Performance Comparison of ACM and GRP Methods for Image Permutation

Abstract

Permutation and substitution processes of an image are most widely used in image encryption algorithms as they are thought to increase system security in cryptography. Permutation is the first process that all pixel positions in an image are shuffled in specific order or randomly in order to break strong correlation between pixels. Secondly, substitution is used to change pixel values by mixing a secret key in the permutated image. In an ordinary image, adjacent pixels have close values so they have strong correlation and this correlation needs to be broken effectively before encryption. The degree to which this process is performed, directly affects the overall system security. In this paper, performance evaluations for Group (GRP) and Arnold’s Cat Map (ACM) method are analyzed through some numerical results and their performances are compared to figure out which one is better. Experimental results consist of numerical and visual results determined in Matlab R2015a.

Keywords

• Image
• GRP
• Arnold’s Cat Map
• Confusion
• Logistic Map

References

1. 1. Patidar, V., Pareek, N. K., Purohit, G., & Sud, K. K. (2011). A robust and secure chaotic standard map based pseudorandom permutation-substitution scheme for image encryption. Optics communications, 284(19), 4331-4339.
2. 2. Enayatifar, R., Abdullah, A. H., Isnin, I. F., Altameem, A., & Lee, M. (2017). Image encryption using a synchronous permutation-diffusion technique. Optics and Lasers in Engineering, 90, 146-154.
3. 3. Huang, L., Cai, S., Xiong, X., & Xiao, M. (2019). On symmetric color image encryption system with permutation-diffusion simultaneous operation. Optics and Lasers in Engineering, 115, 7-20.
4. 4. Belazi, A., El-Latif, A. A. A., & Belghith, S. (2016). A novel image encryption scheme based on substitution-permutation network and chaos. Signal Processing, 128, 155-170.
5. 5. Patro, K. A. K., & Acharya, B. (2019). An efficient colour image encryption scheme based on 1-D chaotic maps. Journal of Information Security and Applications, 46, 23-41.
6. 6. Huang, H., He, X., Xiang, Y., Wen, W., & Zhang, Y. (2018). A compression-diffusion-permutation strategy for securing image. Signal Processing, 150, 183-190.
7. 7. Oğraş, H., & Türk, M. (2017). A Robust Chaos-Based Image Cryptosystem with an Improved Key Generator and Plain Image Sensitivity Mechanism. J. Inf. Secur, 8, 23-41.
8. 8. Patro, K. A. K., & Acharya, B. (2018). Secure multi–level permutation operation based multiple colour image encryption. Journal of information security and applications, 40, 111-133.

9. 9. Ping, P., Xu, F., Mao, Y., & Wang, Z. (2018). Designing permutation–substitution image encryption networks with Henon map. Neurocomputing, 283, 53-63.
10. 10. Oğraş, H., & Türk, M. (2016). A Secure Chaos-based Image Cryptosystem with an Improved Sine Key Generator. American Journal of Signal Processing, 6(3), 67-76.
11. 11. Chen, F., Wong, K. W., Liao, X., & Xiang, T. (2014). Period distribution of generalized discrete Arnold cat map. Theoretical Computer Science, 552, 13-25.
12. 12. Abbas, N. A. (2016). Image encryption based on independent component analysis and arnold’s cat map. Egyptian informatics journal, 17(1), 139-146.
13. 13. Chai, X., Fu, X., Gan, Z., Lu, Y., & Chen, Y. (2019). A color image cryptosystem based on dynamic DNA encryption and chaos. Signal Processing, 155, 44-62.
14. 4. Dhall, S., Pal, S. K., & Sharma, K. (2018). A chaos-based probabilistic block cipher for image encryption. Journal of King Saud University-Computer and Information Sciences.
15. 15. Nazari, S., Moin, M. S., & Kanan, H. R. (2016). A face template protection approach using chaos and GRP permutation. Security and Communication Networks, 9(18), 4957-4972.
16. 16. Hua, Z., & Zhou, Y. (2016). Image encryption using 2D Logistic-adjusted-Sine map. Information Sciences, 339, 237-253.
17. 17. Xiangdong, L. I. U., Junxing, Z., Jinhai, Z., & Xiqin, H. (2008). Image scrambling algorithm based on chaos theory and sorting transformation. IJCSNS International Journal of Computer Science and Network Security, 8(1), 64-68.