Encryption of Color Images with a New Framework

Implementation Using the Elzaki Transformation

  • Mardan A. Pirdawood Department of Mathematics, Faculty of Science and Health, Koya University, Danielle Mitterrand Boulevard, Koya KOY45, Kurdistan Region – F.R. Iraq https://orcid.org/0000-0002-3234-1825
  • Shadman R. Kareem (1) Department of Mathematics, Faculty of Science and Health, Koya University, Danielle Mitterrand Boulevard, Koya KOY45, Kurdistan Region – F.R. Iraq; (2) Department of Computer Science, College of Information Technology and Computer Sciences, Catholic University in Erbil, Kurdistan Region – F.R. Iraq https://orcid.org/0000-0002-7982-156X
  • Omar Al-Rassam Department of Mathematics, Faculty of Science and Health, Koya University, Danielle Mitterrand Boulevard, Koya KOY45, Kurdistan Region – F.R. Iraq http://orcid.org/0000-0002-3235-5477
DOI: https://doi.org/10.14500/aro.11618
Keywords: Cryptography, Elzaki Transformations, Image Encryptions, Maclaurin Series

Abstract

The significance of image encryption has risen due to the widespread use of images as a key means of sharing data across different applications. Encryption methods are crucial in defending the confidentiality and integrity of valuable image data. This work proposes a novel method of image encryption technique based on the Elzaki transformation and substitution process, which is made possible by the extension of the Maclaurin series coefficients. The image is encrypted using an infinite series of hyperbolic functions and the Elzaki transform; the inverse Elzaki transform is then used to decrypt the image. Using modular arithmetic, the coefficients that result from the transformation are keyed.

Downloads

Download data is not yet available.

Author Biographies

Mardan A. Pirdawood, Department of Mathematics, Faculty of Science and Health, Koya University, Danielle Mitterrand Boulevard, Koya KOY45, Kurdistan Region – F.R. Iraq

Mardan A. Pirdawood is a Lecturer at the Department of Mathematics, Faculty of Science and Health, Koya University. He got the B.Sc. degree in Mathematics, the M.Sc. degree in Nonstandard Mathematical Analysis. His research interests are in general topology, numerical analysis and cryptography.

Shadman R. Kareem , (1) Department of Mathematics, Faculty of Science and Health, Koya University, Danielle Mitterrand Boulevard, Koya KOY45, Kurdistan Region – F.R. Iraq; (2) Department of Computer Science, College of Information Technology and Computer Sciences, Catholic University in Erbil, Kurdistan Region – F.R. Iraq

Shadman R. Kareem is a Lecturer at the Department of Mathematics, Faculty of Science, Koya University. He got the B.Sc. degree in Mathematics, the M.Sc. degree in Fuzzy Topology and the Ph.D. degree in Algebraic Topology-Topological Data Analysis. His research interests are in algebraic topology, topological data analysis and cryptography.

Omar Al-Rassam, Department of Mathematics, Faculty of Science and Health, Koya University, Danielle Mitterrand Boulevard, Koya KOY45, Kurdistan Region – F.R. Iraq

Omar Alrassam is a lecturer at the Department of Mathematics, Faculty of science and health/ Koya University. He got the B.Sc. degree in computer science, M.Sc. degree in Advanced computer science. His research interests are in computational linguistic, NLP and text processing.

References

Al-Khazraji, L.R., Abbas, A.R., and Jamil, A.S., 2022. Employing neural style transfer for generating deep dream images. Aro-The Scientific Journal of Koya University, 10(2), pp.134-141. DOI: https://doi.org/10.14500/aro.11051

An, F.P., and Liu, J.E., 2019. Image encryption algorithm based on adaptive wavelet chaos. Journal of Sensors, 2019, pp.1-12. DOI: https://doi.org/10.1155/2019/2768121

Elshamy, A., Hussein, A., Hamed, H.F.A., Abdelghany, M.A., and Kelash, H.M., 2019. Color image encryption technique based on chaos. Procedia Computer Science, 163, p.49-53. DOI: https://doi.org/10.1016/j.procs.2019.12.085

Elzaki, T., 2011. The new integral transform “Elzaki transform”. Global Journal of Pure and Applied Mathematics, 7(1), pp.57-64.

