Nonlinear dynamic systems and chaotic systems have been quite exhaustively researched in the domain of cryptography. However, the possibility of using the fractional chaotic system in the cryptosystem design has been much less explored while it bears advantages such as enlarged keyspace, compared to classical nonlinear systems.This paper, therefore, proposes a novel structure for the pseudo-random number generator based on fractional chaotic systems which consists of 3 different fractional chaotic systems, namely fractional Chen's system, Lu's system, and fractional generalized double-humped logistic map(FGDHL). Then, the outputs of this fractional chaotic pseudo-random number generator(FCPRNG) are used as a keystream for an image encryption scheme. The confusion layer of the scheme is conducted by a dynamic DNA encoding and decoding method combined with a 2D cat map for the permutation in the DNA-bases level. The diffusion layer is performed through the adoption of a 32 bits discrete logistic map. The performance and security analysis have been conducted for the above-designed cryptosystem, proving that the proposed cryptosystem is practical and secure in image encryption.

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This paper is devoted to the analysis of calculation methods for solving fractional chaotic systems and the impact of these different approaches on the behavior of the fractional chaotic system. Two widely used time domain fractional differential equations solving approaches are discussed, the fractional ABM correctorpredictor method based on Caputo fractional derivative definition, and the long memory calculation approach based on Grunwald fractional derivative. These numerical solutions calculation methods are employed to depict the phase portrait of a class of commensurate fractional chaotic systems. The Lyapunov exponent and bifurcation diagrams of the systems over various fractional orders and parameters are illustrated to detect the impact on the dynamics of the chaotic system applying different calculation approaches.

In this paper, we focus on the design of fractional pseudo-chaotic random number generator (FPCRNG) based on the coupling of fractional chaotic systems. The proposed FPCRNG is composed of 3 fractional chaotic systems, including one fractional generalized double humped logistic system, two 3D fractional systems Chen's system and Lu's system, and one classical skew-tent map. A non-uniform gird calculation method is employed by introducing the skew-tent map into the numerical calculation of the states of the Chen's system and Lu's system to obtain greater chaoticity in terms of Lyaponov exponent. The XOR operations are applied to the fractional systems to obtain the final pseudo-random outputs. The security analysis and statistical experiment of a stream cipher implementing the FPCRNG prove that the proposed structure is effective and can be used into cryptosystem.