Feedback with carry shift registers and (in-depth) security of ciphers based on this primitive

This paper presents a mathematical model that describes the behaviour of frequency distribution of various patterns in binary I-sequences. This mathematical model is referred to as, I-distribution for binary I-sequences. The paper also reviews some conspicuous techniques of using I-sequences, generated by feedback with carry shift registers (FCSRs), as building blocks in stream ciphers. In order to thwart cryptanalytic attacks, these techniques rely on hiding the mathematical structures demarcated by I-distribution of binary I-sequences. Moreover, to gauge the efficacy of these techniques, an in-depth security analysis of FCSR-based ciphers is also presented. This analysis is based on Hell-Johansson and linearisation attacks on an eSTREAM candidate known as F-FCSR-H v2. Conceptual foundations of linearisation attacks in the perspective of FCSR-based stream ciphers are also presented in this paper. Moreover, the paper also presents approach-based comparative analysis between Hell-Johansson and linearisation attacks.