Faragallah, O.S., Alzain, M.A., El-Sayed, H.S., Al-Amri, J.F., El-Shafai, W., Afifi, A., Naeem, E.A., and Soh, B., 2018. Block-based optical color image encryption based on double random phase encoding. IEEE Access, 7, pp.4184-4194. DOI: https://doi.org/10.1109/ACCESS.2018.2879857

Farsana, F.J., Devi, V.R., and Gopakumar, K., 2023. An audio encryption scheme based on Fast Walsh Hadamard Transform and mixed chaotic keystreams. Applied Computing and Informatics, 19, pp.239-264. DOI: https://doi.org/10.1016/j.aci.2019.10.001

Hamad, A.S., and Farhan, A.K., 2020. Image encryption algorithm based on substitution principle and shuffling scheme. Journal of Engineering Technology, 38(3B), pp.98-103. DOI: https://doi.org/10.30684/etj.v38i3B.433

Kang, X., Han, Z., Yu, A., and Duan, P., 2017. Double Random Scrambling Encoding in the RPMPFrHT Domain. In: 2017 IEEE International Conference on Image Processing (ICIP), pp.4362-4366. DOI: https://doi.org/10.1109/ICIP.2017.8297106

Kaur, J., and Jindal, N., 2019. A secure image encryption algorithm based on fractional transforms and scrambling in combination with multimodal biometric keys. Multimedia Tools and Applications, 78, pp.11585-11606. DOI: https://doi.org/10.1007/s11042-018-6701-2

Kuffi, E.A., Mehdi, S.A., and Mansour, E.A., 2022. Color image encryption based on new integral transform SEE. Journal of Physics: Conference Series, 2322(1), p.012016. DOI: https://doi.org/10.1088/1742-6596/2322/1/012016

Lang, J., 2012. Image encryption based on the reality-preserving multiple parameter fractional Fourier transform and chaos permutation. Optics and Lasers in Engineering, 50(7), pp.929-937. DOI: https://doi.org/10.1016/j.optlaseng.2012.02.012

Lian, S., 2008. Multimedia Content Encryption: Techniques and Applications. CRC Press, United States. DOI: https://doi.org/10.1201/9781420065282

Liang, Y.R., and Xiao, Z.Y., 2020. Image encryption algorithm based on compressive sensing and fractional DCT via polynomial interpolation. International Journal of Automation and Computing, 17(2), pp.292-304. DOI: https://doi.org/10.1007/s11633-018-1159-2

Liu, W., Sun, K., and Zhu, C., 2016. A fast image encryption algorithm based on chaotic map. Optics and Lasers in Engineering, 84, p.26-36. DOI: https://doi.org/10.1016/j.optlaseng.2016.03.019

Nag, A., Singh, J.P., Khan, S., Ghosh, S., Biswas, S., Sarkar, D., and Sarkar, P.P., 2011. Image Encryption using Affine Transform and XOR Operation. In: International Conference on Signal Processing, Communication, Computing and Networking Technologies. DOI: https://doi.org/10.1109/ICSCCN.2011.6024565

Nasry, H., Abdallah, A.A., Farhan, A.K., Ahmed, H.E., and El Sobky, W.I., 2022. Multi chaotic system to generate novel S-box for image encryption. Journal of Physics: Conference Series, 2304(1), p. 012007. DOI: https://doi.org/10.1088/1742-6596/2304/1/012007

Pan, S.M., Wen, R.H., Zhou, Z.H., and Zhou, N.R., 2017. Optical multi-image encryption scheme based on discrete cosine transform and nonlinear fractional Mellin transform. Multimedia Tools and Applications, 76, pp.2933-2953. DOI: https://doi.org/10.1007/s11042-015-3209-x

Pirdawood, M.A., Kareem, S.R., and Zahir, D.C., 2023. Audio encryption framework using the laplace transformation. Aro-the Scientific Journal of Koya University, 11(2), pp.31-37. DOI: https://doi.org/10.14500/aro.11165

Pradheep, M., 2021. Image Encryption by Using ACGLML. Munich, GRIN Verlag, p.130.

