Linearisation Attacks on FCSR-based Stream Ciphers

This paper presents a new class of cryptanalytic attacks, which are applicable against those binary additive synchronous stream ciphers, whose analysis theory is based on the properties of 2-adic numbers. These attacks are named as ‘Linearisation Attacks’. Linearisation attacks consist of three variants, which are referred as ‘Conventional Linearisation Attacks (CLAs)’, ‘Fast Linearisation Attacks (FLAs)’ and ‘Improved Linearisation Attacks (ILAs)’. The paper demonstrates, these new attacks against F-FCSR-H and an eSTREAM candidate F-FCSR-H v2 stream ciphers by presenting state recovery algorithms based on CLAs, FLAs and ILAs. The paper analyses the efficiency of these attacks in terms of data, time and memory complexities. The paper also presents a comparative analysis of these attacks, which shows that these variants provide a tradeoff of various complexity measures, i.e. data, time and memory complexities when compared with each other. Further more, the paper also presents a key recovery algorithm, which works in conjunction with the state recovery algorithms to recover the effective key used in these ciphers.