forked from cory/tildefriends
342 lines
13 KiB
Groff
342 lines
13 KiB
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.\" ========================================================================
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.\"
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.IX Title "BN_GENERATE_PRIME 3"
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.TH BN_GENERATE_PRIME 3 "2020-04-21" "1.1.1g" "OpenSSL"
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.\" For nroff, turn off justification. Always turn off hyphenation; it makes
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.\" way too many mistakes in technical documents.
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.if n .ad l
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.nh
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.SH "NAME"
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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
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.SH "SYNOPSIS"
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.IX Header "SYNOPSIS"
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.Vb 1
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\& #include <openssl/bn.h>
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\&
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\& int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe, const BIGNUM *add,
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\& const BIGNUM *rem, BN_GENCB *cb);
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\&
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\& int BN_is_prime_ex(const BIGNUM *p, int nchecks, BN_CTX *ctx, BN_GENCB *cb);
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\&
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\& int BN_is_prime_fasttest_ex(const BIGNUM *p, int nchecks, BN_CTX *ctx,
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\& int do_trial_division, BN_GENCB *cb);
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\&
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\& int BN_GENCB_call(BN_GENCB *cb, int a, int b);
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\&
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\& BN_GENCB *BN_GENCB_new(void);
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\&
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\& void BN_GENCB_free(BN_GENCB *cb);
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\&
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\& void BN_GENCB_set_old(BN_GENCB *gencb,
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\& void (*callback)(int, int, void *), void *cb_arg);
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\&
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\& void BN_GENCB_set(BN_GENCB *gencb,
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\& int (*callback)(int, int, BN_GENCB *), void *cb_arg);
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\&
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\& void *BN_GENCB_get_arg(BN_GENCB *cb);
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.Ve
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.PP
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Deprecated:
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.PP
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.Vb 4
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\& #if OPENSSL_API_COMPAT < 0x00908000L
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\& BIGNUM *BN_generate_prime(BIGNUM *ret, int num, int safe, BIGNUM *add,
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\& BIGNUM *rem, void (*callback)(int, int, void *),
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\& void *cb_arg);
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\&
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\& int BN_is_prime(const BIGNUM *a, int checks,
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\& void (*callback)(int, int, void *), BN_CTX *ctx, void *cb_arg);
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\&
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\& int BN_is_prime_fasttest(const BIGNUM *a, int checks,
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\& void (*callback)(int, int, void *), BN_CTX *ctx,
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\& void *cb_arg, int do_trial_division);
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\& #endif
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.Ve
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.SH "DESCRIPTION"
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.IX Header "DESCRIPTION"
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\&\fBBN_generate_prime_ex()\fR generates a pseudo-random prime number of
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at least bit length \fBbits\fR. The returned number is probably prime
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with a negligible error. If \fBadd\fR is \fB\s-1NULL\s0\fR the returned prime
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number will have exact bit length \fBbits\fR with the top most two
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bits set.
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.PP
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If \fBret\fR is not \fB\s-1NULL\s0\fR, it will be used to store the number.
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.PP
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If \fBcb\fR is not \fB\s-1NULL\s0\fR, it is used as follows:
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.IP "\(bu" 2
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\&\fBBN_GENCB_call(cb, 0, i)\fR is called after generating the i\-th
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potential prime number.
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.IP "\(bu" 2
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While the number is being tested for primality,
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\&\fBBN_GENCB_call(cb, 1, j)\fR is called as described below.
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.IP "\(bu" 2
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When a prime has been found, \fBBN_GENCB_call(cb, 2, i)\fR is called.
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.IP "\(bu" 2
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The callers of \fBBN_generate_prime_ex()\fR may call \fBBN_GENCB_call(cb, i, j)\fR with
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other values as described in their respective man pages; see \*(L"\s-1SEE ALSO\*(R"\s0.
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.PP
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The prime may have to fulfill additional requirements for use in
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Diffie-Hellman key exchange:
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.PP
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If \fBadd\fR is not \fB\s-1NULL\s0\fR, the prime will fulfill the condition p % \fBadd\fR
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== \fBrem\fR (p % \fBadd\fR == 1 if \fBrem\fR == \fB\s-1NULL\s0\fR) in order to suit a given
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generator.
