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An image encryption method based on multi-space confusion using hyperchaotic 2D Vincent map derived from optimization benchmark function

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Abstract

A novel multi-space confusion image encryption (MSC-IE) method based on 2D Vincent map is presented in this study. In order to provide a more secure method, the MSC-IE consists of two-stage column and row permutation processing. The 2D Vincent map is derived from the Vincent function, which is an optimization benchmark function. The chaotic performance of the 2D Vincent map is examined through rigorous evaluations such as bifurcation and phase space trajectory diagrams, and Lyapunov exponent, sample entropy, correlation dimension and Kolmogorov entropy which are compared with the state of the art, as well. In the two-stage permutation, the column of the image is scrambled and the rows of the decomposed columns are shuffled, and then the row of the image is scrambled and the columns of the decomposed rows are shuffled. In the diffusion stage, a sequence matrix is converted into an image matrix and diagonally reordered. This reordered image is summed with the permutated image. The result is a completely unrecognizable ciphertext image. The MSC-IE is subjected to reliable cryptanalysis and cyber-attacks, and some results are compared with available reported results. The MSC-IE provides the most secure images due to the superior hyperchaotic performance of the 2D Vincent map.

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Abbreviations

1D:

One-dimensional

PST:

Phase space trajectory

LE:

Lyapunov exponent

SE:

Sample entropy

CD:

Correlation dimension

KE:

Kolmogorov entropy

SC-IE:

Multi-space confusion image encryption

2D-ICM:

2D infinite collapse map

CIEA:

Color image encryption algorithm

CMC:

Cascade modulation couple

FOCM:

Fractional-order chaotic map

PC:

Parameter calculator

SG:

Sequence generator

EP:

Encryption procedure

DP:

Decryption procedure

CC:

Correlation coefficient

NBCR:

Number of bit change rate

LSE:

Local Shannon entropy

NPCR:

Number of pixels changing rate

UACI:

Unified average changing intensity

PSNR:

Peak signal to noise ratio

SPN:

Salt and pepper noise

EPT:

Encryption processing time

NCPB:

Number of cycles per byte

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Authors and Affiliations

  1. Department of Computer Engineering, Faculty of Engineering, Karamanoglu Mehmetbey University, 70200, Karaman, Türkiye

    Uğur Erkan

  2. Department of Artificial Intelligence and Data Engineering, Engineering Faculty, Ankara University, 06830, Gölbaşı, Ankara, Türkiye

    Abdurrahim Toktas

  3. Department of Computer Engineering, Faculty of Engineering and Natural Sciences, İstanbul Rumeli University, 34570, Istanbul, Türkiye

    Samet Memiş

  4. Department of Marine Engineering, Faculty of Maritime, Bandirma Onyedi Eylül University, 10200, Balıkesir, Türkiye

    Samet Memiş

  5. School of Electrical and Automation Engineering, East China Jiaotong University, Nanchang, 330013, China

    Qiang Lai & Genwen Hu

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Erkan, U., Toktas, A., Memiş, S. et al. An image encryption method based on multi-space confusion using hyperchaotic 2D Vincent map derived from optimization benchmark function. Nonlinear Dyn 111, 20377–20405 (2023). https://doi.org/10.1007/s11071-023-08859-z

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