Generation of pseudo-random numbers with the use of inverse chaotic transformation

Lawnik, Marcin

doi:10.1515/math-2018-0004

Cited by 5 publications

(5 citation statements)

References 23 publications

(23 reference statements)

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“…Similar recurrences were analyzed in [9]. Furthermore, in [10] an algorithm for generating pseudo-random values based on the inversed method of "flattening" of probability distributions was shown. This method uses inverse transformations to chaotic recurrences.…”

Section: Related Workmentioning

confidence: 77%

“…Each subinterval on which (4) is defined is visited by the number of iterations that are proportional to its length in a given orbit. Because the invariant density of (4) is uniform, the successive lengths of the subintervals correspond to division (10).…”

Section: Correctness Of the Methodsmentioning

confidence: 99%

“…Due to this reason, in the literature, one can find a lot of publications on the use of chaos in this type of issue. Most of such research works apply to continuous distributions [8,9,10] and generating strings of binary values [11,12,13]. Non-uniform discrete distributions are practically not considered in the literature with the use of chaotic mappings.…”

Section: Introductionmentioning

confidence: 99%

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Generation of Values From Discrete Probability Distributions With the Use of Chaotic Maps

Lawnik¹,

Banasik²,

Kapczyński³

2020

IJC

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The values of random variables are commonly used in the field of artificial intelligence. The literature shows plenty of methods, which allows us to generate them, for example, inverse cumulative density function method. Some of the ways are based on chaotic projection. The chaotic methods of generating random variables are concerned with mainly continuous random variables. This article presents the method of generating values from discrete probability distributions with the use of properly constructed piece-wise linear chaotic map. This method is based on a properly constructed discrete dynamical system with chaotic behavior. Successive probability values cover the unit interval and the corresponding random variable values are assigned to the determined subintervals. In the next step, a piece-wise linear map on the subintervals is constructed. In the course of iterations of the chaotic map, consecutive values from a given discrete distribution are derived. The method is presented on the example of Bernoulli distribution. Furthermore, an analysis of the discussed example is conducted and shows that the presented method is the fastest of all analyzed methods.

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Section: Related Workmentioning

confidence: 77%

Section: Correctness Of the Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Generation of Values From Discrete Probability Distributions With the Use of Chaotic Maps

Lawnik¹,

Banasik²,

Kapczyński³

2020

IJC

Self Cite

View full text Add to dashboard Cite

show abstract

“…Lawnik [25] used adequate chaotic transformation with uniform distribution and recommended a pseudo-random number generation method. This method changes continuous distributions into uniform distributions by flattening, allowing generation of pseudo-random numbers by continuous distribution.…”

Section: Related Workmentioning

confidence: 99%

XORSHIFTUL+: A Novel Hybrid Random Number Generator for Internet Of Things And Wireless Sensor Network Applications

Aydın¹,

Kösemen²

2020

Pamukkale J Eng Sci

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There are an increasing number of lightweight devices such as smart cards, radio frequency identification (RFID) tags, wireless sensor nodes and devices associated with the Internet of Things (IoT) concept, all of which need effective and lightweight security structures. One of the basic elements used in authentication protocols is the nonce values that are generated by PRNGs. Also random numbers are used for encryption process in secure communication. Proposed PRNG has demonstrated great suitability for devices with limited resources in terms of performance, resource usage and randomness. This generator is tested with NIST statistical test suite (NIST STS), which is one of the most comprehensive randomness test tools. It is also implemented, tested on wireless identification and sensing platform (WISP) passive RFID tag and compared with well-known PRNGs. As a result of the comparisons, it has better results than its rivals. Akıllı kartlar, radyo frekansı tanımlama (RFID) etiketleri, kablosuz sensör düğümleri ve Nesnelerin İnterneti (IoT) konsepti ile ilişkili düşük kaynaklı cihazların sayısında artış olmaktadır. Kimlik doğrulama protokollerinde kullanılan temel öğelerden biri SRSÜ'ler tarafından üretilen nonce değerleridir. Ayrıca güvenli iletişimde şifreleme işlemi için rasgele sayılar kullanılır. Önerilen SRSÜ, sınırlı kaynaklara sahip cihazlarda performans, kaynak kullanımı ve rastlantısallık açısından uygunluk göstermiştir. Bu üreteç en kapsamlı rastgele sayı test araçlarından biri olan NIST istatistiksel test takımı (NIST STS) ile test edilmiştir. Ayrıca, kablosuz tanıma ve algılama platformu (WISP) pasif RFID etiketi üzerinde test edilmiş ve uygulanmış ve iyi bilinen SRSÜ'lerle karşılaştırılmıştır. Karşılaştırmalar sonucunda rakiplerinden daha iyi sonuçlar vermiştir.

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“…Qu et al [7] worked on the generation of random variate for the gamma and exponential distributions. For more details, the reader may refer to [8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Truncated variable algorithm using DUS-neutrosophic Weibull distribution

Aslam

2022

Complex Intell. Syst.

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The existing truncated variable method to generate random variate cannot be applied when indeterminacy is presented in either the parameters or observations. This paper addresses the truncated variable simulation under the indeterminate environment. The truncated variable simulation method will be introduced using the DUS-neutrosophic Weibull distribution. The algorithm to generate random variate will be presented and applied in random variate generation. Extensive simulation tables for various values of indeterminacy and truncated variables are presented. The proposed study for other neutrosophic statistical distribution can be extended as future research.

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Generation of pseudo-random numbers with the use of inverse chaotic transformation

Cited by 5 publications

References 23 publications

Generation of Values From Discrete Probability Distributions With the Use of Chaotic Maps

Generation of Values From Discrete Probability Distributions With the Use of Chaotic Maps

XORSHIFTUL+: A Novel Hybrid Random Number Generator for Internet Of Things And Wireless Sensor Network Applications

Truncated variable algorithm using DUS-neutrosophic Weibull distribution

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