Keyed Hash function based on composite nonlinear autoregressive filter

Abstract

In recent years, chaotic dynamic systems are widely applied in information security because of its characteristic that the trajectory is sensitive to initial conditions and seems to be random though it is really a determinate process. The nonlinear autoregressive digital filters satisfying the Kelber conditions can also produce chaotic sequences just like chaotic maps do. The composite filter system consists of several above-mentioned filters, and the filter used for iteration is completely decided by a predetermined sequence called composite sequence. Consequently, the trajectory of the composite filter system is not only sensitive to its initial conditions, but also related with the composite sequence, which determines the choice of iterated sub-filter system in the iterating process. o the trajectory is more complex than that of general chaotic systems or single filter system. After analyzing some properties of composite filter systems such as N-dimensional uniform distribution and invariant distribution density function,a new keyed Hash algorithm based on composite system is presented. The approach selects the sub-filter system with the composite sequence obtained from message to be hashed, uses the initial iteration value of composite system as the secret key, and the coarse-grained trajectory as Hash value. Because of the sensitivity to initial value and randomicity of the iteration process, there is a very complex nonlinear relation between Hash value and the corresponding message and secret key, and then every bit of the Hash value derived from the message M is related with every bit of M. Furthermore, the filter-based algorithm is simple enough without complex operations, so it can be realized easily.