Fast Near Collision Attack on the Grain v1 Stream Cipher

Modern stream ciphers often adopt a large internal state to resist various attacks, where the cryptanalysts have to deal with a large number of variables when mounting state recovery attacks. In this paper, we propose a general new cryptanalytic method on stream ciphers, called fast near collision attack, to address this situation. It combines a near collision property with the divide-and-conquer strategy so that only subsets of the internal state, associated with different keystream vectors, are recovered first and merged carefully later to retrieve the full large internal state. A self-contained method is introduced and improved to derive the target subset of the internal state from the partial state difference efficiently. As an application, we propose a new key recovery attack on Grain v1, one of the 7 finalists selected by the eSTREAM project, in the single-key setting. Both the pre-computation and the online phases are tailored according to its internal structure, to provide an attack for any fixed IV in \(2^{75.7}\) cipher ticks after the pre-computation of \(2^{8.1}\) cipher ticks, given \(2^{28}\)-bit memory and about \(2^{19}\) keystream bits. Practical experiments on Grain v1 itself whenever possible and on a 80-bit reduced version confirmed our results.