One-key compression function based MAC with security beyond birthday bound

Abstract

Gaži et al. [CRYPTO 2014] analyzed the NI-MAC construction proposed by An and Bellare [CRYPTO 1999] and gave a tight birthday-bound of O(ℓq2/2n), as an improvement over the previous bound of O(ℓ2q2/2n). 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(q2ℓ2/22n) provided ℓ ≤ 2n/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(ℓq2/22n) that uses an extra mask, and requires a storage space to store the mask. However, our proposed construction NI+ does not require any extra mask and thereby reduces the state size compared to Yasuda’s proposal [FSE 2008] with providing the same order of security bound for light-weight applications.