An Improved Way to Construct the Parity-check Equations in Fast Correlation Attacks

How to construct the parity-check equations is an open problem in the topic of fast correlation attack. In this paper, we present an improved method to construct the parity-check equations used in the fast correlation attacks. By utilizing the idea of multi-layer match-and-sort combined with the exhaustive searching, we construct the parity-check equations to be used in the decoding, which is not relevant to the number of the LFSR’s feedback taps. Finally, we analyze the time complexity and memory complexity of our method, which are about 5 /8 ( log ) k O N N      and ( 1)/8 ( ) k O N      respectively (where k is the weight of the parity-checks), and the memory complexity is the square root of the Chose et al.’s.