Multiple Modular Additions and Crossword Puzzle Attack on NLSv2

NLS is a stream cipher which was submitted to eSTREAM project. A linear distinguishing attack against NLS was presented by Cho and Pieprzyk, which was called as Crossword Puzzle attack. NLSv2 is the tweak version of NLS which aims mainly at avoiding the CP attack. In this paper, a new distinguishing attack against NLSv2 is presented. The attack exploits high correlation amongst neighboring bits of the cipher. The paper first shows that the modular addition preserves pairwise correlations as demonstrated by existence of linear approximations with large biases. Next it shows how to combine these results with the existence of high correlation between bits 29 and 30 of the S-box to obtain a distinguisher whose bias is around 2. Consequently, we claim that NLSv2 is distinguishable from a random stream cipher after observing around 2 keystream words.