Algebraic and Correlation Attacks against Linearly Filtered Non Linear Feedback Shift Registers

Abstract

The filter generator is a well known and extensively studied stream cipher construction. It consists of a Linear Feedback Shift Register (LFSR) filtered by a non linear Boolean function. In this paper we focus on the dual construction, namely a linearly filtered Non linear Feedback Shift Register (NFSR). We show that the existing algebraic and correlation attacks against the filter generator can be transposed to mount algebraic or correlation attacks against this dual construction. We investigate such attacks and extend them to the case where a linearly filtered NFSR is combined linearly with one or more non linearly filtered LFSRs. We apply our algebraic attack to a modified version of Grain-128, resulting in an attack requiring 2105 computations and 239 keystream bits. Even though this attack does not apply to the original Grain-128, it shows that the use of a NFSR is not sufficient to avoid all algebraic attacks.