A note on the improvement of a fast correlation attack on stream ciphers

The stream cipher, a type of secret-key cipher, gives the key to a pseudorandom number generator and generates a pseudorandom sequence called the key sequence, and generates the ciphertext sequence taking the exclusive-or of this sequence and the plaintext sequence. A nonlinear combiner generator is a type of pseudorandom number generator used by stream ciphers and is configured from multiple linear-feedback shift registers (LFSRs) and one nonlinear function. A correlation attack is a method for attacking this type of pseudorandom number generator. The correlation between the output sequence of an LFSR and the key sequence is used to estimate the initial state of the LFSR. However, a conventional attack method attacks a single LFSR and is used only to estimate a portion of the multidimensional correlations of the multiple LFSR sequences and the key sequence. Therefore, we propose an algorithm that improves the attack method using the belief propagation (BP) algorithm of Mihaljević and colleagues and simultaneously attacks multiple LFSRs using the multidimensional correlation. By increasing the information used in the estimation, an improvement in the decoding success rate is expected. In addition, the computational load of the estimation increases, but this increase can be suppressed by an approximation based on the parallel BP algorithm.