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Title:
One-Key Compression Function Based MAC with Security beyond Birthday Bound
Authors: Avijit Dutta, Mridul Nandi, 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 \leq 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 O(\ell q^2/2^{2n}) 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
ePrint: https://eprint.iacr.org/2015/1016
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