The Decimated Sample Based Improved Algebraic Attacks on the Nonlinear Filters

Abstract

This paper proposes an improved approach for cryptanalysis of keystream generators based on a composition of a linear finite state machine (LFSM) and nonlinear mapping. The main feature of the proposed approach is that it is based on identification and selection for further processing certain suitable positions in the given sample so that only the decimated sample elements are relevant for the attacking. In a number of scenarios this yields a significant gain in the performance sometimes at the expense of a longer sample required or/and the pre-processing cost. The proposed approach employs novel methods for constructing the underlying overdefined system of equations relevant for the attacks and solving the system under a set of the hypothesis. Oppositely to the previously reported methods, the proposed ones also identify and use certain characteristics of the LFSM state-transition matrix in order to reduce the nonlinearity of the system. The novel construction of the equations yields a possibility for the trade-off between the required sample, pre-processing and processing complexity of the cryptanalysis. The pre-processing phase of the developed algorithm for cryptanalysis yields a collection of the output bit positions which are suitable for reducing the equations nonlinearity. The processing phase employs the output bits from the identified collection and it includes an exhaustive search over a subset of the secret key bits.