Convolutional Codes based FCA when Combiner Function is 1-CI

Convolution Code based Fast Correlation Attacks (FCA) are a powerful class of attacks on stream ciphers. Thus stream ciphers are designed so that combiner function is correlation immune. In this paper we propose a method to apply Convolution Code based FCA when the combiner function is first order correlation immune (1-CI) but not 2-CI. We apply the attack on a pair of LFSRs whose sum sequence is correlated to key-stream. Instead of directly computing parity checks of equivalent LFSR for the sum sequence, we collect the parity checks of the individual LFSRs into two sets and from the cross product of the set of parity checks, select those pairs in which the two highest degree terms in both the parity checks are identical. These pairs of parity checks are used for setting up the Viterbi decoding phase of the FCA. The proposed method is more efficient than the direct FCA using the product of feedback polynomials of LFSRs. KeywordsLFSR, Viterbi decoding, Convolutional code, Correlation attack, Correlation immune, Combiner function.