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**2007/032**

**Title:**

An improved collision probability for CBC-MAC and PMAC

**Authors:**
Avradip Mandal, Mridul Nandi

**Abstract:**

In this paper we compute the collision probability of CBC-MAC for suitably chosen messages. We show that the probability is \Omega(\ell q^2/N) where \ell 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^2/N). This improved collision probability will help us to have an efficient distinguishing attack and MAC-forgery attack. We also show collision probability for PMAC with collision probability \Omega(q^2/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, TMAC, OMAC etc. We hope this approach will help us to calculate related probabilities.

**ePrint:**
https://eprint.iacr.org/2007/032

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