Tanıtılmış bir hiperkaotik sistemin yeni bir analizi ve uygulamaları

Bu çalışmada, tanıtılmış bir hiperkaotik denklem setinin yeni bir analizi ele alınmıştır. Denklem seti önce matematiksel olarak analiz edilmiş, ardından aktif elemanlarla daha verimli bir devre tasarlanarak sonuçlar kanıtlanmıştır. Çalışmanın amacı, etkili bir güvenli iletişim uygulaması ve rastgele sayı üreteci uygulaması sunmaktır. Bu nedenle, denklem setinin yeni analizi temel alınarak güvenli iletişim sistemi ve rastgele sayı üretme uygulaması önerilmiştir. Bu bağlamda, bir Sözde Rastgele Sayı Üreticisi oluşturmak, bu çalışmadaki yolun yarısıdır. Kaotik osilatörden alınan sinyaller düşük frekansta örneklenmiş ve basit bir post-processing ile bit dizileri oluşturulmuştur. Elde edilen bit dizisi NIST testinden başarı ile geçmiştir. Çalışmadaki yolun diğer yarısı ise verici ve alıcıda bulunan iki kaotik osilatörün senkronizasyonu ile güvenli bir iletişim sistemi oluşturmaktır. Hem verici hem de alıcı parçalarda özdeş bir gürültü benzeri sinyal üretilir. Verici kısmında bilgiye gürültü benzeri kaotik bir sinyal eklenmektedir. Alıcıda, bu aynı gürültü benzeri sinyal algılanan sinyalden çıkarılır. Böylece bilgiler güvenli bir şekilde iletilebilir. Önerilen iki uygulamanın da SPICE benzetimleri yapılmış, matematiksel analizler ile uyumlu olduğu gösterilmiştir. Önerilen devreler, ticari olarak bulunan devre elemanları ile gerçeklenmeye uygundur.

Anahtar Kelimeler:

Kaotik sistem, Kaotik senkronizasyon, Devre uygulaması, CCII+, Güvenli haberleşme sistemi, Sözde-Rassal sayıüreteci

A novel analysis and applications of an introduced hyperchaotic system

In this study, the new analysis of the introduced hyperchaotic equation set was handled. The equation set was firstly analyzed mathematically and then the results were proven by designing a more efficient circuit with active elements. The aim of the study is offering an effective secure communication application and random number generator application. Hence, based on the new analysis of equation set, secure communication system and random number generation application were proposed. Accordingly, creating a Pseudorandom Number Generator is the halfway house in this study. The signals received from the chaotic oscillator were sampled at low frequency and with a simple post-processing, a bit stream was created. The resulting bit stream passed the NIST test successfully. The other halfway of the study is creating a secure communication system by the synchronization of two chaotic oscillators that are in transmitter and receiver. An identical noise-like signals are generated in both transmitter and receiver parts. At the transmitter part adding a noise-like chaotic signal to the information is done. At the receiver, this same noise-like signal is subtracted from the perceived signal. Thus, the information can be transmitted securely. Spice simulations of both proposed applications have been made and it has been shown that they are compatible with mathematical analysis. The proposed circuits are suitable for realization with commercially available circuit elements.

Keywords:

Chaotic system, Chaotic synchronization, Circuit implementation, CCII+, Secure communication system, Pseudo-Random number generator,

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