Nonlinear equivalence of stream ciphers

Abstract

In this paper we investigate nonlinear equivalence of stream ciphers over a finite field, exemplified by the pure LFSR-based filter generator over . We define a nonlinear equivalence class consisting of filter generators of length n that generate a binary keystream of period dividing 2 n - 1, and investigate certain cryptographic properties of the ciphers in this class. We show that a number of important cryptographic properties, such as algebraic immunity and nonlinearity, are not invariant among elements of the same equivalence class. It follows that analysis of cipher-components in isolation presents some limitations, as it most often involves investigating cryptographic properties that vary among equivalent ciphers. Thus in order to assess the resistance of a cipher against a certain type of attack, one should in theory determine the weakest equivalent cipher and not only a particular instance. This is however likely to be a very difficult task, when we consider the size of the equivalence class for ciphers used in practice; therefore assessing the exact cryptographic properties of a cipher appears to be notoriously difficult. © 2010 Springer-Verlag.