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Cryptanalysis and improvement in an image encryption scheme using combination of the 1D chaotic map

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Abstract

In this paper, we evaluate the security of an image cipher recently proposed. Three different cryptographic primitives, i.e., permutation, diffusion, and cyclic rotation, were integrated in this cipher so as to obtain a satisfactory security performance within a single encryption round. It is found that the equivalent key stream elements can be derived under chosen-plaintext attack. Both mathematical proof and experimental validation are given in detail. Concerning the presented analysis and some common defects of chaos-based image ciphers, an enhanced image cryptosystem based on the single-round permutation–diffusion structure is further developed. Natural and medical images are introduced for experimental verification and performance comparison. The results demonstrate the security superiority of the improved cryptosystem.

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Notes

  1. Interested readers are encouraged to refer to the original paper [33] for a detailed analysis.

  2. The symbols adopted here are slightly different from those of the original paper.

  3. Though \(T^{P^l}(1)\) and \(T^{P^l}(MN-lp+1)\) may be equal to l, yet it is of overwhelming probability to find an effective l to make \(T^{P^{l}}(1)\ne {l}\) and \(T^{P^{l}}(MN-lp+1)\ne {l}\).

  4. The NPCR and UACI values in Pak’s paper [33] is essentially the key sensitivity performance, there is no differential attack analysis in the original publication.

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Acknowledgements

This work is funded by the China Postdoctoral Science Foundation (No. 2018M630301), the Fundamental Research Funds for the Central Universities (Nos. N171903003, N171904009, N151903001), the National Natural Science Foundation of China (Nos. 61672146, 61771121). Thanks to Dr. Leo Yu Zhang (leocityu@gmail.com) for his valuable suggestions and selfless contribution, which are much help ful for promoting the manuscript.

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Authors and Affiliations

  1. Sino-Dutch Biomedical and Information Engineering School, Northeastern University, Shenyang, 110169, China

    Junxin Chen, Fangfang Han, Wei Qian & Yu-Dong Yao

  2. Software College, Northeastern University, Shenyang, 110169, China

    Zhi-liang Zhu

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  1. Junxin Chen
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  2. Fangfang Han
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Correspondence to Zhi-liang Zhu.

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Chen, J., Han, F., Qian, W. et al. Cryptanalysis and improvement in an image encryption scheme using combination of the 1D chaotic map. Nonlinear Dyn 93, 2399–2413 (2018). https://doi.org/10.1007/s11071-018-4332-9

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