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Chosen-plaintext attack of an image encryption scheme based on modified permutation–diffusion structure

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Abstract

Since the first appearance in Fridrich’s design, the usage of permutation–diffusion structure for designing digital image cryptosystem has been receiving increasing research attention in the field of chaos-based cryptography. Recently, a novel chaotic image cipher using a single-round modified permutation–diffusion pattern (ICMPD) was proposed. Unlike traditional permutation–diffusion structure, the permutation of ICMPD is operated on bit level instead of pixel level and its diffusion stage is operated on masked pixels, which are obtained by carrying out the classical affine cipher, instead of plain pixels. Following a divide-and-conquer strategy, this paper reports that ICMPD can be compromised by a chosen-plaintext attack efficiently and the involved data complexity is linear to the size of the plain-image. Moreover, the relationship between the cryptographic kernel at the diffusion stage of ICMPD and the classical modulo addition then XORing operation is explored thoroughly.

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Notes

  1. https://sites.google.com/site/leoyuzhang/.

  2. For simplicity, we slightly modify the permutation techniques described in [18] while keeping its security level unchanged.

  3. The adversary can choose \((\alpha , \beta )\) freely and be aware of the value of y in CPA assumption.

  4. The number of possible solutions of s that satisfy (a) s is coprime to 256 and (b) \(s \in [0, 128]\) is 64.

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Acknowledgments

This research was supported by the National Natural Science Foundation of China (No. 61502399).

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Authors and Affiliations

  1. School of Software, Dalian University of Technology, Dalian, 116024, China

    Yuansheng Liu

  2. Department of Electronic Engineering, City University of Hong Kong, Kowloon Tong, SAR, Hong Kong

    Leo Yu Zhang, Jia Wang & Kwok-wo Wong

  3. School of Electronics and Information Engineering, Southwest University, Chongqing, 400000, China

    Yushu Zhang

  4. College of Computer Science and Engineering, Shenzhen University, Shenzhen, 518060, China

    Yushu Zhang

Authors
  1. Yuansheng Liu
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  2. Leo Yu Zhang
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  3. Jia Wang
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  4. Yushu Zhang
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  5. Kwok-wo Wong
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Correspondence to Leo Yu Zhang.

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Liu, Y., Zhang, L.Y., Wang, J. et al. Chosen-plaintext attack of an image encryption scheme based on modified permutation–diffusion structure. Nonlinear Dyn 84, 2241–2250 (2016). https://doi.org/10.1007/s11071-016-2642-3

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  • DOI: https://doi.org/10.1007/s11071-016-2642-3

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