Paper 2015/1016

One-Key Compression Function Based MAC with Security beyond Birthday Bound

Avijit Dutta, Mridul Nandi, and Goutam Paul

Abstract

Ga{\v z}i et al. [CRYPTO 2014] analyzed the NI-MAC construction proposed by An and Bellare [CRYPTO 1999] and gave a tight birthday-bound of $O(\ell q^2/2^n)$, as an improvement over the previous bound of $O({\ell }^2{q}^2/2^n)$. In this paper, we design a simple extension of NI-MAC, called NI${}^{+}$-MAC, and prove that it has security bound beyond birthday (BBB) of order $O(q^2{\ell }^2/2^{2n})$ provided $\ell \le 2^{n/4}$. Our construction not only lifts the security of NI-MAC beyond birthday, it also reduces the number of keys from 2 (NI uses 2 independent keys) to 1. Before this work, Yasuda had proposed [FSE 2008] a single fixed-keyed compression function based BBB-secure MAC with security bound $$ that uses an extra mask, requires a storage space to store the mask. However, our proposed construction NI$$ does not require any extra mask and thereby has reduced the state size compared to Yasuda's proposal [FSE 2008] with providing the same order of security bound for light-weight applications

Note: BBB in title expanded to full form. Some minor typos corrected. Publication info added.