Logistic Map as a Random Number Generator

Andrecut, M.

doi:10.1142/s021797929800051x

Cited by 83 publications

(34 citation statements)

References 1 publication

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“…There have been proposals of generators based on unimodals chaotic maps, for example in [13,14] proposed a pseudo-random bit generator by using only one logistic map, but in [15] the authors pointed out that bit streams generated through only one chaotic system are potentially insecure due to the output may leak some information about the chaotic system. In order to overcome the aforementioned vicissitude, they proposed a pseudo-random bit generator based on a couple of piecewise linear chaotic maps, which are iterated independently and the bit streams are generated by comparing the outputs of these chaotic maps.…”

Section: Introductionmentioning

confidence: 99%

Pseudo-random bit generator based on multi-modal maps

Canton

Martinez

2015

Nonlinear Dyn

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In this work we present a pseudo-random Bit Generator via unidimensional multi-modal discrete dynamical systems called k-modal maps. These multimodal maps are based on the logistic map and are useful to yield pseudo-random sequences with longer period, i.e., in order to attend the problem of periodicity. In addition the pseudo-random sequences generated via multi-modal maps are evaluated with the statistical suite of test from NIST and satisfactory results are obtained when they are used as key stream. Furthermore, we show the impact of using these sequences in a stream cipher resulting in a better encryption quality correlated with the number of modals of the chaotic map. Finally, a statistical security analysis applied to cipher images is given. The proposed algorithm to encrypt is able to resist the chosen-plaintext attack and differential attack because the same set of encryption keys generates a different cipher image every time it is used.

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Section: Introductionmentioning

confidence: 99%

Pseudo-random bit generator based on multi-modal maps

Canton

Martinez

2015

Nonlinear Dyn

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“…Trying to make use of the chaotic nature of simple maps, many researchers have discussed the possibility of using the logistic map to generate random numbers [12][13][14][15]. One distinct feature of chaotic maps is that at least one Lyapunov exponent of the systems is positive for certain parameter regimes.…”

Section: Test Results and The Clear Correlation With Lyapunov Exponentsmentioning

confidence: 99%

“…In fact, the idea of applying chaos theory to generate random numbers has produced interesting works in recent years [9][10][11][12][13][14][15]. For instance, Collins et al [12] have applied the logit transformation to the logistic map to produce random numbers of uniform distribution.…”

Section: Introductionmentioning

confidence: 99%

Evidence of the correlation between positive Lyapunov exponents and good chaotic random number sequences

Lee

Chen²,

Pei³

et al. 2004

Computer Physics Communications

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“…To guarantee the secrecy of information, numerous techniques have been developed by many researchers [2][3][4]. Over the last two decades, it has been found that there exists a close relationship between cryptology and chaos [5,6]. The behavior of chaotic signals is highly unpredictable and random-like which can be used in the design of cryptographic algorithms.…”

Section: Introductionmentioning

confidence: 99%

Chaos-based diffusion for highly autocorrelated data in encryption algorithms

2015

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In a single substitution box, the same regions (pixels) of an image are encrypted to one unique symbol. To reduce this type of autocorrelation in data, chaos has been extensively applied over the last decade. By using chaotic maps, a single substitution box has been replaced with multiple substitution boxes for the encryption of autocorrelated data. The technique of multiple substitution boxes is becoming very popular among cryptographic algorithm designers to overcome the drawbacks of a single substitution box. In this paper, however, we found that replacing a single substitution box with multiple substitution boxes cannot provide a general solution for highly autocorrelated data. To address this issue, we propose a novel technique by adding chaotic diffusion to the existing substitution process. Extensive security analyses show that the proposed algorithm achieves both higher-level security and fast encryption time when compared with existing algorithms.

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Logistic Map as a Random Number Generator

Cited by 83 publications

References 1 publication

Pseudo-random bit generator based on multi-modal maps

Pseudo-random bit generator based on multi-modal maps

Evidence of the correlation between positive Lyapunov exponents and good chaotic random number sequences

Chaos-based diffusion for highly autocorrelated data in encryption algorithms

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