New Nonlinear CPRNG Based on Tent and Logistic Maps

Garasym²,

Industrial Mathematics and Complex Systems

2017

Self Cite

The study of nonlinear dynamics is relatively recent with respect to the long historical development of early mathematics since the Egyptian and the Greek civilization, even if one includes in this field of research the pioneer works of Gaston Julia and Pierre Fatou related to one-dimensional maps with a complex variable, nearly a century ago. In France, Igor Gumosky and Christian Mira began their mathematical researches in 1958; in Japan, the Hayashi' School (with disciples such as Yoshisuke Ueda and Hiroshi Kawakami), a few years later, was motivated by applications to electric and electronic circuits. In Ukraine, Alexander Sharkovsky found the intriguing Sharkovsky's order, giving the periods of periodic orbits of such nonlinear maps in 1962, although these results were only published in 1964. In 1983, Leon O. Chua invented a famous electronic circuit that generates chaos, built with only two capacitors, one inductor and one nonlinear negative resistance. Since then, thousands of papers have been published on the general topic of chaos. However, the pace of mathematics is slow, because any progress is based on strictly rigorous proof. Therefore, numerous problems still remain unsolved. For example, the long-term dynamics of the Hénon map, the first example of a strange attractor for mappings, remain unknown close to the classical parameter values from a strictly mathematical point of view, 40 years after its original publication. In spite of this lack of rigorous mathematical proofs, nowadays, engineers are actively working on applications of chaos for several purposes: global optimization, genetic algorithms, CPRNG (Chaotic Pseudorandom Number Generators), cryptography, and so on. They use nonlinear maps for practical applications without the need of sophisticated theorems. In this chapter, after giving some prototypical examples of the industrial

Section: Resultsmentioning

confidence: 99%

Section: Two-dimensional Network Topologiesmentioning

confidence: 99%

Section: Two-dimensional Network Topologiesmentioning

confidence: 99%

“…In [38], it is shown that if the impact of component x (1) n is reduced, randomness is improved. Hence, the following MT T L SC map is introduced…”

Section: T T L Scmentioning

confidence: 99%

“…14 Plot of one billion iterates of MT T L SC 2 using the counting box method 15 Successful results of N I ST tests for the MT T LSC 2 alternate map for the variable x(1) (from[38])…”

mentioning

confidence: 99%

See 3 more Smart Citations

The Challenging Problem of Industrial Applications of Multicore-Generated Iterates of Nonlinear Mappings

Garasym²,

Industrial Mathematics and Complex Systems

2017

Self Cite

Zooming into chaos as a pathway for the creation of a fast, light and reliable cryptosystem

2021

Motivated by today’s huge volume of data that needs to be handled in secrecy, there is a wish to develop not only fast and light but also reliably secure cryptosystems. Chaos allows for the creation of pseudo-random numbers (PRNs) by low-dimensional transformations that need to be applied only a small number of times. These two properties may translate into a chaos-based cryptosystem that is both fast (short running time) and light (little computational effort). What we propose here is an approach to generate PRNs—and consequently digital secret keys—that can serve as a seed for an enhanced chaos-based cryptosystem. We use low-dimensional chaotic maps to quickly generate PRNs that have little correlation, and then, we quickly (“fast”) enhance secrecy by several orders (“reliability”) with very little computational cost (“light”) by simply looking at the less significant digits of the initial chaotic trajectory. This paper demonstrates this idea with rigor, by showing that a transformation applied a small number of times to chaotic trajectories significantly increases its entropy and Lyapunov exponents, as a consequence of the smoothing out of the probability density towards a uniform distribution.

Sakarya University Journal of Science

Microcontroller-based Random Number Generator Implementation by Using Discrete Chaotic Maps

Çiçek

2020

In recent decades, chaos theory has been used in different engineering applications of different disciplines. Discrete chaotic maps can be used in encryption applications for digital applications. In this study, firstly, Lozi, Tinkerbell and Barnsley Fern discrete chaotic maps are implemented based on microcontroller. Then, microcontroller based random number generator is implemented by using the three different two-dimensional discrete chaotic maps. The designed random number generator outputs are applied to NIST (National Institute of Standards and Technology) 800-22 and FIPS (Federal Information Processing Standard) tests for randomness validity. The random numbers are successful in all tests.