Cryptology ePrint Archive: Report 2015/1016

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

Avijit Dutta and 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 $\ell \leq 2^{n/4}$. 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

Category / Keywords: Beyond Birthday, MAC, NI, Structure-Graph.

Original Publication (with minor differences): ACISP 2016

Date: received 20 Oct 2015, last revised 20 Apr 2016

Contact author: avirocks dutta13 at gmail com, goutam paul@isical ac in, mridul nandi@gmail com

Available format(s): PDF | BibTeX Citation

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

Version: 20160420:141857 (All versions of this report)

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