MANDELBROT VE LOJİSTİK KAOTİK HARİTA KULLANILARAK GÖRÜNTÜ ŞİFRELEME

Yıl 2023, , 79 - 95, 28.02.2023

Gülseren Kibar , Mustafa Cem Kasapbaşı

https://doi.org/10.56809/icujtas.1150309

Öz

Son yıllarda, görüntü şifreleme popüler ve önemli bir araştırma alanı olmuştur. İnternet ve ağlar üzerinden iletişime olan bağımlılığın gün geçtikçe artmasıyla birlikte, verilerin iletimi güvenlik ihlaline karşı açık hale geliyor. Bu güvenlik ihlallerine karşı en iyi çözümlerden biri de verinin şifrelenmesidir. Günümüzde çoğunlukla kullanılan geleneksel algoritmalar, düşük güvenlik seviyesi göstermesinden dolayı kaos tabanlı kripto sistemler son yıllarda fazlasıyla ilgi çekici hale gelmiştir. Buraya olan yoğun ilgiden sonra çeşitli kaotik haritalar kriptografi alanına kazandırılmıştır. Eski şifreleme yöntemlerinin kullanılmasıyla ortaya çıkan düşük güvenlik seviyesi problemi kaos şifrelemesi kullanılarak çözülmüştür. Bunun yanı sıra kaos şifrelemede anahtarın rastgeleliğinin ve boyutunun büyüklüğünün de görüntü şifrelemedeki önemi ortaya çıkmıştır. Bu araştırma makalesi görüntüleri işlemek için çeşitli türleri olan kaotik haritalar ile mandelbrot fraktallarını içeren yeni bir hibrit şifreleme algoritması sunmaktadır. Bunun sebebi fraktal görüntülerin rastgeleliğinin fazla olması nedeniyle, şifreleme için güçlü bir anahtar olarak kullanılabilmesidir. Araştırmacıların çalışmaları sonucu literatürde de yer alan pek çok kaotik metot ortaya çıkmıştır. Makalede de bunlardan birisi olan lojistik harita kaotik methodunda oluşturulan anahtar ile mandelbrot fraktal setlerinden elde bir başka anahtarın işleme tabi tutularak ortaya çıkan yeni bir anahtar ile görüntü şifrelemesi yapılmıştır. Ayrıca makalede bu kaotik harita ile fraktalların birlikte kullanılmasının sonucu elde edilen şifreli görüntülerin analizi ve karşılaştırılması yapılmaktadır. Bu analiz yapılırken oluşturulan şifreli görüntünün ve görüntünün orjinal halinin görsel değerleri karşılaştırılarak algoritmanın başarısı PSNR, Entropi, SSIM, MSE, Korelasyon Katsayısı, Histogram Analizi, NPCR ve UACI yöntemleri ile ölçülmüştür.

Anahtar Kelimeler

Kaos Teorisi, Kaotik Görüntü Şifreleme, Lojistik Harita, Mandelbrot Set, Performans Analizi

IMAGE ENCRYPTION USING MANDELBROT AND LOGISTIC CHAOTIC MAP

Öz

In recent years, image encryption has been a popular and important research area. With the increasing dependence on communication over the Internet and networks, the transmission of data becomes vulnerable to security breaches. One of the best solutions against these security breaches is data encryption. Chaos-based cryptosystems have become very interesting in recent years, since traditional algorithms, which are mostly used today, show a low level of security. After the intense interest here, various chaotic maps have been brought to the field of cryptography. The low security level problem caused by using old encryption methods has been solved by using chaos encryption. In addition, the importance of the randomness and size of the key in image encryption has emerged in chaos encryption. This research paper presents a new hybrid encryption algorithm for processing images, including several types of chaotic maps and mandelbrot fractals. This is because fractal images are so random that they can be used as a strong key for encryption. As a result of the studies of the researchers, many chaotic methods have emerged in the literature. In the article, one of them, the logistic map chaotic method, and another key obtained from the mandelbrot fractal sets are processed and image encryption is made with a new key. In addition, this article analyzes and compares the encrypted images obtained as a result of using this chaotic map and fractals together. The success of the algorithm was measured by PSNR, Entropy, SSIM, MSE, Correlation Coefficient, Histogram Analysis, NPCR and UACI methods by comparing the visual values of the encrypted image and the original version of the image created during this analysis.

