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Title "BN_GENERATE_PRIME 3"
way too many mistakes in technical documents.
The following functions have been deprecated since OpenSSL 0.9.8, and can be hidden entirely by defining \s-1OPENSSL_API_COMPAT\s0 with a suitable version value, see openssl_user_macros\|(7):
.Vb 3 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 *p, int nchecks, void (*callback)(int, int, void *), BN_CTX *ctx, void *cb_arg); \& 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); .Ve
The following functions have been deprecated since OpenSSL 3.0, and can be hidden entirely by defining \s-1OPENSSL_API_COMPAT\s0 with a suitable version value, see openssl_user_macros\|(7):
.Vb 1 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); .Ve
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 add is \s-1NULL\s0 the returned prime number will have exact bit length bits with the top most two bits set.
If ret is not \s-1NULL\s0, it will be used to store the number.
If cb is not \s-1NULL\s0, it is used as follows:
The prime may have to fulfill additional requirements for use in Diffie-Hellman key exchange:
If add is not \s-1NULL\s0, the prime will fulfill the condition p % add == rem (p % add == 1 if rem == \s-1NULL\s0) in order to suit a given generator.
If safe is true, it will be a safe prime (i.e. a prime p so that (p-1)/2 is also prime). If safe is true, and rem == \s-1NULL\s0 the condition will be p % add == 3. It is recommended that 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 \s-1CSPRNG\s0 fails due to external circumstances (see \s-1RAND\s0\|(7)), the operation will fail. The random number generator configured for the \s-1OSSL_LIB_CTX\s0 associated with \fBctx will be used.
\fBBN_generate_prime_ex() is the same as BN_generate_prime_ex2() except that no \fBctx parameter is passed. In this case the random number generator associated with the default \s-1OSSL_LIB_CTX\s0 will be used.
\fBBN_check_prime(), BN_is_prime_ex(), BN_is_prime_fasttest_ex(), BN_is_prime() and BN_is_prime_fasttest() test if the number p is prime. The functions tests until one of the tests shows that p is composite, or all the tests passed. If p passes all these tests, it is considered a probable prime.
The test performed on 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 p is more than 2048 bits, they do at least 128 rounds giving a maximum false positive rate of 2^-256.
If nchecks is larger than the minimum above (64 or 128), nchecks rounds of the Miller-Rabin test will be done.
If do_trial_division set to 0, the trial division will be skipped. \fBBN_is_prime_ex() and BN_is_prime() always skip the trial division.
\fBBN_is_prime_ex(), BN_is_prime_fasttest_ex(), BN_is_prime() and BN_is_prime_fasttest() are deprecated.
\fBBN_is_prime_fasttest() and BN_is_prime() behave just like \fBBN_is_prime_fasttest_ex() and BN_is_prime_ex() respectively, but with the old style call back.
\fBctx is a preallocated \s-1BN_CTX\s0 (to save the overhead of allocating and freeing the structure in a loop), or \s-1NULL\s0.
If the trial division is done, and no divisors are found and cb is not \s-1NULL\s0, BN_GENCB_call(cb, 1, -1) is called.
After each round of the Miller-Rabin probabilistic primality test, if cb is not \s-1NULL\s0, BN_GENCB_call(cb, 1, j) is called with j the iteration (j = 0, 1, ...).
\fBBN_GENCB_call() calls the callback function held in the \s-1BN_GENCB\s0 structure and passes the ints a and b as arguments. There are two types of \fB\s-1BN_GENCB\s0 structure that are supported: \*(L"new\*(R" style and \*(L"old\*(R" style. New programs should prefer the \*(L"new\*(R" style, whilst the \*(L"old\*(R" style is provided for backwards compatibility purposes.
A \s-1BN_GENCB\s0 structure should be created through a call to BN_GENCB_new(), and freed through a call to BN_GENCB_free().
For \*(L"new\*(R" style callbacks a \s-1BN_GENCB\s0 structure should be initialised with a call to BN_GENCB_set(), where gencb is a \s-1BN_GENCB\s0 *, callback is of type int (*callback)(int, int, \s-1BN_GENCB\s0 *) and cb_arg is a void *. \*(L"Old\*(R" style callbacks are the same except they are initialised with a call to BN_GENCB_set_old() and callback is of type \fBvoid (*callback)(int, int, void *).
A callback is invoked through a call to BN_GENCB_call. This will check the type of the callback and will invoke callback(a, b, gencb) for new style callbacks or callback(a, b, cb_arg) for old style.
It is possible to obtain the argument associated with a \s-1BN_GENCB\s0 structure (set via a call to BN_GENCB_set or BN_GENCB_set_old) using BN_GENCB_get_arg.
\fBBN_generate_prime() (deprecated) works in the same way as \fBBN_generate_prime_ex() but expects an old-style callback function directly in the callback parameter, and an argument to pass to it in the cb_arg. BN_is_prime() and BN_is_prime_fasttest() can similarly be compared to BN_is_prime_ex() and \fBBN_is_prime_fasttest_ex(), respectively.
\fBBN_is_prime_ex(), BN_is_prime_fasttest_ex(), BN_is_prime(), \fBBN_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^nchecks, and \-1 on error.
\fBBN_generate_prime() returns the prime number on success, \s-1NULL\s0 otherwise.
BN_GENCB_new returns a pointer to a \s-1BN_GENCB\s0 structure on success, or \s-1NULL\s0 otherwise.
BN_GENCB_get_arg returns the argument previously associated with a \s-1BN_GENCB\s0 structure.
Callback functions should return 1 on success or 0 on error.
The error codes can be obtained by ERR_get_error\|(3).
.Vb 1 BN_GENCB callback; .Ve
Instead applications should create a \s-1BN_GENCB\s0 structure using BN_GENCB_new:
.Vb 6 BN_GENCB *callback; callback = BN_GENCB_new(); if (!callback) /* error */ ... BN_GENCB_free(callback); .Ve
The BN_GENCB_new(), BN_GENCB_free(), and BN_GENCB_get_arg() functions were added in OpenSSL 1.1.0.
\fBBN_check_prime() was added in OpenSSL 3.0.
Licensed under the Apache License 2.0 (the \*(L"License\*(R"). You may not use this file except in compliance with the License. You can obtain a copy in the file \s-1LICENSE\s0 in the source distribution or at <https://www.openssl.org/source/license.html>.