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A new one-dimensional chaotic map and its application in a novel permutation-less image encryption scheme

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Abstract

In this paper, we propose a new real one-dimensional cosine fractional (1-DCF) chaotic map. Several chaos-theory analysis tests demonstrate that the proposed map has many good cryptography properties, such as a highly chaotic behavior, a large chaotic range, an infinite number of unstable fixed points, and a widely superior sensitivity to the initial conditions than most of the low-dimensional chaotic maps. Regarding these attractive features, we use the 1-DCF map to design a novel fast image encryption scheme for real-time image processing. Unlike most of the existing encryption schemes, we adopt a permutation-less architecture to increase the encryption speed. Regardless of the permutation phase absence, a high-security level is obtained by using a substitution process with a high sensitivity to the plain image. Moreover, we replace the natural row-order encryption with a more secure random-like encryption order generated from the secret key. Experimentation and simulations show that the new scheme is better than many recently proposed encryption schemes in both security and rapidity.

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Acknowledgements

This research is supported by the National Natural Science Foundation of China (No. 61672124), the Password Theory Project of the 13th Five-Year Plan National Cryptography Development Fund (No. MMJJ20170203), Liaoning Province Science and Technology Innovation Leading Talents Program Project (No. XLYC1802013), Key R&D Projects of Liaoning Province (No. 2019020105-JH2/103), Jinan City ’20 universities’ Funding Projects Introducing Innovation Team Program (No. 2019GXRC031).

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Authors and Affiliations

  1. School of Information Science and Technology, Dalian Maritime University, Dalian, 116026, China

    Xingyuan Wang

  2. Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian, 116024, China

    Mohamed Zakariya Talhaoui & Xingyuan Wang

  3. Department of FPST, Ecole Nationale Polytechnique d’Oran, Oran, 31000, Algeria

    Abdallah Talhaoui

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  1. Mohamed Zakariya Talhaoui
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  2. Xingyuan Wang
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  3. Abdallah Talhaoui
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Correspondence to Xingyuan Wang.

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Talhaoui, M.Z., Wang, X. & Talhaoui, A. A new one-dimensional chaotic map and its application in a novel permutation-less image encryption scheme. Vis Comput 37, 1757–1768 (2021). https://doi.org/10.1007/s00371-020-01936-z

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