=head1 NAME
-BN_generate_prime_ex, BN_is_prime_ex, BN_is_prime_fasttest_ex, BN_GENCB_call,
-BN_GENCB_new, BN_GENCB_free, BN_GENCB_set_old, BN_GENCB_set, BN_GENCB_get_arg,
-BN_generate_prime, BN_is_prime, BN_is_prime_fasttest - generate primes and test
-for primality
+BN_generate_prime_ex2, BN_generate_prime_ex, BN_is_prime_ex, BN_check_prime,
+BN_is_prime_fasttest_ex, BN_GENCB_call, BN_GENCB_new, BN_GENCB_free,
+BN_GENCB_set_old, BN_GENCB_set, BN_GENCB_get_arg, BN_generate_prime,
+BN_is_prime, BN_is_prime_fasttest - generate primes and test for primality
=head1 SYNOPSIS
#include <openssl/bn.h>
+ int BN_generate_prime_ex2(BIGNUM *ret, int bits, int safe,
+ const BIGNUM *add, const BIGNUM *rem, BN_GENCB *cb,
+ BN_CTX *ctx);
+
int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe, const BIGNUM *add,
const BIGNUM *rem, BN_GENCB *cb);
- int BN_is_prime_ex(const BIGNUM *p, int nchecks, BN_CTX *ctx, BN_GENCB *cb);
-
- int BN_is_prime_fasttest_ex(const BIGNUM *p, int nchecks, BN_CTX *ctx,
- int do_trial_division, BN_GENCB *cb);
+ int BN_check_prime(const BIGNUM *p, BN_CTX *ctx, BN_GENCB *cb);
int BN_GENCB_call(BN_GENCB *cb, int a, int b);
void *BN_GENCB_get_arg(BN_GENCB *cb);
-Deprecated since OpenSSL 0.9.8, can be hidden entirely by defining
-B<OPENSSL_API_COMPAT> with a suitable version value, see
-L<openssl_user_macros(7)>:
+The following functions have been deprecated since OpenSSL 0.9.8, and can be
+hidden entirely by defining B<OPENSSL_API_COMPAT> with a suitable version value,
+see L<openssl_user_macros(7)>:
BIGNUM *BN_generate_prime(BIGNUM *ret, int num, int safe, BIGNUM *add,
BIGNUM *rem, void (*callback)(int, int, void *),
void *cb_arg);
- int BN_is_prime(const BIGNUM *a, int checks,
+ int BN_is_prime(const BIGNUM *p, int nchecks,
void (*callback)(int, int, void *), BN_CTX *ctx, void *cb_arg);
- int BN_is_prime_fasttest(const BIGNUM *a, int checks,
+ int BN_is_prime_fasttest(const BIGNUM *p, int nchecks,
void (*callback)(int, int, void *), BN_CTX *ctx,
void *cb_arg, int do_trial_division);
+The following functions have been deprecated since OpenSSL 3.0, and can be
+hidden entirely by defining B<OPENSSL_API_COMPAT> with a suitable version value,
+see L<openssl_user_macros(7)>:
+
+ int BN_is_prime_ex(const BIGNUM *p, int nchecks, BN_CTX *ctx, BN_GENCB *cb);
+
+ int BN_is_prime_fasttest_ex(const BIGNUM *p, int nchecks, BN_CTX *ctx,
+ int do_trial_division, BN_GENCB *cb);
+
=head1 DESCRIPTION
-BN_generate_prime_ex() generates a pseudo-random prime number of
-at least bit length B<bits>.
+BN_generate_prime_ex2() generates a pseudo-random prime number of
+at least bit length B<bits> using the BN_CTX provided in B<ctx>. The value of
+B<ctx> must not be NULL.
+
+The returned number is probably prime with a negligible error.
+The maximum error rate is 2^-128.
+It's 2^-287 for a 512 bit prime, 2^-435 for a 1024 bit prime,
+2^-648 for a 2048 bit prime, and lower than 2^-882 for primes larger
+than 2048 bit.
+
+If B<add> is B<NULL> the returned prime number will have exact bit
+length B<bits> with the top most two bits set.
+
If B<ret> is not B<NULL>, it will be used to store the number.
If B<cb> is not B<NULL>, it is used as follows:
generator.
If B<safe> is true, it will be a safe prime (i.e. a prime p so
-that (p-1)/2 is also prime).
-
-The PRNG must be seeded prior to calling BN_generate_prime_ex().
-The prime number generation has a negligible error probability.
-
-BN_is_prime_ex() and BN_is_prime_fasttest_ex() test if the number B<p> is
-prime. The following tests are performed until one of them shows that
-B<p> is composite; if B<p> passes all these tests, it is considered
-prime.
-
-BN_is_prime_fasttest_ex(), when called with B<do_trial_division == 1>,
-first attempts trial division by a number of small primes;
-if no divisors are found by this test and B<cb> is not B<NULL>,
-B<BN_GENCB_call(cb, 1, -1)> is called.
-If B<do_trial_division == 0>, this test is skipped.
-
-Both BN_is_prime_ex() and BN_is_prime_fasttest_ex() perform a Miller-Rabin
-probabilistic primality test with B<nchecks> iterations. If
-B<nchecks == BN_prime_checks>, a number of iterations is used that
-yields a false positive rate of at most 2^-64 for random input.
-The error rate depends on the size of the prime and goes down for bigger primes.
