Pseudorandom Bit Generator Based On Chaotic Parameter Hopping Chaos

Ahmed I. El-Naggary, Karim H. Moussa
2019 International Journal of Engineering and Technology  
Pseudorandom bit generators which produce bit sequences have become a significant factor serving human's life in many fields, such as cryptography, spread spectrum wireless communication, computer simulations and error correcting coding. So far, the main source for producing pseudorandom binary sequences was the chaotic systems. Most of the used chaotic systems were stationary ones based on fixed logistic maps or code books. Accordingly, the pseudorandom binary sequences produced were almost
more » ... tionary and insufficiently secured. In this paper, we propose a novel algorithm for generating pseudorandom codes based on a logistic map with a dynamic hopping parameter. While the main chaotic map is used to generate a chaotic sequence, another chaotic map is utilized to hop the chaotic parameter of the main map. The model numerical analysis, correlation behaviours and statistical tests showed that the proposed algorithm improved the statistical properties, robustness, security against phase space reconstruction methods, ideal correlation properties, and predictable behaviour for the generated bit sequence. Keyword -Pseudorandom, NIST, Chaotic, Hopping, Bifurcation I. INTRODUCTION Mobile telecommunications are exposing rapid growth and sensitive data interception which in turn necessitates the establishment of more secure media for such communication data. As a consequence continuous development and researches for data encryption algorithms and cryptography is pervasively growing (Clark 2000) . The main aspect of the cryptographic system is to generate artificially unpredictable random numbers (RNs) as a source for key generation and encryption applications. Random number generators (RNGs) can be broadly classified as true RNGs (TRNGs), and pseudo RNGs (PRNGs). A TRNG is based on a source sequence emission using natural physical phenomena such as white noise, radioactive decay and chaotic systems (Gude 1985; Yalçın, Suykens, and Vandewalle 2004). The pseudorandom bit generators (PRBGs) based on chaotic maps are very significant, due to its high security and random behaviour. A chaotic system for generating a pseudorandom sequence are proposed in (Oishi and Inoue 1982). Despite being more complex, but the time-varying chaotic sequence proved to be much better than a fixed one. Due to the non-stationary output behaviour, such type of encryption technique turns to be difficult in prediction and analysis. Constructing a time-varied chaotic system can be effectively done by changing the chaotic system parameters continuously. In this paper, a novel PRBG which produce pseudorandom bit sequences utilizing a main logistic map with a dynamic hopping parameter. The hopping parameter is also generated in a pseudo-random behavior utilizing another different logistic map. The numerical analysis showed a great performance enhancement over previous bit generator versions considering the randomness and time-varying parameters which in turn leads to more security systems. In this paper, we propose a novel technique for generating a PRBS based on chaotic parameters that were generated using another hopped chaotic map. This dynamic hopping algorithm proved to make chaotic system parameters act in a random-like way which yields to more secure binary sequence generation. The statistical and experimental results show that the proposed dynamic hopping algorithm is hardly predictable and highly secured in terms of phase space reconstruction which makes it very competitive with other PRBS algorithms. The rest of the paper is organized as follows: Previous related works in the same field are summarized in section II. Traditional logistic maps were briefly discussed in section III. In section IV we propose our PRBG model based on chaotic parameter hopping chaotic system. Experimental statistical tests results for our newly developed bit generator are depicted in section V. In section VI, the simulation results for the generated pseudorandom binary sequence obtained using both traditional and parameter hopped logistic maps are discussed. Finally, the conclusions for our simulation results and related future work are stated in section VII.
doi:10.21817/ijet/2019/v11i6/191106013 fatcat:zcol5c4ui5glhiyb32sub4icr4