Anahtar Kelimeler

Chaos Theory, Chaotic Image Encryption, Logistic Map, Mandelbrot Set, Performance Analysis

Kaynakça

• Abdul N., Abbas M. (2015) Image encryption based on Independent Component Analysis and Arnold’s Cat Map
• Ahmad J., Hwang S. (2015) ‘‘Chaos-based diffusion for highly autocorrelated data in encryption algorithms,’’ Nonlinear Dyn., vol. 82, no. 4, pp. 1839–1850.
• Abdulgader A, Ismail M, Zainal N, Idbeaa T (2015) Enhancement of AES algorithm based on chaotic maps and shift operation for image encryption. Journal of Theoretical and Applied Information Technology ; 71(1): 1-12
• Akhshani A., Akhavan A., Lim S., Hassan Z. (2012) An image encryption scheme based on quantum logistic map
• Anees A., Siddiqui A. M., Ahmed F. (2014) ‘‘Chaotic substitution for highly autocorrelated data in encryption algorithm,’’ Commun. Nonlinear Sci. Numer. Simul., vol. 19, no. 9, pp. 3106–3118.
• Belazi A, Talha M, Kharbech S, Xiang W (2019) “Novel Medical Image Encryption Scheme Based on Chaos and DNA Encoding”, IEEE Access, vol. 7, pp. 36667–36681.
• Cheng, G., Wang, C., & Chen, H. (2019). A Novel Color Image Encryption Algorithm Based on Hyperchaotic System and Permutation-Diffusion Architecture. International Journal of Bifurcation and Chaos, 29(9).
• Crownover, R.M. (1995) Introduction to Fractals and Chaos; Jones and Bartlett: Burlington, MA, USA.; ISBN 978-0-86720-464-3.
• Dong Y., Liu J., Zhu C., Wang Y.(2010) Image encryption algorithm based on chaotic mapping. (ICCSIT), 2010 3rd IEEE International Conference : 289-291.
• El-Alfy E, Al-Utaibi K. (2011) An Encryption Scheme for Color Images Based on Chaotic Maps and Genetic Operators. The Seventh International Conference on Networking and Services : 92-97
• Erdem Y. (2021) A new parallel processing architecture for accelerating image encryption based on chaos
• Han B, Jia Y, Huang G, Cai L, (2020) “A Medical Image Encryption Algorithm Based On Hermite Chaotic Neutral Network”, 2020 IEEE 4th Information Technology, Networking, Electronic and Automation Control Conference (ITNEC), vol. 1, pp.2644-2648.
• Huang, C. K., Liao, C. W., Hsu, S. L., & Jeng, Y. C. (2013). Implementation of gray image encryption with pixel shuffling and gray-level encryption by single chaotic system. Telecommunication Systems, 52(2), 563-571.
• Huang, C. K., Nien, H. H (2009). Multi chaotic systems-based pixel shuffle for image encryption. Optics communications, 282(11), 2123-2127
• Huang, H. (2019). Novel Scheme for Image Encryption Combining 2D Logistic-SineCosine Map and Double Random-Phase Encoding. IEEE Access, 7, 177988–177996. https://doi.org/10.1109/ACCESS.2019.2958319 Hussain S., Jamal S. S., Shah T., Hussain I. (2020) A Power Associative Loop Structure For The Construction Of Non-Linear Components Of Block Cipher
• Jain A., Rajpal N. (2016) “A robust image encryption algorithm resistant to attacks using DNA and chaotic logistic maps,” Multimed. Tools. Appl., Vol. 75, no. 10, pp. 5455–72.
• Jolfaei A, Mirghadri A (2010). An image encryption approach using chaos and stream cipher. Journal of Theoretical and Applied Information Technology. 19(2): 117-125.
• Krishnamoorthi R., Murali P. (2014) “Chaos based image encryption with orthogonal polynomials model and bit shuffling,” in Proceedings of the IEEE International Conference on Signal Processing and Integrated Networks, Noida India, pp. 107–12.
