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Autonomous implicit models of pinched hystereses with application to memristors

Marszalek W.

Przegląd Elektrotechniczny

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2018

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R. 94, nr 4

13--16

EN

This paper analyzes systems with an autonomous dynamics equivalent to that of mem-inductors and mem-capacitors. The systems have oscillatory inductive and capacitive pinched self-crossing hystereses that follow the folded saddle dynamics around the origin and two equilibria of the center type, each located on the opposite sides of singularity (impasse curve). When parameters of the systems change to yield an increased frequency of oscillations, then the areas enclosed by the hystereses decrease. The time zero-crossing property of the systems is also discussed.

PL

W artykule dokonano analizy dynamiki pewnej klasy układów autonomcznych. Rozważane układy charakteryzują się indukcyjnymi i pojemnościowymi, ścisniętymi i przecinającymi się histerezami, powstajacymi w dynamice siodła na fałdzie wraz z dwoma punktami równowagi typu centrum, położonymi po przeciwnych stronach krzywej osobliwej z punktami impasowymi. Wraz ze zmianą parametrów prowadzącą do zwiększenia częstotliwosci oscylacji obszar objęty histerezą zmniejsza się . Własność jednoczesnego zerowania się sygnałów w czasie jest rownież rozważana.

2

Hardware Trojans detection in chaos-based cryptography

Melosik M., Sniatala P., Marszalek W.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2017

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Vol. 65, nr 5

725--732

EN

The paper deals with the security problems in chaotic-based cryptography. In particular, the 0–1 test for chaos is used to detect hardware Trojans in electronic circuits – generators of chaotic bit sequences. The proposed method of detecting hardware Trojans is based on analyzing the original bit sequences through the 0–1 test yielding a simple result, either a number close to 1, when the examined bit sequence is chaotic, or a number close to 0, when the sequence is non-chaotic. A complementary result is a graph of translation variables qc and pc which form a basis of the 0–1 test. The method does not require any extra corrections and can be applied to relatively short sequences of bits. This makes the method quite attractive as the security problems are dealt with at the chaotic generator level, with no need to apply any extractors of randomness. The method is illustrated by numerical examples of simulated Trojans in chaotic bit generators based on the analog Lindberg circuit as well as a discrete system based on the logistic map.

3

On the 0/1 test for chaos in continuous systems

Melosik M., Marszalek W.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2016

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Vol. 64, nr 3

521--528

EN

In this paper we discuss in detail the resonance and oversampling features of the 0/1 test for chaos in continuous systems and propose methods to avoid those undesired features. Our method is based on certain frequency properties of the 0/1 test. When reconstructing the phase space, our approach is compared with the first minimum of the mutual information method. Several numerical results for typical chaotic systems (including memristive circuits) are included.