Conditional differential attacks on Grain-128a stream cipher

Abstract

The well-known stream cipher Grain-128a is the new version of Grain-128. While Grain-128 is vulnerable against several introduced attacks, Grain-128a is claimed to be secure against all known attacks and observations on Grain-128. So far the only published single-key attack on Grain-128a is the conditional differential cryptanalysis proposed by Michael Lehmann et al. at CANS 2012. In their analysis, a distinguishing attack on 189-round Grain-128a in a weak-key setting was proposed. In this study, the authors present two new conditional differential attacks on Grain-128a, i.e. attack A and attack B. In attack A, the authors successfully retrieve 18 secret key expressions for 169-round Grain-128a. To the best of our knowledge, attack A is the first attack to retrieve secret key expressions for reduced Grain-128a. In attack B, the authors extend the distinguishing attack against Grain-128a up to 195 rounds in a weak-key setting. Thus far, attack B is the best known attack for reduced Grain-128a as far as the number of rounds attacked is concerned. Hopefully, the authors’ reflections on the design of Grain-128a provide insights on such compact stream ciphers.