Analysis and description S-box generation for the AES algorithm-a new 3D hyperchaotic system

Hayder Kadhim Zghair, Mehdi Ebady Manaa, Safa Saad A. AL-Murieb, Fryal Jassim Abd Al-Razaq

Abstract


In this paper, a description, and analysis of a novel 3-D dimension hyperchaotic system is implemented. The proposed system oscillation is two-order autonomous and consisted of a nine-term and symmetric oscillation w.r.t x-axis. It is proved analysis by Kaplan-York dimension, waveform analysis, phase portrait, and Lyapunov exponent. This work-study stability and equilibrium point and Routh stability criteria produced that the new system has one unstable point from the type saddle-focus point. One of the characteristics of the proposed system is hyperchaotic since this system has two Lyapunov large than zero. This system is applied to generate a chaotic  (S-box) based in advanced encryption standard (AES) algorithm for text encryption and gives a high level of security. In addition to the description, and analysis S-box. Therefore. the proposed algorithm is satisfied the high randomness of entropy value and passes the National Institute of Standards and Technology (NIST) parameters and another test. Mathematica and MATLAB programs simulated some results.


Keywords


3-D hyperchaotic system; AES algorithm; Fractional-Kaplien dimension; Lyapunov exponent; SDIC; Waveform analysis

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DOI: https://doi.org/10.11591/eei.v12i3.4824

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