Fast correlation attacks and multiple linear approximations

The fast correlation attack based on iterative probabilistic decoding is applied to nonlinear filter generators in order to investigate the effect of multiple linear transforms of the same linear recurring sequence being correlated to the keystream sequence. Systematic computer simulations on random balanced filter functions reveal that the attack is successful if the number of parity-checks used is sufficiently large given the correlation coefficient of the best affine approximation to the filter function. Nevertheless, the attack is more successful when applied to the independent correlation noise which appears in memoryless combiners where a multiple linear transform effect is not present. The experiments conducted show that the attack is successful on many publicly proposed filter functions and indicate that some bent filter functions may be easier to attack than the others.