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M. Jessa
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ABSTRACT: In the paper, we describe how to design the security of number sequences generated by a generator, exploiting the concept of partition of the state space of the sawtooth chaotic map into disjoint subspaces. We prove that the generator can generate nonperiodic and periodic sequences with arbitrary order of elements when the map is implemented in an uncountable set, and periodic sequences with arbitrary order of elements when the map is implemented in a countable set. The numerical security of the generated sequences is shown to be comparable when we limit our observations to finite time intervals. A method of designing the security of sequences produced by the generator was proposed. It was also demonstrated that the existence of methods for reconstructing the linear congruential generator does not imply automatic reconstruction of the generator, exploiting the concept of partition of the state space of the sawtooth map implemented in a finite-state machine.
Circuits and Systems I: Regular Papers, IEEE Transactions on 06/2006; · 1.97 Impact Factor
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M. Jessa
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ABSTRACT: In brief, we describe how to use knowledge about the sequence
period generated by the linear multiplicative congruential generator of
pseudorandom number sequences to determine the sequence period generated
by continuous piecewise-linear chaotic maps of the unit interval or by
maps topologically conjugate to these maps. The method exploits a
relation between a continuous piecewise-linear map and a
piecewise-linear but noncontinuous map of the unit interval with
uniformly distributed extrema points, as well as the fact that the
latter map can be considered as the generalization of the map describing
the linear multiplicative congruential generator
IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications 02/2002;
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ABSTRACT: In the paper we consider the usage of the discrete-time phase-locked loop (DT-PLL) as a source of random sequences with different distributions. The proposed approach enables relatively simple and very fast generation of random sequences with different distributions by chaotic maps topologically conjugate to the sawtooth map. The sequences can be obtained directly or indirectly, i.e. from uniformly distributed sequences, also generated in the real circuit of DT-PLL.
Circuits and Systems, 2002. ISCAS 2002. IEEE International Symposium on; 02/2002
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M. Jessa
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ABSTRACT: In the paper we propose a new algorithm of data encryption, exploiting maps, also chaotic, of the unit interval. We consider the finite-state implementation of the systems, e.g. in computers. The characteristic feature of the algorithm is the possibility of adjusting security of data to be transmitted by means of the security index and the usage of chaos-based pseudorandom number generators as the source of running encryption keys. The algorithm enables fast encryption of those parts of data, which do not require high security. The change in encryption speed is achieved without any change of the length of encryption key, which can be fixed and constant during transmission. It is a distinguishing feature of the proposed system as compared to existing schemes.
Circuits and Systems, 2002. ISCAS 2002. IEEE International Symposium on; 02/2002
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ABSTRACT: The basic statistical properties of sequences generated by
sawtooth maps and tent-like maps as a function of parameter determining
the Kolmogorov-Sinai entropy are considered. The statistical properties
of sequences generated by both maps for the same value of parameter and
the same initial point are also compared. It has been also shown that
tent-like maps may have a serious drawback from the perspective of their
application as a source of pseudorandom sequences: they cannot generate
the maximal-length sequences
Electronics, Circuits and Systems, 2001. ICECS 2001. The 8th IEEE International Conference on; 02/2001
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M. Jessa
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ABSTRACT: In the paper we consider the maximal cycle length of pseudochaotic
sequences generated by piecewise linear maps of the unit interval. We
define two families of piecewise linear maps: piecewise linear
noncontinuous maps (sawtooth maps) and piecewise linear continuous maps
(tent-like maps). We formulate and prove an equation relating both
families of maps. We show also that there may exist a dependence between
the cycle length of sequences generated by sawtooth maps and the cycle
length of sequences obtained for tent-like maps for the same value of a
parameter and the same initial point
Circuits and Systems, 1999. ISCAS '99. Proceedings of the 1999 IEEE International Symposium on; 02/1999
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M. Jessa
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ABSTRACT: A generation of random and pseudorandom numbers with good
statistical properties is one of the most important subjects of modern
communication and simulation. The author discusses the possibility of
generating random and pseudorandom numbers in the area of the strange
attractor of the tent map. To estimate basic properties of generated
numbers four measures are used: the value of Lyapunov exponent being a
measure of average speed of divergance of initially close trajectories,
the value of topological entropy being a measure of the average speed of
`mixing' of trajectory points and values of autocorrelation,
crosscorrelation functions and their FFT transforms being the measure of
`self-similarity' or `crossimilarity' of trajectory fragments
Singapore ICCS/ISITA '92. 'Communications on the Move'; 12/1992
