log_printf ("\n"); } else progress('^'); for (i = 0; i < n + 2; i++) { mpi_fdiv_q (tmp, pmin1, factors[i]); /* No mpi_pow(), but it is okay to use this with mod prime. */ gcry_mpi_powm (b, g, tmp, prime); if (! mpi_cmp_ui (b, 1)) break; } if (DBG_CIPHER) progress('\n'); } while (i < n + 2); mpi_free (factors[n+1]); mpi_free (tmp); mpi_free (b); mpi_free (pmin1); } } if (! DBG_CIPHER) progress ('\n'); leave: if (pool) { for(i = 0; i < m; i++) mpi_free (pool[i]); gcry_free (pool); } if (factors) gcry_free (factors); /* Factors are shallow copies. */ if (perms) gcry_free (perms); mpi_free (val_2); mpi_free (q); mpi_free (q_factor); if (! err) { *prime_generated = prime; if (ret_factors) *ret_factors = factors_new; } else { if (factors_new) { for (i = 0; factors_new[i]; i++) mpi_free (factors_new[i]); gcry_free (factors_new); } mpi_free (prime); } return err; }
/**************** * Calculate the multiplicative inverse X of A mod N * That is: Find the solution x for * 1 = (a*x) mod n */ int _gcry_mpi_invm (gcry_mpi_t x, gcry_mpi_t a, gcry_mpi_t n) { #if 0 gcry_mpi_t u, v, u1, u2, u3, v1, v2, v3, q, t1, t2, t3; gcry_mpi_t ta, tb, tc; u = mpi_copy(a); v = mpi_copy(n); u1 = mpi_alloc_set_ui(1); u2 = mpi_alloc_set_ui(0); u3 = mpi_copy(u); v1 = mpi_alloc_set_ui(0); v2 = mpi_alloc_set_ui(1); v3 = mpi_copy(v); q = mpi_alloc( mpi_get_nlimbs(u)+1 ); t1 = mpi_alloc( mpi_get_nlimbs(u)+1 ); t2 = mpi_alloc( mpi_get_nlimbs(u)+1 ); t3 = mpi_alloc( mpi_get_nlimbs(u)+1 ); while( mpi_cmp_ui( v3, 0 ) ) { mpi_fdiv_q( q, u3, v3 ); mpi_mul(t1, v1, q); mpi_mul(t2, v2, q); mpi_mul(t3, v3, q); mpi_sub(t1, u1, t1); mpi_sub(t2, u2, t2); mpi_sub(t3, u3, t3); mpi_set(u1, v1); mpi_set(u2, v2); mpi_set(u3, v3); mpi_set(v1, t1); mpi_set(v2, t2); mpi_set(v3, t3); } /* log_debug("result:\n"); log_mpidump("q =", q ); log_mpidump("u1=", u1); log_mpidump("u2=", u2); log_mpidump("u3=", u3); log_mpidump("v1=", v1); log_mpidump("v2=", v2); */ mpi_set(x, u1); mpi_free(u1); mpi_free(u2); mpi_free(u3); mpi_free(v1); mpi_free(v2); mpi_free(v3); mpi_free(q); mpi_free(t1); mpi_free(t2); mpi_free(t3); mpi_free(u); mpi_free(v); #elif 0 /* Extended Euclid's algorithm (See TAOCP Vol II, 4.5.2, Alg X) * modified according to Michael Penk's solution for Exercise 35 */ /* FIXME: we can simplify this in most cases (see Knuth) */ gcry_mpi_t u, v, u1, u2, u3, v1, v2, v3, t1, t2, t3; unsigned k; int sign; u = mpi_copy(a); v = mpi_copy(n); for(k=0; !mpi_test_bit(u,0) && !mpi_test_bit(v,0); k++ ) { mpi_rshift(u, u, 1); mpi_rshift(v, v, 1); } u1 = mpi_alloc_set_ui(1); u2 = mpi_alloc_set_ui(0); u3 = mpi_copy(u); v1 = mpi_copy(v); /* !