Observer Attack on Stream Ciphers

Abstract

This paper proposes an application of a new observer theory for non-linear systems developed previously to solve the Cryptanalysis problem of a special class of pseudorandom generators which are commonly used in Cryptography. The Cryptanalysis problem addressed here is that of the recovery of internal state of the non-linear dynamic stream generator from the output stream. The proposed methodology is termed as observability attack. It is also shown that for a special class of generators, the computations are of complexity O(D4) in pre-computation and of O(D) for online computation, where D = σdi=0(n i) for this class of stream generators with n states and d the degree of the output function. The attack is technically applicable over general finite fields as well as most dynamic systems arising from models of stream ciphers and appropriate bounds on computation are estimated. From these complexity bounds, it follows that this attack is feasible in realistic cases and gives important estimates of time and memory resources required for Cryptanalysis of a class of stream ciphers.