On the fog of RSA key lengths: Verifying public key cryptography strength recommendations

Finite-field cryptography plays a major role in current cyberspace infrastructure. Most notable examples include the RSA public key cryptosystem based on the assumed difficulty of finding factorization of large integers in general; and Diffie-Hellman (DH) key exchange, based on the hardness of finding discrete logarithms in finite fields. In order to use strong enough parameters for cryptography intended to protect classified information, the hardness of these problems needs to be measured and associated with a security level (e.g. RESTRICTED and SECRET). This is, however, a multi-step, nation-dependent and usually classified process, with no unified understanding on how certain parameters should be measured. In this paper we investigate the public key length recommendations for RSA and DH, their background and reasoning. Based on this research, we suggest an updated method for the measurement of sufficient RSA and DH key sizes, and benchmark it against the public Finnish security level recommendation.