Algebraic Attacks on Filter and Combiner Generators

A short survey of a recent attack on the filter generator due to Ronjom and Helleseth is presented. The attack is generalized to the nonlinear combiner generator. The original attack uses linear combinations of bits in the binary keystream in order to arrive at a linear equation system to be solved for the secret key. Here an argument shows that, when adopting the attack to the nonlinear combiner, then using linear combinations over an extension field is sometimes essential to make the attack work or to reduce the complexity of the attack. Even though a correlation attack may work better for a badly chosen Boolean function used in the combiner generator, the attack presented in this paper does not depend on the Boolean function in the same way and hence can be applied to some correlation-immune combiner generators.