• Lan R, He J, Wang S, Gu T, Luo X. (2018) Integrated chaotic systems for image encryption. Signal Processing 2018;147:133–45.
• Li, A., Belazi, A., Kharbech, S., Talha, M., & Xiang, W. (2019). Fourth Order MCA and Chaos-Based Image Encryption Scheme. IEEE Access, 7, 66395–66409
• Liu X, Xiao D, Xiang Y (2019) Quantum image encryption using intra and inter bit permutation based on logistic map. IEEE Access 7:6937–6946.
• Liu, Z., Wu, C., Wang, J., & Hu, Y. (2019). A Color Image Encryption Using Dynamic DNA and 4-D Memristive Hyper-Chaos. IEEE Access, 7, 78367–78378.
• Loukhaoukha, K., Chouinard, J. Y., & Berdai, A. (2012). A secure image encryption algorithm based on Rubik's cube principle. Journal of Electrical and Computer Engineering, 2012, 7.
• Ma, S., Zhang, Y., Yang, Z., Hu, J., & Lei, X. (2019). A New Plaintext-Related Image Encryption Scheme Based on Chaotic Sequence. IEEE Access, 7, 30344–30360.
• Mandelbrot, B.B. (1982) The Fractal Geometry of Nature; Henry Holt and Company: New York, NY, USA; ISBN 978-0-7167-1186-5.
• Mary R, Eswaran P, Shankar K (2018) “Multi Secret Image Sharing Scheme Based on DNA Cryptography with XOR”, Pure and Applied Mathematics, vol. 118, No. 7, pp. 393-398.
• Menezes, A. J., Van Oorschot, P. C., & Vanstone, S. A. (1996) Handbook of applied cryptography, CRC press. Negi, D.; Negi, A. (2016) Agarwal, S. The complex key cryptosystem. Int. J. Appl. Eng. Res., 11, 681–684.
• Niyat AY, Moattar MH, Torshiz MN (2017). Color image encryption based on hybrid hyper-chaotic system and cellular automata. Opt Lasers Eng 2017; 90:225–37.
• Patel S, Bharath K P, Muthu R. (2020) Image Encryption Decryption Using Chaotic Logistic Mapping and DNA Encoding
• Pickover, C.A. (2001) Computers, Pattern, Chaos, and Beauty: Graphics from an Unseen World; Courier Corporation: North Chelmsford, MA, USA; ISBN 978-0-486-41709-7.
• Shubo L, Sun J, Xu Z. (2009) An improved image encryption algorithm based on chaotic system. Journal of Computers; 4(11): 1091-1100.
• Stallings, W. (2006) Cryptography and network security: principles and practices. Pearson Education India.
• Soni, A., Acharya A. K. (2012) A Novel Image Encryption Approach using an Index based Chaos and DNA Encoding and its Performance Analysis
• Verma A, Jain A (2016) Pixel chaotic shuffling and Arnold map based Image Security Using Complex Wavelet Transform. Journal of Network Communications and Emerging Technologies (JNCET); 6(5): 8-11.
• Xua Q., Suna K., Caoa C., Zhub C. (2019) A fast image encryption algorithm based on compressive sensing and hyperchaotic map Yin Q., Wang C. (2018) A New Chaotic Image Encryption Scheme Using Breadth-First Search and Dynamic Diffusion
• Zhang, X., Wang, L., Zhou, Z., & Niu, Y. (2019). A Chaos-Based Image Encryption Technique Utilizing Hilbert Curves and H-Fractals. IEEE Access, 7, 74734–74746.
• Zhao, J., Guo, W., & Ye, R. (2014) “Achaos-based image encryption scheme using permutation-substitution architecture”, Int. J. Comput. Trends Technol, 15(4), 174- 185.
• Zhou N, Chen W, Yan X, Wang Y (2018) Bit-level quantum color image encryption scheme with quantum cross-exchange operation and hyper-chaotic system. Quantum Inf Process 17(6):137