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Image encryption algorithm based on factorial decomposition

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Abstract

This study proposes a highly efficient image encryption algorithm by employing a rapid key generation approach and permutation structure. The image is converted to a matrix, and then an encryption algorithm based on factorial decomposition permutation is applied. Two variants of the algorithm have been proposed in this study, where each variant is distinguished by the elements of the matrix to be permutated. The first variant is based on the permutation of the pixels of the image. In the second variant, the permutation is applied to both columns and rows of the matrix. These variants of the algorithm have been tested and compared. To create a permutation of a collection of elements, the factorial decomposition mathematical technique is applied, where the Euclidian division of a given key is obtained by adding the factorials of all the integers. The experimental results indicate that the proposed approach provides sufficient and optimistic results in terms of computational complexity, Keyspace analysis, Statistical analysis, and Sensitivity analysis attacks. The statistical analysis shows the superiority of the algorithm using two permutation methods, where sensitivity analysis indicates that the number of pixels changing rate (NPCR) achieved around 99.7 and the unified average changed intensity (UACI) is around 33.5, which showed better performance than the other approaches in the literature. Moreover, the proposed approach provided less computational complexity compared with the existing approaches.

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Data availability

The data that support the findings of this study are openly available in [Volume 3: Miscellaneous] at https://sipi.usc.edu/database/database.php?volume=misc.

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Author information

Authors and Affiliations

  1. Department of Computer Science, College of Computing and Informatics, Saudi Electronic University, 11673, Riyadh, Kingdom of Saudi Arabia

    Muath AlShaikh & Sultan Alamri

  2. Department of Mathematics, College of Science, Imam Abdulrahman Bin Faisal University, P.O. Box 1982, Dammam, Saudi Arabia

    Malek Alzaqebah, Nabil Gmati & Nashat Alrefai

  3. Basic and Applied Scientific Research Center, Imam Abdulrahman Bin Faisal University, P.O. Box 1982, Dammam, Saudi Arabia

    Malek Alzaqebah, Nabil Gmati & Nashat Alrefai

  4. Department of Management of Information Systems, College of Applied Studies and Community Service, Imam Abdulrahman Bin Faisal University, Dammam, Saudi Arabia

    Mutasem K. Alsmadi & Ibrahim Almarashdeh

  5. Computer Information Systems Department, College of Computer Science and Information Technology, Imam Abdulrahman Bin Faisal University, Dammam, Saudi Arabia

    Rami Mustafa A. Mohammad

  6. National Higher School of Mathematics, Scientific and Technology Hub of Sidi Abdellah, P.O. Box 75, Algiers, 16093, Algeria

    Mostefa Kara

Authors
  1. Muath AlShaikh
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  2. Malek Alzaqebah
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  3. Nabil Gmati
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  4. Nashat Alrefai
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  5. Mutasem K. Alsmadi
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  6. Ibrahim Almarashdeh
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  7. Rami Mustafa A. Mohammad
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  8. Sultan Alamri
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  9. Mostefa Kara
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Contributions

The authors' contributions statement of the paper is the introduction Muath and Malek, the second section is done by Mutasem and Ibrahim which is the related work. Section number three is done by Nabil, Mostefa and Rami, the proposed encryption and decryption approach process. The fourth section is done by Sultan and Malek. In the fifth section, we compare and provide a comparative analysis of the current and relevant approaches in the domain and this section is done by Neshat. Last section illustrates the conclusion of our research and is done by Muath, Malek and Nabil.

Corresponding author

Correspondence to Muath AlShaikh.

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AlShaikh, M., Alzaqebah, M., Gmati, N. et al. Image encryption algorithm based on factorial decomposition. Multimed Tools Appl 83, 88447–88467 (2024). https://doi.org/10.1007/s11042-023-17663-1

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  • DOI: https://doi.org/10.1007/s11042-023-17663-1

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