Using coding techniques to analyze weak feedback polynomials

Abstract

We consider a class of weak feedback polynomials for LFSRs in the nonlinear combiner. When feedback taps are located in small groups, a distinguishing attack can sometimes be improved considerably, compared to the common attack that uses low weight multiples. This class of weak polynomials was introduced in 2004 and the main property of the attack is that the noise variables are represented as vectors. We analyze the complexity of the attack using coding theory. We show that the groups of polynomials can be seen as generator polynomials of a convolutional code. Then, the problem of finding the attack complexity is equivalent to finding the minimum row distance of the corresponding generator matrix. A modified version of BEAST is used to search all encoders of memory up to 13. Moreover, we give a tight upper bound on the required size of the vectors in the attack.