## Cryptology ePrint Archive: Report 2003/082

Stronger Security Bounds for OMAC, TMAC and XCBC

Tetsu Iwata and Kaoru Kurosawa

Abstract: OMAC, TMAC and XCBC are CBC-type MAC schemes which are provably secure for arbitrary message length. In this paper, we present a more tight upper bound on ${\tt Adv}^{\sf mac}$ for each scheme, where ${\tt Adv}^{\sf mac}$ denotes the maximum success (forgery) probability of adversaries. Our bounds are expressed in terms of the \textit{total length} of all queries of an adversary to the MAC generation oracle while the previous bounds are expressed in terms of the \textit{maximum length} of each query. In particular, a significant improvement occurs if the lengths of queries are heavily unbalanced.

Category / Keywords: secret-key cryptography / modes of operation, message authentication codes, block cipher, provable security.