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BentSign: keyed hash algorithm based on bent Boolean function and chaotic attractor

Todorova M., Stoyanov B., Szczypiorski K., Graniszewski W., Kordov K.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2019

Vol. 67, nr 3

557--569

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.

On the boundary crises of chaotic attractors

Tyrkiel E., Szemplińska-Stupnicka W.

Computer Assisted Mechanics and Engineering Sciences

2000

Vol. 7, No. 4

743-755

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

On the new scenario of annihilation of the Cross-Well chaotic attractor in a nonlinear oscillator

Szemplińska W., Zubrzycki A., Tyrkiel E.

Journal of Technical Physics

1999

Vol. 40, no 2

163-173

The twin-well potential Duffing oscillator is considered and the investigations are focused on a new scenario of destruction of the cross-well chaotic attractor. The new phenomenon belongs to the category of subduction bifurcation and consists in replacement of the cross-well chaotic attractor by a pair of unsymmetric 2T-periodic attractors. It is shown that the new scenario forms a transition zone in the system control parameter plane, the zone, which separates the two known scenarios of annihilation of the cross-well chaotic attractor: the boundary crisis, and the subduction in which the two single-well T-periodic attractors are born in a saddle-node bifurcation.