Paper 2007/031 Original: eprint.iacr.org/2007/031 ↗

Improved Security Analysis of PMAC

Abstract

In this paper we provide a simple, concrete and improved security analysis of {\bf PMAC}, a Parallelizable Message Authentication Code. We show that the advantage of any distinguisher for {\bf PMAC} based on a random permutation is at most $\mathbf{\frac{5q\sigma - 3.5 q^2}{2^n}}$, where $\sigma$ is the total number of message blocks in all $q$ queries made by the distinguisher. In the original paper by Black and Rogaway in Eurocrypt-2002, the bound was $\frac{(\sigma+1)^2}{2^{n-1}}$. Very recently, Minematsu and Matsushima in FSE-2007, have provided a bound $\frac{10\ell q^2}{2^n}$ where $\ell$ is the maximum block length of all messages queried by the distinguisher. Our new bound is better than both original and recently proposed bound and guarantees much more security of PMAC. We also have provided a complete, independent and simple combinatorial proof. This proof idea may help us to find a similar result for other MAC algorithms.