Fast Correlation Attacks on the Summation Generator

Abstract. The linear sequential circuit approximation method for combiners with memory is used to find mutually correlated linear transforms of the input and output sequences in the well-known summation generator with any number of inputs. It is shown that the determined correlation coefficient is large enough for applying a fast correlation attack to the output sequence to reconstruct the initial states of the input linear feedback shift registers. The proposed attack is based on iterative probabilistic decoding and appropriately generated low-weight parity-checks. The required output sequence length and the computational complexity are both derived. Successful experimental results for the summation generators with three and five inputs are obtained.