sizes. we present some correspondence between key sizes of
symmetric algorithms and public key algorithms based on [*note
ECRYPT::].  Those can be used to generate certificates with appropriate
key sizes as well as select parameters for Diffie-Hellman and SRP
authentication.

SecurityRSA, DH   ECC     Security       Description
bits    and SRP   key     parameter      
        parameter size    (profile)
        size
-----------------------------------------------------------------
<64     <768      <128    ‘INSECURE’     Considered to be
                                         insecure
                                         
64      768       128     ‘VERY WEAK’    Short term protection
                                         against individuals
                                         
72      1008      160     ‘WEAK’         Short term protection
                                         against small
                                         organizations
                                         
80      1024      160     ‘LOW’          Very short term
                                         protection against
                                         agencies (corresponds
                                         to ENISA legacy
                                         level)
                                         
96      1776      192     ‘LEGACY’       Legacy standard level
                                         
112     2048      224     ‘MEDIUM’       Medium-term
                                         protection
                                         
128     3072      256     ‘HIGH’         Long term protection
                                         (corresponds to ENISA
                                         future level)
                                         
192     8192      384     ‘ULTRA’        Even longer term
                                         protection
                                         
256     15424     512     ‘FUTURE’       Foreseeable future
                                         

Table 6.7: Key sizes and security parameters.

The first column provides a security parameter in a number of bits.
This gives an indication of the number of combinations to be tried by an
adversary to brute force a key.  For example to test all possible keys
in a 112 bit security parameter 2^{112} combinations have to be tried.
For today's technology this is infeasible.  The next two columns
correlate the security parameter with actual bit sizes of parameters for
DH, RSA, SRP and ECC algorithms.  A mapping to ‘gnutls_sec_param_t’
value is given for each security parameter, on the next column, and
finally a brief description of the level.

Note, however, that the values suggested here are nothing more than an
educated guess that is valid today.  There are no guarantees that an
algorithm will remain unbreakable or that these values will remain
constant in time.  There could be scientific breakthroughs that cannot
be predicted or total failure of the current public key systems by
quantum computers.  On the other hand though the cryptosystems used in
TLS are selected in a conservative way and such catastrophic
breakthroughs or failures are believed to be unlikely.  The NIST
publication SP 800-57 [*note NISTSP80057::] contains a similar table.

When using GnuTLS and a decision on bit sizes for a public key algorithm
is required, use of the following functions is recommended:

 -- Function: unsigned int gnutls_sec_param_to_pk_bits
          (gnutls_pk_algorithm_t ALGO, gnutls_sec_param_t PARAM)
     ALGO: is a public key algorithm

     PARAM: is a security parameter

     When generating private and public key pairs a difficult question
     is which size of "bits" the modulus will be in RSA and the group
     size in DSA. The easy answer is 1024, which is also wrong.  This
     function will convert a human understandable security parameter to
     an appropriate size for the specific algorithm.

     *Returns:* The number of bits, or (0).

     *Since:* 2.12.0

 -- Function: gnutls_sec_param_t gnutls_pk_bits_to_sec_param
          (gnutls_pk_algorithm_t ALGO, unsigned int BITS)
     ALGO: is a public key algorithm

     BITS: is the number of bits

     This is the inverse of ‘gnutls_sec_param_to_pk_bits()’ .  Given an
     algorithm and the number of bits, it will return the security
     parameter.  This is a rough indication.

     *Returns:* The security parameter.

     *Since:* 2.12.0

Those functions will convert a human understandable security parameter
of ‘gnutls_sec_param_t’ type, to a number of bits suitable for a public
key algorithm.

‘CONST CHAR * *note gnutls_sec_param_get_name:: (gnutls_sec_param_t PARAM)’

The following functions will set the minimum acceptable group size for
Diffie-Hellman and SRP authentication.
‘VOID *note gnutls_dh_set_prime_bits:: (gnutls_session_t SESSION, unsigned int BITS)’
‘VOID *note gnutls_srp_set_prime_bits:: (gnutls_session_t SESSION, unsigned int BITS)’

