This paper presents the mathematical aspects of a generalized Sine map with arbitrary powers and scaling factor. The added parameters increase the degrees of freedom of the Sine map and give a versatile response that can be utilized in many applications. For each added parameter, the map’s chaotic behavior is analyzed using fixed points, bifurcation diagrams and Lyapunov exponents. Furthermore, two image encryption applications are introduced based on the generalized Sinemap. The first system only performs pixelvalue substitutions to focus on the effect of utilizing the generalized map. This system is controlled by fifteen different parameters and initial conditions of three generalized Sine maps.The second system performs both permutations and substitutions to achieve Shannon’s diffusion and confusion properties. The two systems are analyzed using miscellaneous evaluation criteria such as pixel correlation coefficients, differential attack measures, histogram distributions and the National Institute of Standards and Technology (NIST) statistical test suite. Key sensitivity analysis is also performed and the mean square error and entropy measures are calculated. The analysis results are promising and demonstrate the benefits of utilizing the designed generalized map in image encryption applications.
K. Abd-El-Hafiz, Salwa; G. Radwan, Ahmed; and H. AbdEl-Haleem, Sherif
"Encryption Applications of a Generalized Chaotic Map,"
Applied Mathematics & Information Sciences: Vol. 09
, Article 50.
Available at: https://dc.naturalspublishing.com/amis/vol09/iss6/50