/* * pr_fact - print the factors of a number * * If the number is 0 or 1, then print the number and return. * If the number is < 0, print -1, negate the number and continue * processing. * * Print the factors of the number, from the lowest to the highest. * A factor will be printed numtiple times if it divides the value * multiple times. * * Factors are printed with leading tabs. */ static void pr_fact(BIGNUM *val) { const ubig *fact; /* The factor found. */ /* Firewall - catch 0 and 1. */ if (BN_is_zero(val) || BN_is_one(val)) errx(1, "numbers <= 1 aren't permitted."); /* Factor value. */ BN_print_dec_fp(stdout, val); putchar(':'); for (fact = &prime[0]; !BN_is_one(val); ++fact) { /* Look for the smallest factor. */ while (fact <= pr_limit) { if (BN_mod_word(val, (BN_ULONG)*fact) == 0) break; fact++; } /* Watch for primes larger than the table. */ if (fact > pr_limit) { #ifdef HAVE_OPENSSL BIGNUM *bnfact; bnfact = BN_new(); BN_set_word(bnfact, (BN_ULONG)*(fact - 1)); BN_sqr(bnfact, bnfact, ctx); if (BN_cmp(bnfact, val) > 0 || BN_is_prime(val, PRIME_CHECKS, NULL, NULL, NULL) == 1) { putchar(' '); BN_print_dec_fp(stdout, val); } else pollard_rho(val); #else printf(" %s", BN_bn2dec(val)); #endif break; } /* Divide factor out until none are left. */ do { printf(" %lu", *fact); BN_div_word(val, (BN_ULONG)*fact); } while (BN_mod_word(val, (BN_ULONG)*fact) == 0); /* Let the user know we're doing something. */ fflush(stdout); } putchar('\n'); }
/* * pr_fact - print the factors of a number * * Print the factors of the number, from the lowest to the highest. * A factor will be printed multiple times if it divides the value * multiple times. * * Factors are printed with leading tabs. */ static void pr_fact(BIGNUM *val) { const ubig *fact; /* The factor found. */ /* Firewall - catch 0 and 1. */ if (BN_is_zero(val)) /* Historical practice; 0 just exits. */ exit(0); if (BN_is_one(val)) { printf("1: 1\n"); return; } /* Factor value. */ if (hflag) { fputs("0x", stdout); BN_print_fp(stdout, val); } else BN_print_dec_fp(stdout, val); putchar(':'); for (fact = &prime[0]; !BN_is_one(val); ++fact) { /* Look for the smallest factor. */ do { if (BN_mod_word(val, (BN_ULONG)*fact) == 0) break; } while (++fact <= pr_limit); /* Watch for primes larger than the table. */ if (fact > pr_limit) { #ifdef HAVE_OPENSSL BIGNUM *bnfact; bnfact = BN_new(); BN_set_word(bnfact, *(fact - 1)); if (!BN_sqr(bnfact, bnfact, ctx)) errx(1, "error in BN_sqr()"); if (BN_cmp(bnfact, val) > 0 || BN_is_prime(val, PRIME_CHECKS, NULL, NULL, NULL) == 1) pr_print(val); else pollard_pminus1(val); #else pr_print(val); #endif break; } /* Divide factor out until none are left. */ do { printf(hflag ? " 0x%lx" : " %lu", *fact); BN_div_word(val, (BN_ULONG)*fact); } while (BN_mod_word(val, (BN_ULONG)*fact) == 0); /* Let the user know we're doing something. */ fflush(stdout); } putchar('\n'); }
static void pr_print(BIGNUM *val) { if (hflag) { fputs(" 0x", stdout); BN_print_fp(stdout, val); } else { putchar(' '); BN_print_dec_fp(stdout, val); } }
static void pollard_rho(BIGNUM *val) { BIGNUM *x, *y, *tmp, *num; BN_ULONG a; unsigned int steps_taken, steps_limit; x = BN_new(); y = BN_new(); tmp = BN_new(); num = BN_new(); a = 1; restart: steps_taken = 0; steps_limit = 2; BN_set_word(x, 1); BN_copy(y, x); for (;;) { BN_sqr(tmp, x, ctx); BN_add_word(tmp, a); BN_mod(x, tmp, val, ctx); BN_sub(tmp, x, y); if (BN_is_zero(tmp)) { #ifdef DEBUG printf(" (loop)"); #endif a++; goto restart; } BN_gcd(tmp, tmp, val, ctx); if (!BN_is_one(tmp)) { if (BN_is_prime(tmp, PRIME_CHECKS, NULL, NULL, NULL) == 1) { putchar(' '); BN_print_dec_fp(stdout, tmp); } else { #ifdef DEBUG printf(" (recurse for "); BN_print_dec_fp(stdout, tmp); putchar(')'); #endif pollard_rho(BN_dup(tmp)); #ifdef DEBUG printf(" (back)"); #endif } fflush(stdout); BN_div(num, NULL, val, tmp, ctx); if (BN_is_one(num)) return; if (BN_is_prime(num, PRIME_CHECKS, NULL, NULL, NULL) == 1) { putchar(' '); BN_print_dec_fp(stdout, num); fflush(stdout); return; } BN_copy(val, num); goto restart; } steps_taken++; if (steps_taken == steps_limit) { BN_copy(y, x); /* teleport the turtle */ steps_taken = 0; steps_limit *= 2; if (steps_limit == 0) { #ifdef DEBUG printf(" (overflow)"); #endif a++; goto restart; } } } }