## Cryptology ePrint Archive: Report 2005/267

Stream Cipher Design based on Jumping Finite State Machines

Cees J.A. Jansen

Abstract: This paper presents a new way of constructing binary cascade clock-controlled LFSR sequence generators as building blocks for stream ciphers. In these constructions the bottleneck of multiple clocking shift registers is removed, resulting in so called jump-controlled sequence generators, that operate in a single clock pulse and are most efficient to implement. The constructions make use of special properties of irreducible polynomials over finite fields. This paper also aims at giving insight into the mathematical theory behind the constructions. To this end, theory is developed and many of the rich set of properties of irreducible polynomials over GF(2), such as periods, jump indices and the number and cardinalities of various classes of polynomials are presented.

Category / Keywords: secret-key cryptography / LFSR, finite state machine, sequence generation, clock-control, irreducible polynomial, transition matrix, jump index, dual polynomial

Publication Info: Revised and extended version of papers at RECSI-VII 2002 and SASC 2004 containing all proofs