7.11 Selecting cryptographic key sizes

Because many algorithms are involved in TLS, it is not easy to set a consistent security level. For this reason in Table 7.5 we present some correspondence between key sizes of symmetric algorithms and public key algorithms based on [ECRYPT]. Those can be used to generate certificates with appropriate key sizes as well as select parameters for Diffie-Hellman and SRP authentication.

Table 7.5: 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 [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:

• gnutls_sec_param_to_pk_bits

• gnutls_pk_bits_to_sec_param

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.

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