Cryptanalysis of LFSR-encrypted codes with unknown combining function

Abstract

This paper proposes an approach for the cryptanalysis of stream ciphers where the encryption is performed by multiple linear feedback shift registers (LFSR) combined by a nonlinear function. The attack assumes no knowledge of either the LFSR initial conditions or the combining function. Thus, the actual architecture of the encryption system can be arbitrary. The attack is also generalized for the situation when the combining function is correlation immune of any particular order. This is in direct contrast with the existing methods which depend heavily not only on the correlation between the output of a particular LFSR and the ciphertext but also on the actual configuration of the encryption system used. Thus, the proposed method is the first ciphertext only attack in the true sense of the phrase. The paper also gives theoretical estimates of the cipherlengths involved in the determination of the initial conditions as well as estimation of the combining function.