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Cryptanalysis of a color image encryption using minimax differential evolution-based 7D hyper-chaotic map

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Abstract

This paper proposes two attack methods to break the encryption algorithm using minimax differential evolution-based 7D hyper-chaotic map. In attack method 1, the secret keys generated by the 7D hyper-chaotic map can be directly revealed through two pairs of plain/cipher images. Once the secret keys are known, any cipher image can be decrypted easily. In attack method 2, we build three dictionary matrices of R, G and B channels firstly, and the corresponding plain image pixel value can be queried in the dictionary matrix one by one without using the secret keys or any system parameter. Experimental results demonstrate that the cryptosystem can be broken successfully by either of the proposed methods, thus avoiding the potential unexpected loss caused by the use of insecure encryption schemes.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (61602158) and the Science and Technology Research Project of Henan Province (212102210413).

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Authors and Affiliations

  1. College of Computer and Information Engineering, Henan Normal University, Xinxiang, 453007, China

    Yanfang Liu, Ming Li & Haiju Fan

  2. Engineering Lab of Intelligence Business & Internet of Things, Xinxiang, Henan Province, China

    Yanfang Liu, Ming Li & Haiju Fan

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  1. Yanfang Liu
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Correspondence to Ming Li.

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Appendix A

Appendix A

Proposition

Suppose that x is an 8-bit unsigned integer, then

$$255\oplus x=255-x$$

Proof

XOR is a binary bitwise operation. Suppose that the binary form of x and another number y are as follows:

$$\left\{\begin{array}{c}{(x)}_{10}={\left({x}_1{x}_2{x}_3{x}_4{x}_5{x}_6{x}_7{x}_8\right)}_2\\ {}{(y)}_{10}={\left({y}_1{y}_2{y}_3{y}_4{y}_5{y}_6{y}_7{y}_8\right)}_2\end{array}\right.,$$
(55)

where the subscript denotes the corresponding base. We know

$${\displaystyle \begin{array}{c}255\oplus x={\left(11111111\oplus {x}_1{x}_2\cdots {x}_8\right)}_2\\ {}={\left(1\oplus {x}_1,1\oplus {x}_2,\cdots, 1\oplus {x}_8\right)}_2\end{array}},$$
(56)

where the i-th operation

$$1\oplus x_i=\left\{\begin{array}{c}0\;\text{if}\;x_i=1\\1\;\text{if}\;x_i=0\end{array}\right..$$
(57)

On the other side, (255-x)10 = (11111111- x1x2x3x4x5x6x7x8)2, where the i-th operation

$$1-x_i=\left\{\begin{array}{c}0\;\text{if}\;x_i=1\\1\;\text{if}\;x_i=0\end{array}\right.$$
(58)

There is neither carry nor borrow after the corresponding position subtraction. Comparing Eqs. (57) and Eq. (58),we get

$$255\oplus x=255-x.$$
(59)

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Liu, Y., Li, M. & Fan, H. Cryptanalysis of a color image encryption using minimax differential evolution-based 7D hyper-chaotic map. Multimed Tools Appl 82, 44209–44225 (2023). https://doi.org/10.1007/s11042-023-15445-3

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