-- used as const 1 */ v2 = mpi_alloc( mpi_get_nlimbs(u) ); mpi_sub( v2, u1, u ); v3 = mpi_copy(v); if( mpi_test_bit(u, 0) ) { /* u is odd */ t1 = mpi_alloc_set_ui(0); t2 = mpi_alloc_set_ui(1); t2->sign = 1; t3 = mpi_copy(v); t3->sign = !t3->sign; goto Y4; } else { t1 = mpi_alloc_set_ui(1); t2 = mpi_alloc_set_ui(0); t3 = mpi_copy(u); } do { do { if( mpi_test_bit(t1, 0) || mpi_test_bit(t2, 0) ) { /* one is odd */ mpi_add(t1, t1, v); mpi_sub(t2, t2, u); } mpi_rshift(t1, t1, 1); mpi_rshift(t2, t2, 1); mpi_rshift(t3, t3, 1); Y4: ; } while( !mpi_test_bit( t3, 0 ) ); /* while t3 is even */ if( !t3->sign ) { mpi_set(u1, t1); mpi_set(u2, t2); mpi_set(u3, t3); } else { mpi_sub(v1, v, t1); sign = u->sign; u->sign = !u->sign; mpi_sub(v2, u, t2); u->sign = sign; sign = t3->sign; t3->sign = !t3->sign; mpi_set(v3, t3); t3->sign = sign; } mpi_sub(t1, u1, v1); mpi_sub(t2, u2, v2); mpi_sub(t3, u3, v3); if( t1->sign ) { mpi_add(t1, t1, v); mpi_sub(t2, t2, u); } } while( mpi_cmp_ui( t3, 0 ) ); /* while t3 != 0 */ /* mpi_lshift( u3, k ); */ mpi_set(x, u1); mpi_free(u1); mpi_free(u2); mpi_free(u3); mpi_free(v1); mpi_free(v2); mpi_free(v3); mpi_free(t1); mpi_free(t2); mpi_free(t3); #else /* Extended Euclid's algorithm (See TAOCP Vol II, 4.5.2, Alg X) * modified according to Michael Penk's solution for Exercise 35 * with further enhancement */ gcry_mpi_t u, v, u1, u2=NULL, u3, v1, v2=NULL, v3, t1, t2=NULL, t3; unsigned k; int sign; int odd ; if (!mpi_cmp_ui (a, 0)) return 0; /* Inverse does not exists. */ if (!mpi_cmp_ui (n, 1)) return 0; /* Inverse does not exists. */ u = mpi_copy(a); v = mpi_copy(n); for(k=0; !mpi_test_bit(u,0) && !mpi_test_bit(v,0); k++ ) { mpi_rshift(u, u, 1); mpi_rshift(v, v, 1); } odd = mpi_test_bit(v,0); u1 = mpi_alloc_set_ui(1); if( !odd ) u2 = mpi_alloc_set_ui(0); u3 = mpi_copy(u); v1 = mpi_copy(v); if( !odd ) { v2 = mpi_alloc( mpi_get_nlimbs(u) ); mpi_sub( v2, u1, u ); /* U is used as const 1 */ } v3 = mpi_copy(v); if( mpi_test_bit(u, 0) ) { /* u is odd */ t1 = mpi_alloc_set_ui(0); if( !odd ) { t2 = mpi_alloc_set_ui(1); t2->sign = 1; } t3 = mpi_copy(v); t3->sign = !t3->sign; goto Y4; } else { t1 = mpi_alloc_set_ui(1); if( !odd ) t2 = mpi_alloc_set_ui(0); t3 = mpi_copy(u); } do { do { if( !odd ) { if( mpi_test_bit(t1, 0) || mpi_test_bit(t2, 0) ) { /* one is odd */ mpi_add(t1, t1, v); mpi_sub(t2, t2, u); } mpi_rshift(t1, t1, 1); mpi_rshift(t2, t2, 1); mpi_rshift(t3, t3, 1); } else { if( mpi_test_bit(t1, 0) ) mpi_add(t1, t1, v); mpi_rshift(t1, t1, 1); mpi_rshift(t3, t3, 1); } Y4: ; } while( !mpi_test_bit( t3, 0 ) ); /* while t3 is even */ if( !t3->sign ) { mpi_set(u1, t1); if( !odd ) mpi_set(u2, t2); mpi_set(u3, t3); } else { mpi_sub(v1, v, t1); sign = u->sign; u->sign = !u->sign; if( !odd ) mpi_sub(v2, u, t2); u->sign = sign; sign = t3->sign; t3->sign = !t3->sign; mpi_set(v3, t3); t3->sign = sign; } mpi_sub(t1, u1, v1); if( !odd ) mpi_sub(t2, u2, v2); mpi_sub(t3, u3, v3); if( t1->sign ) { mpi_add(t1, t1, v); if( !odd ) mpi_sub(t2, t2, u); } } while( mpi_cmp_ui( t3, 0 ) ); /* while t3 != 0 */ /* mpi_lshift( u3, k ); */ mpi_set(x, u1); mpi_free(u1); mpi_free(v1); mpi_free(t1); if( !odd ) { mpi_free(u2); mpi_free(v2); mpi_free(t2); } mpi_free(u3); mpi_free(v3); mpi_free(t3); mpi_free(u); mpi_free(v); #endif return 1; }
/**************** * We do not need to use the strongest RNG because we gain no extra * security from it - The prime number is public and we could also * offer the factors for those who are willing to check that it is * indeed a strong prime. * * mode 0: Standard * 1: Make sure that at least one factor is of size qbits. */ MPI generate_elg_prime( int mode, unsigned pbits, unsigned qbits, MPI g, MPI **ret_factors ) { int n; /* number of factors */ int m; /* number of primes in pool */ unsigned fbits; /* length of prime factors */ MPI *factors; /* current factors */ MPI *pool; /* pool of primes */ MPI q; /* first prime factor (variable)*/ MPI prime; /* prime test value */ MPI q_factor; /* used for mode 1 */ byte *perms = NULL; int i, j; int count1, count2; unsigned nprime; unsigned req_qbits = qbits; /* the requested q bits size */ MPI val_2 = mpi_alloc_set_ui( 2 ); /* find number of needed prime factors */ for(n=1; (pbits - qbits - 1) / n >= qbits; n++ ) ; n--; if( !n || (mode==1 && n < 2) ) log_fatal("can't gen prime with pbits=%u qbits=%u\n", pbits, qbits ); if( mode == 1 ) { n--; fbits = (pbits - 2*req_qbits -1) / n; qbits = pbits - req_qbits - n*fbits; } else { fbits = (pbits - req_qbits -1) / n; qbits = pbits - n*fbits; } if( DBG_CIPHER ) log_debug("gen prime: pbits=%u qbits=%u fbits=%u/%u n=%d\n", pbits, req_qbits, qbits, fbits, n ); prime = mpi_alloc( (pbits + BITS_PER_MPI_LIMB - 1) / BITS_PER_MPI_LIMB ); q = gen_prime( qbits, 0, 0 ); q_factor = mode==1? gen_prime( req_qbits, 0, 0 ) : NULL; /* allocate an array to hold the factors + 2 for later usage */ factors = m_alloc_clear( (n+2) * sizeof *factors ); /* make a pool of 3n+5 primes (this is an arbitrary value) */ m = n*3+5; if( mode == 1 ) m += 5; /* need some more for DSA */ if( m < 25 ) m = 25; pool = m_alloc_clear( m * sizeof *pool ); /* permutate over the pool of primes */ count1=count2=0; do { next_try: if( !perms ) { /* allocate new primes */ for(i=0; i < m; i++ ) { mpi_free(pool[i]); pool[i] = NULL; } /* init m_out_of_n() */ perms = m_alloc_clear( m ); for(i=0; i < n; i++ ) { perms[i] = 1; pool[i] = gen_prime( fbits, 0, 0 ); factors[i] = pool[i]; } } else { m_out_of_n( perms, n, m ); for(i=j=0; i < m && j < n ; i++ ) if( perms[i] ) { if( !pool[i] ) pool[i] = gen_prime( fbits, 0, 0 ); factors[j++] = pool[i]; } if( i == n ) { m_free(perms); perms = NULL; progress('!'); goto next_try; /* allocate new primes */ } } mpi_set( prime, q ); mpi_mul_ui( prime, prime, 2 ); if( mode == 1 ) mpi_mul( prime, prime, q_factor ); for(i=0; i < n; i++ ) mpi_mul( prime, prime, factors[i] ); mpi_add_ui( prime, prime, 1 ); nprime = mpi_get_nbits(prime); if( nprime < pbits ) { if( ++count1 > 20 ) { count1 = 0; qbits++; progress('>'); mpi_free (q); q = gen_prime( qbits, 0, 0 ); goto next_try; } } else count1 = 0; if( nprime > pbits ) { if( ++count2 > 20 ) { count2 = 0; qbits--; progress('<'); mpi_free (q); q = gen_prime( qbits, 0, 0 ); goto next_try; } } else count2 = 0; } while( !(nprime == pbits && check_prime( prime, val_2 )) ); if( DBG_CIPHER ) { progress('\n'); log_mpidump( "prime : ", prime ); log_mpidump( "factor q: ", q ); if( mode == 1 ) log_mpidump( "factor q0: ", q_factor ); for(i=0; i < n; i++ ) log_mpidump( "factor pi: ", factors[i] ); log_debug("bit sizes: prime=%u, q=%u", mpi_get_nbits(prime), mpi_get_nbits(q) ); if( mode == 1 ) fprintf(stderr, ", q0=%u", mpi_get_nbits(q_factor) ); for(i=0; i < n; i++ ) fprintf(stderr, ", p%d=%u", i, mpi_get_nbits(factors[i]) ); progress('\n'); } if( ret_factors ) { /* caller wants the factors */ *ret_factors = m_alloc_clear( (n+2) * sizeof **ret_factors); i = 0; if( mode == 1 ) { (*ret_factors)[i++] = mpi_copy( q_factor ); for(; i <= n; i++ ) (*ret_factors)[i] = mpi_copy( factors[i] ); } else { for(; i < n; i++ ) (*ret_factors)[i] = mpi_copy( factors[i] ); } } if( g ) { /* create a generator (start with 3)*/ MPI tmp = mpi_alloc( mpi_get_nlimbs(prime) ); MPI b = mpi_alloc( mpi_get_nlimbs(prime) ); MPI pmin1 = mpi_alloc( mpi_get_nlimbs(prime) ); if( mode == 1 ) BUG(); /* not yet implemented */ factors[n] = q; factors[n+1] = mpi_alloc_set_ui(2); mpi_sub_ui( pmin1, prime, 1 ); mpi_set_ui(g,2); do { mpi_add_ui(g, g, 1); if( DBG_CIPHER ) { log_debug("checking g: "); mpi_print( stderr, g, 1 ); } else progress('^'); for(i=0; i < n+2; i++ ) { /*fputc('~', stderr);*/ mpi_fdiv_q(tmp, pmin1, factors[i] ); /* (no mpi_pow(), but it is okay to use this with mod prime) */ mpi_powm(b, g, tmp, prime ); if( !mpi_cmp_ui(b, 1) ) break; } if( DBG_CIPHER ) progress('\n'); } while( i < n+2 ); mpi_free(factors[n+1]); mpi_free(tmp); mpi_free(b); mpi_free(pmin1); } if( !DBG_CIPHER ) progress('\n'); m_free( factors ); /* (factors are shallow copies) */ for(i=0; i < m; i++ ) mpi_free( pool[i] ); m_free( pool ); m_free(perms); mpi_free(val_2); mpi_free(q); return prime; }