Return-Map Cryptanalysis Revisited

As a powerful cryptanalysis tool, the method of return-map attacks can be used to extract secret messages masked by chaos in secure communication schemes. Recently, a simple defensive mechanism was presented to enhance the security of chaotic parameter modulation schemes against return-map attacks. Two techniques are combined in the proposed defensive mechanism: multistep parameter modulation and alternative driving of two different transmitter variables. This paper re-studies the security of this proposed defensive mechanism against return-map attacks, and points out that the security was much over-estimated in the original publication for both ciphertext-only attack and known/chosen-plaintext attacks. It is found that a deterministic relationship exists between the shape of the return map and the modulated parameter, and that such a relationship can be used to dramatically enhance return-map attacks thereby making them quite easy to break the defensive mechanism.Comment: 11 pages, 7 figure

A Mathematical Model for the Dynamics and Synchronization of Cows

We formulate a mathematical model for daily activities of a cow (eating, lying down, and standing) in terms of a piecewise affine dynamical system. We analyze the properties of this bovine dynamical system representing the single animal and develop an exact integrative form as a discrete-time mapping. We then couple multiple cow "oscillators" together to study synchrony and cooperation in cattle herds. We comment on the relevant biology and discuss extensions of our model. With this abstract approach, we not only investigate equations with interesting dynamics but also develop interesting biological predictions. In particular, our model illustrates that it is possible for cows to synchronize \emph{less} when the coupling is increased.Comment: to appear in Physica