Global Linear Complexity Analysis of Filter Keystream Generators

TL;DR

This paper introduces an efficient algorithm to compute lower bounds on the global linear complexity of nonlinearly filtered PN-sequences, demonstrating exponential growth in complexity for various filter generators.

Contribution

It presents a new logic-based algorithm applicable to any nonlinear filter with a maximum order term, broadening analysis capabilities for keystream generators.

Findings

Large lower bounds confirm exponential growth of linear complexity.

Algorithm suitable for software and hardware implementation.

Applicable to a wide range of nonlinear filter generators.

Abstract

An efficient algorithm for computing lower bounds on the global linear complexity of nonlinearly filtered PN-sequences is presented. The technique here developed is based exclusively on the realization of bit wise logic operations, which makes it appropriate for both software simulation and hardware implementation. The present algorithm can be applied to any arbitrary nonlinear function with a unique term of maximum order. Thus, the extent of its application for different types of filter generators is quite broad. Furthermore, emphasis is on the large lower bounds obtained that confirm the exponential growth of the global linear complexity for the class of nonlinearly filtered sequences.