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The study of chaotic pseudo-random sequence generator on the basis of the ODE solvers
Butusov Denis Nikolaevich

PhD in Technical Science

Associate Professor, Ulyanov (Lenin) St. Petersburg State Electrotechnical University "LETI"

197376, Russia, Saint Petersburg, ul. Professora Popova, 5

dnbutusov@etu.ru
Другие публикации этого автора
 

 
Tutueva Aleksandra Vadimovna

programmer, Ulyanov (Lenin) St. Petersburg State Electrotechnical University "LETI"

197376, Russia, Saint Petersburg, ul. Professora Popova, 5

avtutueva@etu.ru
Pesterev Dmitrii Olegovich

technician, Ulyanov (Lenin) St. Petersburg State Electrotechnical University "LETI"

197376, Russia, Saint Petersburg, ul. Professora Popova, 5

dopesterev@etu.ru
Ostrovskii Valerii Yur'evich

Graduate Student, Ulyanov (Lenin) St. Petersburg State Electrotechnical University "LETI"

197376, Russia, Saint Petersburg, ul. Professora Popova, 5

vyostrovskii@etu.ru
Другие публикации этого автора
 

 

Abstract.

An approach to the selection of a finite-difference scheme of a chaotic pseudo-random sequence generator based on the use of step diagrams (h-diagrams) is proposed. As a test problem, a generator is considered based on the random Rössler system discretized by explicit, implicit and semiquant numerical methods of the first and second order of algebraic accuracy. The sequences generated by different variants of the generator are randomly checked by a battery of NIST statistical tests. Advantages of the proposed approach in the design of chaotic signal generators are shown, consisting in an essential (by an order of magnitude) acceleration of the device design time due to a new method of selecting the discretization step and the discrete operator. The effectiveness of using semi-implicit finite difference schemes in the generation of pseudo-random sequences by the method of numerical solution of chaotic differential equations is confirmed. The obtained results can be used in cryptography applications, in the design of secure communication systems, in solving problems of numerical simulation of dynamical systems and mathematical statistics.

Keywords: bifurcation, semi-implicit method, ODE solver, Rossler system, step diagram, NIST tests, numerical integration method, dynamical chaos, pseudo-random numbers, discrete operator

DOI:

10.7256/2454-0714.2017.4.24786

Article was received:

07-12-2017


Review date:

08-12-2017


Publish date:

11-01-2018


This article written in Russian. You can find full text of article in Russian here .

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