Remarks on improved inversion attacks on nonlinear filter generators

Abstract

The subject of this paper are inversion attacks on stream ciphers (nonlinear filter generators), which were first introduced by Golić [3] and extended by Golić, Clark and Dawson [4]. These original attacks have computational complexity O(2^M), where M is the so-called "memory size" - distance between outer taps to filter function. In [6] we have proposed improved inversion attacks which have computational complexity O(2^{r-m}), where r denotes the length of the shift register and m denotes the largest gap between cells with taps to filter function or to connection polynomial. In this paper we describe further extension of our previous results obtained by considering shifts of the feedback polynomial which maximise the largest gap between cells with taps to filter function or to connection polynomial. We show that the previously proposed set of design criteria [3, 6] does not prevent the new version of improved inversion attack and we propose an additional criterion based on the relationship between positions of taps to filter function and positions of taps to the multiples of the connection polynomial.