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A novel image encryption algorithm based on a 3D chaotic map. (English) Zbl 1335.94058

Summary: Recently E. Solak et al. [Int. J. Bifurcation Chaos Appl. Sci. Eng. 20, No. 5, 1405–1413 (2010; Zbl 1193.94065)] cryptanalyzed the chaotic image encryption algorithm of J. Fridrich [Int. J. Bifurcation Chaos Appl. Sci. Eng. 8, No. 6, 1259–1284 (1998; Zbl 0935.94019)], which was considered a benchmark for measuring security of many image encryption algorithms. This attack can also be applied to other encryption algorithms that have a structure similar to Fridrich’s algorithm, such as that of G. Chen, Y. Mao and C. Chui [Chaos Solitons Fractals 21, No. 3, 749–761 (2004; Zbl 1049.94009)]. In this paper, we suggest a novel image encryption algorithm based on a three dimensional (3D) chaotic map that can defeat the aforementioned attack among other existing attacks. The design of the proposed algorithm is simple and efficient, and based on three phases which provide the necessary properties for a secure image encryption algorithm including the confusion and diffusion properties. In phase I, the image pixels are shuffled according to a search rule based on the 3D chaotic map. In phases II and III, 3D chaotic maps are used to scramble shuffled pixels through mixing and masking rules, respectively. Simulation results show that the suggested algorithm satisfies the required performance tests such as high level security, large key space and acceptable encryption speed. These characteristics make it a suitable candidate for use in cryptographic applications.

MSC:

94A60 Cryptography
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
68P25 Data encryption (aspects in computer science)
68U10 Computing methodologies for image processing

Software:

Diehard
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