A recently proposed secure image encryption scheme has drawn attention to the limited security offered by chaos-based image encryption schemes (mainly due to their relatively small key space) proposing a highly robust approach, based on Rubik's cube principle. This paper aims to study a newly designed image cryptosystem that uses the Rubik's cube principle in conjunction with a digital chaotic cipher. Thus, the original image is shuffled on Rubik's cube principle (due to its proven confusion properties), and then XOR operator is applied to rows and columns of the scrambled image using a chaos-based cipher (due to its proven diffusion properties). Finally, the experimental results and security analysis show that the newly proposed image encryption scheme not only can achieve good encryption and perfect hiding ability but also can resist any cryptanalytic attacks (e.g., exhaustive attack, differential attack, statistical attack, etc.).
Nowadays, increasingly, it seems that the use of rule sets of the most popular games, particularly in new images’ encryption algorithms designing branch, leads to the crystallization of a new paradigm in the field of cryptography. Thus, motivated by this, the present paper aims to study a newly designed digital image scrambler (as part of the two fundamental techniques used to encrypt a block of pixels, i.e., the permutation stage) that uses knight’s moving rules (i.e., from the game of chess), in conjunction with a chaos-based pseudorandom bit generator, abbreviated PRBG, in order to transpose original image’s pixels between RGB channels. Theoretical and practical arguments, rounded by good numerical results on scrambler’s performances analysis (i.e., under various investigation methods, including visual inspection, adjacent pixels’ correlation coefficients’ computation, key’s space and sensitivity assessment, etc.) confirm viability of the proposed method (i.e., it ensures the coveted confusion factor) recommending its usage within cryptographic applications.
A new chaotic discrete dynamical system, built on trigonometric functions, is proposed. With intent to use this system within cryptographic applications, we proved with the aid of specific tools from chaos theory (e.g., Lyapunov exponent, attractor’s fractal dimension, and Kolmogorov-Smirnov test) and statistics (e.g., NIST suite of tests) that the newly proposed dynamical system has a chaotic behavior, for a large parameter’s value space, and very good statistical properties, respectively. Further, the proposed chaotic dynamical system is used, in conjunction with a binary operation, in the designing of a new pseudorandom bit generator (PRBG) model. The PRBG is subjected, by turns, to an assessment of statistical properties. Theoretical and practical arguments, rounded by good statistical results, confirm viability of the proposed chaotic dynamical system and newly designed PRBG, recommending them for usage within cryptographic applications.
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