NAME    [Toc]    [Back]

       BN_generate_prime,   BN_is_prime,  BN_is_prime_fasttest  -
       Generate primes and test for primality

SYNOPSIS    [Toc]    [Back]

       #include <openssl/bn.h>

       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, void (*callback)(int,
       int,   void   *),   BN_CTX   *ctx,  void  *cb_arg  );  int
       BN_is_prime_fasttest(
               const BIGNUM *a, int checks, void (*callback)(int,
       int,   void   *),   BN_CTX   *ctx,   void   *cb_arg,   int
       do_trial_division );

DESCRIPTION    [Toc]    [Back]

       The BN_generate_prime() function generates a pseudo-random
       prime  number  of num bits. If ret is not NULL, it will be
       used to store the number.

       If callback is not NULL, it is called  as  follows:  callback(0,
  i,  cb_arg)  is  called after generating the i-th
       potential prime number.  While the number is being  tested
       for   primality,  callback(1,  j,  cb_arg)  is  called  as
       described below.  When a prime has been found, callback(2,
       i, cb_arg) is called.

       The  prime may have to fulfill additional requirements for
       use in Diffie-Hellman key exchange:

       If add is not NULL, the prime will fulfill the condition p
       %  add  ==  rem  (p % add == 1 if rem == NULL) 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).

       The  PRNG  must  be  seeded  prior  to  calling  BN_generate_prime().
 The prime number generation has a  negligible
       error probability.

       BN_is_prime()  and BN_is_prime_fasttest() test if the number
 a is prime.  The following tests are  performed  until
       one  of  them  shows  that a is composite; if a passes all
       these tests, it is considered prime.

       BN_is_prime_fasttest(), when called with do_trial_division
       ==  1,  first attempts trial division by a number of small
       primes; if no divisors are found by this test and callback
       is  not  NULL,  callback(1,  -1,  cb_arg)  is  called.  If
       do_trial_division == 0, this test is skipped.

       Both BN_is_prime() and  BN_is_prime_fasttest()  perform  a
       Miller-Rabin  probabilistic  primality  test  with  checks
       iterations. If checks == BN_prime_check, a number of iterations
  is  used  that  yields a false positive rate of at
       most 2^-80 for random input.

       If callback is not NULL, callback(1, j, cb_arg) is  called
       after  the  j-th iteration (j = 0, 1, ...).  ctx is a preallocated
 BN_CTX (to save the overhead of  allocating  and
       freeing the structure in a loop), or NULL.

RETURN VALUES    [Toc]    [Back]

       The  BN_generate_prime() function returns the prime number
       on success, NULL otherwise.

       The BN_is_prime() function returns 0 if the number is composite,
 1 if it is prime with an error probability of less
       than 0.25^checks, and -1 on error.

       The  error  codes   can   be   obtained   by   using   the
       ERR_get_error() function.

HISTORY    [Toc]    [Back]

       The   cb_arg   arguments  to  BN_generate_prime()  and  to
       BN_is_prime() were added in SSLeay 0.9.0.  The  ret  argument
 to BN_generate_prime() was added in SSLeay 0.9.1. The
       BN_is_prime_fasttest()  function  was  added  in   OpenSSL
       0.9.5.

SEE ALSO    [Toc]    [Back]

       Functions: bn(3), err(3), rand(3)



                                             BN_generate_prime(3)