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.PP
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If \fBsafe\fR is true, it will be a safe prime (i.e. a prime p so
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that (p\-1)/2 is also prime). If \fBsafe\fR is true, and \fBrem\fR == \fB\s-1NULL\s0\fR
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the condition will be p % \fBadd\fR == 3.
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It is recommended that \fBadd\fR is a multiple of 4.
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.PP
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The random generator must be seeded prior to calling \fBBN_generate_prime_ex()\fR.
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If the automatic seeding or reseeding of the OpenSSL \s-1CSPRNG\s0 fails due to
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external circumstances (see \s-1\fBRAND\s0\fR\|(7)), the operation will fail.
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.PP
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\&\fBBN_is_prime_ex()\fR and \fBBN_is_prime_fasttest_ex()\fR test if the number \fBp\fR is
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prime. The following tests are performed until one of them shows that
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\&\fBp\fR is composite; if \fBp\fR passes all these tests, it is considered
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prime.
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.PP
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\&\fBBN_is_prime_fasttest_ex()\fR, when called with \fBdo_trial_division == 1\fR,
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first attempts trial division by a number of small primes;
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if no divisors are found by this test and \fBcb\fR is not \fB\s-1NULL\s0\fR,
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\&\fBBN_GENCB_call(cb, 1, \-1)\fR is called.
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If \fBdo_trial_division == 0\fR, this test is skipped.
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.PP
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Both \fBBN_is_prime_ex()\fR and \fBBN_is_prime_fasttest_ex()\fR perform a Miller-Rabin
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probabilistic primality test with \fBnchecks\fR iterations. If
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\&\fBnchecks == BN_prime_checks\fR, a number of iterations is used that
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yields a false positive rate of at most 2^\-64 for random input.
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The error rate depends on the size of the prime and goes down for bigger primes.
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The rate is 2^\-80 starting at 308 bits, 2^\-112 at 852 bits, 2^\-128 at 1080 bits,
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2^\-192 at 3747 bits and 2^\-256 at 6394 bits.
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.PP
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When the source of the prime is not random or not trusted, the number
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of checks needs to be much higher to reach the same level of assurance:
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It should equal half of the targeted security level in bits (rounded up to the
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next integer if necessary).
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For instance, to reach the 128 bit security level, \fBnchecks\fR should be set to
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64.
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.PP
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If \fBcb\fR is not \fB\s-1NULL\s0\fR, \fBBN_GENCB_call(cb, 1, j)\fR is called
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after the j\-th iteration (j = 0, 1, ...). \fBctx\fR is a
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pre-allocated \fB\s-1BN_CTX\s0\fR (to save the overhead of allocating and
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freeing the structure in a loop), or \fB\s-1NULL\s0\fR.
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.PP
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\&\fBBN_GENCB_call()\fR calls the callback function held in the \fB\s-1BN_GENCB\s0\fR structure
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and passes the ints \fBa\fR and \fBb\fR as arguments. There are two types of
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\&\fB\s-1BN_GENCB\s0\fR structure that are supported: \*(L"new\*(R" style and \*(L"old\*(R" style. New
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programs should prefer the \*(L"new\*(R" style, whilst the \*(L"old\*(R" style is provided
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for backwards compatibility purposes.
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.PP
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A \fB\s-1BN_GENCB\s0\fR structure should be created through a call to \fBBN_GENCB_new()\fR,
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and freed through a call to \fBBN_GENCB_free()\fR.
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.PP
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For \*(L"new\*(R" style callbacks a \s-1BN_GENCB\s0 structure should be initialised with a
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call to \fBBN_GENCB_set()\fR, where \fBgencb\fR is a \fB\s-1BN_GENCB\s0 *\fR, \fBcallback\fR is of
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type \fBint (*callback)(int, int, \s-1BN_GENCB\s0 *)\fR and \fBcb_arg\fR is a \fBvoid *\fR.
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\&\*(L"Old\*(R" style callbacks are the same except they are initialised with a call
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to \fBBN_GENCB_set_old()\fR and \fBcallback\fR is of type
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\&\fBvoid (*callback)(int, int, void *)\fR.
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.PP
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A callback is invoked through a call to \fBBN_GENCB_call\fR. This will check
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the type of the callback and will invoke \fBcallback(a, b, gencb)\fR for new
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style callbacks or \fBcallback(a, b, cb_arg)\fR for old style.
