On the generation of multiple ℓ-sequences from single WFCSR automaton for cryptographic applications

Feedback with carry shift registers (FCSRs) have been proposed as a promising alternate to the Linear feedback shift registers (LFSRs) in recent years. An approach based on traditional matrix representation has been proposed to design a Word oriented FCSR (WFCSR) automaton in [2], [3]. This automaton always generates a fixed ℓ-sequence, which is not desired for some cryptographic applications. In this paper, we present a new WFCSR automaton which enhances the traditional matrix representation by incorporating α-mask and/or β-mask operations on certain blocks (or words) of WFCSR automaton. By applying different α-mask and/or β-mask on certain blocks (or words) of WFCSR automaton, we can generate multiple ℓ-sequences without changing its structure. We can use the proposed approach to design WFCSR automaton in Fibonacci, Galois and Ring representations. The proposed WFCSR automaton can be adopted as a basic primitive to design any pseudo random number generator or stream cipher for cryptographic applications.