  LFSR-based stream ciphers with nonlinear filters or combiners are susceptible
to algebraic attacks using linearization methods to solve an overdefined system
of nonlinear equations. And this process is greatly enhanced if the filtering
or 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 its
annihilator becomes large enough. As computing power is continuously
increasing, a choice that seems secure today, becomes insecure tomorrow.
Therefore, a tool is needed to estimate the probability of the existence of
annihilators for balanced boolean functions with parameters that are beyond the
current computing power. Based on experimental and calculational observations,
we give in this paper an almost exact estimate of that probability, which
represent a great improvement over the upper bound previously known.