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.PP
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It is possible to obtain the argument associated with a \s-1BN_GENCB\s0 structure
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(set via a call to BN_GENCB_set or BN_GENCB_set_old) using BN_GENCB_get_arg.
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.PP
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\&\fBBN_generate_prime()\fR (deprecated) works in the same way as
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\&\fBBN_generate_prime_ex()\fR but expects an old-style callback function
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directly in the \fBcallback\fR parameter, and an argument to pass to it in
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the \fBcb_arg\fR. \fBBN_is_prime()\fR and \fBBN_is_prime_fasttest()\fR
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can similarly be compared to \fBBN_is_prime_ex()\fR and
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\&\fBBN_is_prime_fasttest_ex()\fR, respectively.
|
||
|
|
.SH "RETURN VALUES"
|
||
|
|
.IX Header "RETURN VALUES"
|
||
|
|
\&\fBBN_generate_prime_ex()\fR return 1 on success or 0 on error.
|
||
|
|
.PP
|
||
|
|
\&\fBBN_is_prime_ex()\fR, \fBBN_is_prime_fasttest_ex()\fR, \fBBN_is_prime()\fR and
|
||
|
|
\&\fBBN_is_prime_fasttest()\fR return 0 if the number is composite, 1 if it is
|
||
|
|
prime with an error probability of less than 0.25^\fBnchecks\fR, and
|
||
|
|
\&\-1 on error.
|
||
|
|
.PP
|
||
|
|
\&\fBBN_generate_prime()\fR returns the prime number on success, \fB\s-1NULL\s0\fR otherwise.
|
||
|
|
.PP
|
||
|
|
BN_GENCB_new returns a pointer to a \s-1BN_GENCB\s0 structure on success, or \fB\s-1NULL\s0\fR
|
||
|
|
otherwise.
|
||
|
|
.PP
|
||
|
|
BN_GENCB_get_arg returns the argument previously associated with a \s-1BN_GENCB\s0
|
||
|
|
structure.
|
||
|
|
.PP
|
||
|
|
Callback functions should return 1 on success or 0 on error.
|
||
|
|
.PP
|
||
|
|
The error codes can be obtained by \fBERR_get_error\fR\|(3).
|
||
|
|
.SH "REMOVED FUNCTIONALITY"
|
||
|
|
.IX Header "REMOVED FUNCTIONALITY"
|
||
|
|
As of OpenSSL 1.1.0 it is no longer possible to create a \s-1BN_GENCB\s0 structure
|
||
|
|
directly, as in:
|
||
|
|
.PP
|
||
|
|
.Vb 1
|
||
|
|
\& BN_GENCB callback;
|
||
|
|
.Ve
|
||
|
|
.PP
|
||
|
|
Instead applications should create a \s-1BN_GENCB\s0 structure using BN_GENCB_new:
|
||
|
|
.PP
|
||
|
|
.Vb 6
|
||
|
|
\& BN_GENCB *callback;
|
||
|
|
\& callback = BN_GENCB_new();
|
||
|
|
\& if (!callback)
|
||
|
|
\& /* error */
|
||
|
|
\& ...
|
||
|
|
\& BN_GENCB_free(callback);
|
||
|
|
.Ve
|
||
|
|
.SH "SEE ALSO"
|
||
|
|
.IX Header "SEE ALSO"
|
||
|
|
\&\fBDH_generate_parameters\fR\|(3), \fBDSA_generate_parameters\fR\|(3),
|
||
|
|
\&\fBRSA_generate_key\fR\|(3), \fBERR_get_error\fR\|(3), \fBRAND_bytes\fR\|(3),
|
||
|
|
\&\s-1\fBRAND\s0\fR\|(7)
|
||
|
|
.SH "HISTORY"
|
||
|
|
.IX Header "HISTORY"
|
||
|
|
The \fBBN_GENCB_new()\fR, \fBBN_GENCB_free()\fR,
|
||
|
|
and \fBBN_GENCB_get_arg()\fR functions were added in OpenSSL 1.1.0.
|
||
|
|
.SH "COPYRIGHT"
|
||
|
|
.IX Header "COPYRIGHT"
|
||
|
|
Copyright 2000\-2020 The OpenSSL Project Authors. All Rights Reserved.
|
||
|
|
.PP
|
||
|
|
Licensed under the OpenSSL license (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>.
|