A matrix approach for FCSR automata

LFSRs are primitives widely used in information theory, coding theory and cryptography. However since 2002, they have faced algebraic attacks. To avoid this kind of attacks, FCSRs have been proposed as an alternative in [ 2 – 4 ]. In this paper, we first give a general representation of 2-adic automata using a traditional matrix representation. We then explore the special case of binary and ternary automata. We also study the complexity in terms of memory to implement such automata. Finally, we expose some proposed FCSR constructions for hardware and software oriented stream ciphers.