A Fast Correlation Attack via Unequal Error Correcting LDPC Codes

Abstract

In this paper, an improved fast correlation attack on stream ciphers is presented. The proposed technique is based on the construction of an unequal error protecting LDPC code from the LFSR output sequence. The unequal error protection allows to achieve lower bit-error probability for initial bits of the LFSR in compared to the rest of the output bits. We show that constructing the unequal error protecting code has also the advantage of reducing the number of output bits involved in decoding to less than the available keystream output bits. Our decoding approach is based on combination of exhaustive search over a subset of information bits and a soft-decision iterative message passing decoding algorithm. We compare the performance of the proposed algorithm with the recent fast correlation attacks. Our results show that we can reduce the number of bits obtained by exhaustive search in half and still get better performance comparing to recent fast correlation attacks based on iterative decoding algorithm. Using the expected number of parity-check equations of certain weights, we find the lower bound on the number of information bits that needs to be obtained by the exhaustive search without compromising the performance.