A random number generator based on unpredictable chaotic functions

We introduce an interesting hierarchy of rational order chaotic maps that posses an invariant measure. In contrast to the previously introduced hierarchy of chaotic maps [1,2,3,4,5], with merely entropy production, the rational order chaotic maps can simultaneously produce and consume entropy . We compute the Kolmogorov-Sinai entropy of theses maps analytically and also their Lyapunov exponent numerically, where that obtained numerical results support the analytical calculations.

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“…|, (4)(5)(6)(7)(8)(9)(10) where in the last line above we have used the following normalization relation…”

Section: Kolmogorov-sinai Entropymentioning

confidence: 99%

“…There has been some attempts [1,2,3,4,5,6] at introducing the hierarchy of chaotic maps with an invariant measure in the recent years. The objective of these papers is to describe the dynamic behavior of chaotic maps using Kolmogorov-Sinai entropy.…”

Section: Introductionmentioning

confidence: 99%

Hierarchy of rational order families of chaotic maps with an invariant measure

2006

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“…1, using chaos to generate pseudo-random numbers (PRN) is a general way to design digital chaotic stream ciphers. Besides in chaotic cryptography area, chaotic pseudo-random number generators (PRNG) have also attracted much attention in other research areas, such as communications [33,36,37] and physics [38]. Most chaotic PRNG-s are based on single chaotic system and generate PRN directly from its orbit.…”

Section: Couple Chaotic Systems Based Prbg (Ccs-prbg)mentioning

confidence: 99%

Pseudo-random Bit Generator Based on Couple Chaotic Systems and Its Applications in Stream-Cipher Cryptography

Mou

Cai

2001

Lecture Notes in Computer Science

129

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Abstract. Chaotic cryptology is widely investigated recently. This paper reviews the progress in this area and points out some existent problems in digital chaotic ciphers. As a comprehensive solution to these problems, a novel pseudo-random bit generator based on a couple of chaotic systems called CCS-PRBG is presented. Detailed theoretical analyses show that it has perfect cryptographic properties, and can be used to construct stream ciphers with higher security than other chaotic ciphers. Some experiments are made for confirmation. Finally, several examples of stream ciphers based on digital CCS-PRBG are given, and their security is discussed.

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“…Recently, we have introduced explicit functions that produce truly random sequences [12][13][14]. For instance, let us define the function:…”

Section: Introductionmentioning

confidence: 99%

A mechanism for randomness

et al. 2002

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We investigate explicit functions that can produce truly random numbers. We use the analytical properties of the explicit functions to show that certain class of autonomous dynamical systems can generate random dynamics. This dynamics presents fundamental differences with the known chaotic systems. We present real physical systems that can produce this kind of random time-series. We report the results of real experiments with nonlinear circuits containing direct evidence for this new phenomenon. In particular, we show that a Josephson junction coupled to a chaotic circuit can generate unpredictable dynamics. Some applications are discussed.

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A random number generator based on unpredictable chaotic functions

Cited by 51 publications

References 13 publications

Hierarchy of rational order families of chaotic maps with an invariant measure

Hierarchy of rational order families of chaotic maps with an invariant measure

Pseudo-random Bit Generator Based on Couple Chaotic Systems and Its Applications in Stream-Cipher Cryptography

A mechanism for randomness

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