A Fast Correlation Attack for LFSR-Based Stream Ciphers

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Abstract

This paper describes a novel fast correlation attack of stream ciphers. The salient feature of the algorithm is the absence of any pre-processing or iterative phase, an usual feature of existing fast correlation attacks. The algorithm attempts to identify a number of bits of the original linear feedback shift register (LFSR) output from the received bits of the ciphertext. These are then used to construct a system of linear equations which are subsequently solved to obtain the initial conditions. The algorithm is found to perform well for LFSRs of large sizes but having sparse polynomials. It may be noted that such polynomials have low Hamming weight which is one more than the number of feedback connections or “taps” of the corresponding LFSR. Its performance is good in situations even where limited cipherlength is available. Another important contribution of the paper is a modification of the approach when the LFSR outputs are combined by a function which is correlation immune and perhaps, unknown to the decrypter.