Priya, S.S.S., KarthigaiKumar, P., Mangai, N.S., and Vanathi, P.T., 2012. Survey on efficient, Low-Power, AES image encryption and bio-cryptography schemes. SmartCR, 2, pp.379-390. DOI: https://doi.org/10.6029/smartcr.2012.06.001

Salim, S.J., and Ashruji, M.G., 2016. Application of El-Zaki transform in cryptography. International Journal of Modern Sciences and Engineering Technology, 3, pp.46-48.

Shivaji, J.S., and Hiwarekar, A.P., 2021. Cryptographic method based on Laplace-Elzaki transform. Journal of the Maharaja Sayajirao University of Baroda, 55(1), pp.187-191.

Sui, L., Duan, K., and Liang, J., 2015. Double-image encryption based on discrete multiple-parameter fractional angular transform and two-coupled logistic maps. Optics Communications, 343, pp.140-149. DOI: https://doi.org/10.1016/j.optcom.2015.01.021

Wang, X., Liu, C., and Jiang, D., 2021. A novel triple-image encryption and hiding algorithm based on chaos, compressive sensing and 3D DCT. Information Sciences, 574, p.505-527. DOI: https://doi.org/10.1016/j.ins.2021.06.032

Wang, Z.Y., Zhang, Y.Q., and Bao, X.M., 2015. A novel chaotic image encryption scheme using DNA sequence operations. Optics and Lasers in Engineering, 73, p.53-61. DOI: https://doi.org/10.1016/j.optlaseng.2015.03.022

Weber, A.G., 2006. The USC-SIPI Image Database: Version 5. Available from: http://sipi.usc.edu/database [Last accessed on 2023 Oct 01].

Wei, L., and Shi, H., 2023. Chaotic image encryption algorithm based on wavelet transform. Journal of Applied Mathematics and Computation, 7(3), pp.359-364. DOI: https://doi.org/10.26855/jamc.2023.09.004

Wu, J., Guo, F., Liang, Y., and Zhou, N., 2014. Triple color images encryption algorithm based on scrambling and the reality-preserving fractional discrete cosine transform. Optik, 125(16), pp.4474-4479. DOI: https://doi.org/10.1016/j.ijleo.2014.02.026

Yang, J., and Wang, X., 2021. A privacy image encryption algorithm based on piecewise coupled map lattice with multi dynamic coupling coefficient. Information Sciences, 569, p.217-240. DOI: https://doi.org/10.1016/j.ins.2021.04.013

Zhou, N., Zhang, A., Zheng, F., and Gong, L., 2014. Novel image compression encryption hybrid algorithm based on key-controlled measurement matrix in compressive sensing. Optics and Laser Technology, 62, pp.152-160 DOI: https://doi.org/10.1016/j.optlastec.2014.02.015

Published
2024-06-14
How to Cite
Pirdawood, M. A., Kareem, S. and Al-Rassam, O. (2024) “Encryption of Color Images with a New Framework: Implementation Using the Elzaki Transformation”, ARO-THE SCIENTIFIC JOURNAL OF KOYA UNIVERSITY, 12(1), pp. 170-180. doi: 10.14500/aro.11618.
Issue
Vol. 12 No. 1 (2024): Issue Twenty Two
Section
Articles

Copyright (c) 2024 Mardan A. Pirdawood, Shadman Kareem, Omar Al-Rassam

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Authors who choose to publish their work with Aro agree to the following terms:

  • Authors retain the copyright to their work and grant the journal the right of first publication. The work is simultaneously licensed under a Creative Commons Attribution License [CC BY-NC-SA 4.0]. This license allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.

  • Authors have the freedom to enter into separate agreements for the non-exclusive distribution of the journal's published version of the work. This includes options such as posting it to an institutional repository or publishing it in a book, as long as proper acknowledgement is given to its initial publication in this journal.

  • Authors are encouraged to share and post their work online, including in institutional repositories or on their personal websites, both prior to and during the submission process. This practice can lead to productive exchanges and increase the visibility and citation of the published work.

By agreeing to these terms, authors acknowledge the importance of open access and the benefits it brings to the scholarly community.

Crossref
Scopus
Google Scholar
Europe PMC