The convergence properties of a clipped Hopfield network and its application in the design of keystream generator

We first present a modified Hopfield network,the clipped Hopfield network, with synaptic,weights assigned to three values {-1, 0, +1}, We give the nec essary conditions under which a set of 2n binary vectors can be stored as s table points of the network. We show that in the parallel updating mode, fo r most of the state vectors, the network will always converge to these 2n s table points. We further demonstrate that these 2n stable points can be div ided into two groups, the alpha group and the beta group, each with n stabl e points. It is shown that the basins of attraction of the stable points in the alpha group are evenly distributed, and the basins of attraction of th e stable points in the beta group are also evenly distributed. By ways of a pplication, we show that this class of Hopfield network can be used to buil d a cryptographically secure keystream generator.