An improved collision probability for CBC-MAC and PMAC

In this paper we compute the coliision probability of CBC-MAC [3] for suitably chosen messages. We show that the probability is Ω(`q/N) where ` is the number of message block, N is the size of the domain and q is the total number of queries. For random oracle the probability is O(q/N). This improved collision prbability will help us to have an efficient distinguishing attack and MAC-forgery attack. We also show collision probability for PMAC with collision probability Ω(q/N) (strictly more than birth day bound). We have used a purely combinatorial approach to obtain this bound. The similar analysis can be made for other MAC like XCBC [5], TMAC [9], OMAC [7] etc. We hope this apporach will help us to calculate related probabilties.