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LFSR-based stream ciphers with nonlinear filters or combiners are susceptibleto algebraic attacks using linearization methods to solve an overdefined systemof nonlinear equations. And this process is greatly enhanced if the filteringor combining function has a low degree annihilator. To prevent such an attack,one would choose the parameters of that function so that the degree of itsannihilator becomes large enough. As computing power is continuouslyincreasing, a choice that seems secure today, becomes insecure tomorrow.Therefore, a tool is needed to estimate the probability of the existence ofannihilators for balanced boolean functions with parameters that are beyond thecurrent computing power. Based on experimental and calculational observations,we give in this paper an almost exact estimate of that probability, whichrepresent a great improvement over the upper bound previously known.

Observations Concerning the probability of the existence of annihilators for balanced boolean functions