Extended models for message authentication

In recent years, several side channel attacks have been given to some provably secure Message Authentication (MA) schemes. These side channel attacks help adversaries to get some information about secret values (such like internal states) in MA-schemes, which is beyond the original models consider about, so the provable security completely lose. To fix this problem, we extend the original models for message authentication, taking the information about secret values in MA-schemes into account. The extended models can not only provide a framework under which one can discuss security of MA-schemes facing side channel attacks, but also give us an insight view of MA-schemes. As an example, we consider the security of f 9 (a MA-scheme in 3GPP) and its variants in an extended model. The result helps us to know f 9better, e.g. howtouse it safely and what measures need to be taken in case of potential attacks.