-The rate is 2^-80 starting at 308 bits, 2^-112 at 852 bits, 2^-128 at 1080 bits,
-2^-192 at 3747 bits and 2^-256 at 6394 bits.
-
-When the source of the prime is not random or not trusted, the number
-of checks needs to be much higher to reach the same level of assurance:
-It should equal half of the targeted security level in bits (rounded up to the
-next integer if necessary).
-For instance, to reach the 128 bit security level, B<nchecks> should be set to
-64.
-
-If B<cb> is not B<NULL>, B<BN_GENCB_call(cb, 1, j)> is called
-after the j-th iteration (j = 0, 1, ...). B<ctx> is a
-pre-allocated B<BN_CTX> (to save the overhead of allocating and
+that (p-1)/2 is also prime). If B<safe> is true, and B<rem> == B<NULL>
+the condition will be p % B<add> == 3.
+It is recommended that B<add> is a multiple of 4.
+
+The random generator must be seeded prior to calling BN_generate_prime_ex().
+If the automatic seeding or reseeding of the OpenSSL CSPRNG fails due to
+external circumstances (see L<RAND(7)>), the operation will fail.
+The random number generator configured for the OSSL_LIB_CTX associated with
+B<ctx> will be used.
+
+BN_generate_prime_ex() is the same as BN_generate_prime_ex2() except that no
+B<ctx> parameter is passed.
+In this case the random number generator associated with the default OSSL_LIB_CTX
+will be used.
+
+BN_check_prime(), BN_is_prime_ex(), BN_is_prime_fasttest_ex(), BN_is_prime()
+and BN_is_prime_fasttest() test if the number B<p> is prime.
+The functions tests until one of the tests shows that B<p> is composite,
+or all the tests passed.
+If B<p> passes all these tests, it is considered a probable prime.
+
+The test performed on B<p> are trial division by a number of small primes
+and rounds of the of the Miller-Rabin probabilistic primality test.
+
+The functions do at least 64 rounds of the Miller-Rabin test giving a maximum
+false positive rate of 2^-128.
+If the size of B<p> is more than 2048 bits, they do at least 128 rounds
+giving a maximum false positive rate of 2^-256.
+
+If B<nchecks> is larger than the minimum above (64 or 128), B<nchecks>
+rounds of the Miller-Rabin test will be done.
+
+If B<do_trial_division> set to B<0>, the trial division will be skipped.
+BN_is_prime_ex() and BN_is_prime() always skip the trial division.
+
+BN_is_prime_ex(), BN_is_prime_fasttest_ex(), BN_is_prime()
+and BN_is_prime_fasttest() are deprecated.
+
+BN_is_prime_fasttest() and BN_is_prime() behave just like
+BN_is_prime_fasttest_ex() and BN_is_prime_ex() respectively, but with the old
+style call back.
+
+B<ctx> is a preallocated B<BN_CTX> (to save the overhead of allocating and
freeing the structure in a loop), or B<NULL>.
+If the trial division is done, and no divisors are found and B<cb>
+is not B<NULL>, B<BN_GENCB_call(cb, 1, -1)> is called.
+
+After each round of the Miller-Rabin probabilistic primality test,
+if B<cb> is not B<NULL>, B<BN_GENCB_call(cb, 1, j)> is called
+with B<j> the iteration (j = 0, 1, ...).
+
BN_GENCB_call() calls the callback function held in the B<BN_GENCB> structure
and passes the ints B<a> and B<b> as arguments. There are two types of
B<BN_GENCB> structure that are supported: "new" style and "old" style. New
BN_generate_prime_ex() return 1 on success or 0 on error.
-BN_is_prime_ex(), BN_is_prime_fasttest_ex(), BN_is_prime() and
-BN_is_prime_fasttest() return 0 if the number is composite, 1 if it is
-prime with an error probability of less than 0.25^B<nchecks>, and
+BN_is_prime_ex(), BN_is_prime_fasttest_ex(), BN_is_prime(),
+BN_is_prime_fasttest() and BN_check_prime return 0 if the number is composite,
+1 if it is prime with an error probability of less than 0.25^B<nchecks>, and
-1 on error.
BN_generate_prime() returns the prime number on success, B<NULL> otherwise.
=head1 SEE ALSO
L<DH_generate_parameters(3)>, L<DSA_generate_parameters(3)>,
-L<RSA_generate_key(3)>, L<ERR_get_error(3)>, L<RAND_bytes(3)>
+L<RSA_generate_key(3)>, L<ERR_get_error(3)>, L<RAND_bytes(3)>,
+L<RAND(7)>
=head1 HISTORY
-BN_GENCB_new(), BN_GENCB_free(),
-and BN_GENCB_get_arg() were added in OpenSSL 1.1.0
+The BN_is_prime_ex() and BN_is_prime_fasttest_ex() functions were
+deprecated in OpenSSL 3.0.
+
+The BN_GENCB_new(), BN_GENCB_free(),
+and BN_GENCB_get_arg() functions were added in OpenSSL 1.1.0.
+
+BN_check_prime() was added in OpenSSL 3.0.
=head1 COPYRIGHT
-Copyright 2000-2018 The OpenSSL Project Authors. All Rights Reserved.
+Copyright 2000-2021 The OpenSSL Project Authors. All Rights Reserved.
Licensed under the Apache License 2.0 (the "License"). You may not use
this file except in compliance with the License. You can obtain a copy
projects / openssl.git / blobdiff