Weak Equivalents for Nonlinear Filtering Functions

TL;DR

This paper explores the equivalence of nonlinear filtering functions applied to LFSRs, providing methods to compute weaker equivalents that can be used to assess cryptographic security.

Contribution

It introduces a novel approach to compute weaker equivalents of nonlinear filters using reciprocal LFSRs, aiding cryptanalysis of sequence generators.

Findings

Weaker equivalents can be computed for nonlinear filters.

Reciprocal LFSRs facilitate the analysis of filter equivalences.

Weakest equivalents are crucial for evaluating cryptographic resistance.

Abstract

The application of a nonlinear filtering function to a Linear Feedback Shift Register (LFSR) is a general technique for designing pseudorandom sequence generators with cryptographic application. In this paper, we investigate the equivalence between different nonlinear filtering functions applied to distinct LFSRs. It is a well known fact that given a binary sequence generated from a pair (nonlinear filtering function, LFSR), the same sequence can be generated from any other LFSR of the same length by using another filtering function. However, until now no solution has been found for the problem of computing such an equivalent. This paper analyzes the specific case in which the reciprocal LFSR of a given register is used to generate an equivalent of the original nonlinear filtering function. The main advantage of the contribution is that weaker equivalents can be computed for any nonlinear filter, in the sense that such equivalents could be used to cryptanalyze apparently secure generators. Consequently, to evaluate the cryptographic resistance of a sequence generator, the weakest equivalent cipher should be determined and not only a particular instance.