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EN
In this study, we propose a novel keyed hash algorithm based on a Boolean function and chaotic attractor. The hash algorithm called BentSign is based on two Signature attractors and XOR function and a bent Boolean function. The provided theoretical and experimental results confirm that the novel scheme can generate output hashes with a good level of security, collision resistance, and protection against most common attacks.
EN
The correlation dimension and Lyapunov coefficients for a dynamic system constructed on the basis of tropospheric mean temperature time series are presented. The calculations proved that the attractor is strange and his geometrical structure is fractal. The attractor's strangeness results from the existence of positive values of the Lyapunov coefficients. Based upon these results, the estimated time of the dynamic system prediction is 13 days.
3
Content available remote On the boundary crises of chaotic attractors
EN
In nonlinear dissipative mechanical systems, bifurcations of chaotic attractors called boundary crises appear to be the cause of most sudden changes in chaotic dynamics. They result in a sudden loss of stability of chaotic attractor, together with destruction of its basin of attraction and its disappearance from the phase portrait. Chaotic attractor is destroyed in the collision with an unstable orbit (destroyer saddle) sitting on its basin boundary, and the structure of the saddle defines the type of the crisis - regular or chaotic one. In the paper we exemplify both types of the boundary crisis by using a mathematical model of the symmetric twin-well Duffing oscillator; we consider the regular boundary crisis of the cross-well chaotic attractor, and the chaotic boundary crisis of the single-well chaotic attractor. Our numerical analysis makes use of the underlying topological structure of the phase space, namely the geometry of relevant invariant manifolds, as well as the structure of basins of attraction of the coexisting attractors. The study allows us to establish some relevant relations between the properties of the regular and chaotic boundary crisis, and to outline the differences that result mainly in the post-crisis
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