382 lines
14 KiB
Plaintext
382 lines
14 KiB
Plaintext
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.\" ========================================================================
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.\"
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.IX Title "BN_GENERATE_PRIME 3ossl"
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.TH BN_GENERATE_PRIME 3ossl "2024-01-30" "3.2.1" "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_ex2, BN_generate_prime_ex, BN_is_prime_ex, BN_check_prime,
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BN_is_prime_fasttest_ex, BN_GENCB_call, BN_GENCB_new, BN_GENCB_free,
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BN_GENCB_set_old, BN_GENCB_set, BN_GENCB_get_arg, BN_generate_prime,
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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_ex2(BIGNUM *ret, int bits, int safe,
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\& const BIGNUM *add, const BIGNUM *rem, BN_GENCB *cb,
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\& BN_CTX *ctx);
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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_check_prime(const BIGNUM *p, BN_CTX *ctx, 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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The following functions have been deprecated since OpenSSL 0.9.8, and can be
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hidden entirely by defining \fB\s-1OPENSSL_API_COMPAT\s0\fR with a suitable version value,
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see \fIopenssl_user_macros\fR\|(7):
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.PP
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.Vb 3
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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 *p, int nchecks,
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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 *p, int nchecks,
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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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.Ve
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.PP
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The following functions have been deprecated since OpenSSL 3.0, and can be
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hidden entirely by defining \fB\s-1OPENSSL_API_COMPAT\s0\fR with a suitable version value,
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see \fIopenssl_user_macros\fR\|(7):
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.PP
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.Vb 1
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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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.Ve
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.SH "DESCRIPTION"
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.IX Header "DESCRIPTION"
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\&\fIBN_generate_prime_ex2()\fR generates a pseudo-random prime number of
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at least bit length \fBbits\fR using the \s-1BN_CTX\s0 provided in \fBctx\fR. The value of
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\&\fBctx\fR must not be \s-1NULL.\s0
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.PP
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The returned number is probably prime with a negligible error.
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The maximum error rate is 2^\-128.
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It's 2^\-287 for a 512 bit prime, 2^\-435 for a 1024 bit prime,
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2^\-648 for a 2048 bit prime, and lower than 2^\-882 for primes larger
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than 2048 bit.
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.PP
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If \fBadd\fR is \fB\s-1NULL\s0\fR the returned prime number will have exact bit
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length \fBbits\fR with the top most two 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 \fIBN_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 \fIBN_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\fIRAND\s0\fR\|(7)), the operation will fail.
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The random number generator configured for the \s-1OSSL_LIB_CTX\s0 associated with
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\&\fBctx\fR will be used.
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.PP
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\&\fIBN_generate_prime_ex()\fR is the same as \fIBN_generate_prime_ex2()\fR except that no
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\&\fBctx\fR parameter is passed.
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In this case the random number generator associated with the default \s-1OSSL_LIB_CTX\s0
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will be used.
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.PP
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\&\fIBN_check_prime()\fR, \fIBN_is_prime_ex()\fR, \fIBN_is_prime_fasttest_ex()\fR, \fIBN_is_prime()\fR
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and \fIBN_is_prime_fasttest()\fR test if the number \fBp\fR is prime.
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The functions tests until one of the tests shows that \fBp\fR is composite,
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or all the tests passed.
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If \fBp\fR passes all these tests, it is considered a probable prime.
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.PP
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The test performed on \fBp\fR are trial division by a number of small primes
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and rounds of the of the Miller-Rabin probabilistic primality test.
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.PP
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The functions do at least 64 rounds of the Miller-Rabin test giving a maximum
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false positive rate of 2^\-128.
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If the size of \fBp\fR is more than 2048 bits, they do at least 128 rounds
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giving a maximum false positive rate of 2^\-256.
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.PP
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If \fBnchecks\fR is larger than the minimum above (64 or 128), \fBnchecks\fR
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rounds of the Miller-Rabin test will be done.
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.PP
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If \fBdo_trial_division\fR set to \fB0\fR, the trial division will be skipped.
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\&\fIBN_is_prime_ex()\fR and \fIBN_is_prime()\fR always skip the trial division.
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.PP
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\&\fIBN_is_prime_ex()\fR, \fIBN_is_prime_fasttest_ex()\fR, \fIBN_is_prime()\fR
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and \fIBN_is_prime_fasttest()\fR are deprecated.
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.PP
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\&\fIBN_is_prime_fasttest()\fR and \fIBN_is_prime()\fR behave just like
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\&\fIBN_is_prime_fasttest_ex()\fR and \fIBN_is_prime_ex()\fR respectively, but with the old
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style call back.
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.PP
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\&\fBctx\fR is a preallocated \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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If the trial division is done, and no divisors are found and \fBcb\fR
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is not \fB\s-1NULL\s0\fR, \fBBN_GENCB_call(cb, 1, \-1)\fR is called.
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.PP
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After each round of the Miller-Rabin probabilistic primality test,
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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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with \fBj\fR the iteration (j = 0, 1, ...).
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.PP
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\&\fIBN_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 \fIBN_GENCB_new()\fR,
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and freed through a call to \fIBN_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 \fIBN_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 \fIBN_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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\&\fIBN_generate_prime()\fR (deprecated) works in the same way as
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\&\fIBN_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. \fIBN_is_prime()\fR and \fIBN_is_prime_fasttest()\fR
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can similarly be compared to \fIBN_is_prime_ex()\fR and
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\&\fIBN_is_prime_fasttest_ex()\fR, respectively.
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.SH "RETURN VALUES"
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.IX Header "RETURN VALUES"
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\&\fIBN_generate_prime_ex()\fR return 1 on success or 0 on error.
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.PP
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\&\fIBN_is_prime_ex()\fR, \fIBN_is_prime_fasttest_ex()\fR, \fIBN_is_prime()\fR,
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\&\fIBN_is_prime_fasttest()\fR and BN_check_prime return 0 if the number is composite,
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1 if it is prime with an error probability of less than 0.25^\fBnchecks\fR, and
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\&\-1 on error.
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.PP
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\&\fIBN_generate_prime()\fR returns the prime number on success, \fB\s-1NULL\s0\fR otherwise.
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.PP
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BN_GENCB_new returns a pointer to a \s-1BN_GENCB\s0 structure on success, or \fB\s-1NULL\s0\fR
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otherwise.
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.PP
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BN_GENCB_get_arg returns the argument previously associated with a \s-1BN_GENCB\s0
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structure.
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.PP
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Callback functions should return 1 on success or 0 on error.
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.PP
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The error codes can be obtained by \fIERR_get_error\fR\|(3).
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.SH "REMOVED FUNCTIONALITY"
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.IX Header "REMOVED FUNCTIONALITY"
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As of OpenSSL 1.1.0 it is no longer possible to create a \s-1BN_GENCB\s0 structure
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directly, as in:
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.PP
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.Vb 1
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\& BN_GENCB callback;
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.Ve
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.PP
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Instead applications should create a \s-1BN_GENCB\s0 structure using BN_GENCB_new:
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.PP
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.Vb 6
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\& BN_GENCB *callback;
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\& callback = BN_GENCB_new();
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\& if (!callback)
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\& /* error */
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\& ...
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\& BN_GENCB_free(callback);
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.Ve
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.SH "SEE ALSO"
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.IX Header "SEE ALSO"
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\&\fIDH_generate_parameters\fR\|(3), \fIDSA_generate_parameters\fR\|(3),
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\&\fIRSA_generate_key\fR\|(3), \fIERR_get_error\fR\|(3), \fIRAND_bytes\fR\|(3),
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\&\s-1\fIRAND\s0\fR\|(7)
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.SH "HISTORY"
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.IX Header "HISTORY"
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The \fIBN_is_prime_ex()\fR and \fIBN_is_prime_fasttest_ex()\fR functions were
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deprecated in OpenSSL 3.0.
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.PP
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The \fIBN_GENCB_new()\fR, \fIBN_GENCB_free()\fR,
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and \fIBN_GENCB_get_arg()\fR functions were added in OpenSSL 1.1.0.
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.PP
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\&\fIBN_check_prime()\fR was added in OpenSSL 3.0.
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.SH "COPYRIGHT"
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.IX Header "COPYRIGHT"
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Copyright 2000\-2021 The OpenSSL Project Authors. All Rights Reserved.
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.PP
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Licensed under the Apache License 2.0 (the \*(L"License\*(R"). You may not use
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this file except in compliance with the License. You can obtain a copy
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in the file \s-1LICENSE\s0 in the source distribution or at
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<https://www.openssl.org/source/license.html>.
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