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JULİA SETLERİ VE LOJİSTİK HARİTA KULLANILARAK GÖRÜNTÜ ŞİFRELEME

Year 2023, Volume: 5 Issue: 2, 65 - 78, 28.02.2023
https://doi.org/10.56809/icujtas.1150308

Abstract

Açık ağlar ve internet üzerinden veri alışverişi hızla büyüdüğü için, verilerin güvenlik açığı incelenecek büyük bir sorun haline gelmektedir. Bu soruna olası bir çözüm olarak ise metin, görüntü, ses, video gibi verilerin şifrelenmesi yöntemi önerilir. Bu işlem yapılacağı zaman Gelişmiş Şifreleme Standardı (AES) gibi klasik şifreleme algoritmaları her zaman birincil seçimdir, ancak görüntü veya video şifreleme söz konusu olduğunda, literatürdeki birçok araştırmaya bakıldığı zaman hesaplama verimliliği nedeniyle yazarların kaos tabanlı şifreleme tekniklerini önerdiği sıkça görülmektedir. Kaos şifrelemenin ana özelliklerine bakıldığında anahtarların rastgeleliği, başlangıç koşullarına duyarlılığı ve daha büyük anahtarlarla çalışıldığında daha verimli sonuçlar elde edildiği göze çarpar. Bu araştırma makalesinde görüntü işleme konusunda kriptografik yeni bir yaklaşım önerilmiştir. Bu yaklaşımda kaotik haritalardan birisi olan lojistik harita ile julia fraktal setlerinin birlikte kullanılarak bir şifreleme algoritması sunulmaktadır. Yaklaşımda fraktal tabanlı setin kullanılmasının sebebi anahtarın gücünün arttırılarak şifrelemenin daha başarılı olmasını sağlamasıdır. Bu algoritma iki anahtarın işlemden geçirilmesiyle oluşturulan yeni anahtarın görüntü şifrelemede kullanılması ile ortaya çıkmıştır. Buna ilave olarak da algoritmanın başarı oranının arttırılması için çalışmalar yapılmıştır. Sunulan yeni yaklaşımla birlikte oluşan şifreli görüntülerin asıl görüntüler ile birlikte analizinin çıkarılması ve yapılan analiz sonucu elde edilen nicel değerler mevcuttur. Bu değerlerin iyileştirilmesi için de algoritmada çeşitli değişiklikler yapılarak testler yapılmıştır. Bu testler sonucunda şifreli görüntü ile asıl görüntünün karşılaştırılarak yöntemin başarısı ölçülmüştür. Bu başarıyı ölçmek için Piksel Sayısı Değişim Hızı (NPCR), Tepe Sinyal Gürültü Oranı (PSNR), Sinyal Gürültü Oranı (SNR), Korelasyon Katsayısı, Birleşik Ortalama Değişen Yoğunluk (UACI), Yapısal Benzerlik İndeks Ölçüsü (SSIM), Entropi ve Yerel Shannon Entropisi, Ortalama Karesel Hata (MSE), Histogram Analizi metrikleri kullanılmıştır.

References

  • Agarwal S.(2018) Secure Image Transmission Using Fractal and 2D-Chaotic Map. Journal of Imaging, 4, 17.
  • Akhshani A ,Akhavan A ,Lim S, Hassan Z (2012) An image encryption scheme based on quantum logistic map; Communications in Nonlinear Science and Numerical Simulation Volume 17, Issue 12, Pages 4653-4661
  • Al-Maadeed S, Al-Ali A, Abdalla T (2012) A New Chaos-Based Image-Encryption and Compression Algorithm”,Hindawi Publishing Corporation, Journal of Electrical and Computer Engineering, Article ID 179693.
  • Al-Najjar H., AL-Najjar A.,(2011) ”Image Encryption Algorithm Based on Logistic Map and Pixel Mapping Table”
  • Alsafasfeh Q, Arfoa A(2011). Image encryption based on the general approach for multiple chaotic systems. Journal of Intelligent Learning Systems and Applications.; 3(3): 238-244.
  • Anchal J, Navin R (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.
  • 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.
  • Askar S.; Karawia A.; Al-Khedhairi A.; Al-Ammar F.(2018) “An Algorithm Of Image Encryption Using Logistic and Two-Dimensional Chaotic Economic Maps”, Entropy, MDPI,Vol.20, Issue 1.
  • Baker G, Gollub J .(1996) Chaotic dynamics: an introduction. Cambridge University Press; second ed.
  • Barnsley, M.F., Demko S.(1985) ‘Iterated function systems and the global construction of fractals’, Proc. R. Soc. Lond. A, Math. Phys. Sci., 399, pp. 243–275
  • Brahim A., Pacha A., Said H. (2020) Image encryption based on compressive sensing and chaos systems, Optics & Laser Technology Volume 132, 106489
  • Diab H. (2018) An efficient chaotic image cryptosystem based on simultaneous permutation and diffusion operations. IEEE Access;6:42227–44.
  • Edgar G.(2004). Classics on Fractals. Boulder, CO: Westview Press. ISBN 978-0-8133-4153-8.
  • El-Latif A., El-Atty B., Talha M,(2018) “Robust Encryption of Quantum Medical Images”, IEEE Access, vol. 6, pp. 1073 – 1081
  • Hua Z, Zhou Y, Huang H. (2019)Cosine-transform-based chaotic system for image encryption. Inform Sci;480:403–19.
  • Kaur G, Agarwal R, Patidar V. (2020) Chaos based multiple order optical transform for 2D image encryption, Engineering Science and Technology, an International Journal 23, 998–1014
  • Khanzadi H, Eshghi M, Borujeni S (2014). Image encryption using random bit sequence based on chaotic maps. Arabian Journal for Science and engineering; 39(2): 1039-1047.
  • 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.
  • Kumar M., Chahal A.(2014) Effect of Encryption Technique and Size of Image on Correlation Coefficient in Encrypted Image, International Journal of Computer Applications (0975 – 8887), Volume 97– No.12
  • Li T., Du B., Liang X. (2020). Image Encryption Algorithm Based on Logistic and Two-Dimensional Lorenz. IEEE Access, 8, 13792–13805.
  • Liu H, Zhao B, Huang L,(2019) “A RemoteSensing Image Encryption Scheme Using DNA Bases Probability and Two-Dimensional Logistic Map”, IEEE Access, vol. 7, pp. 65450–65459.
  • Liu J, Zhang L,Yue G (2003). "Fractal Dimension in Human Cerebellum Measured by Magnetic Resonance Imaging". Biophysical Journal. 85 (6): 4041–4046
  • Liu L., Lei Y., Wang D. (2020). A Fast Chaotic Image Encryption Scheme with Simultaneous Permutation-Diffusion Operation. IEEE Access, 8, 27361–27374.
  • Liu L., Wang D., Lei Y. (2020). An Image Encryption Scheme Based on Hyper Chaotic System and DNA with Fixed Secret Keys. IEEE Access, 8, 46400–46416.
  • Lu Q., Zhu C., Deng X. (2020). An Efficient Image Encryption Scheme Based on the LSS Chaotic Map and Single S-Box. IEEE Access, 8, 25664–2567
  • Roy A., Misra A. P., Banerjee S.(2017) “Chaos-based image encryption using vertical-cavity surface-emitting lasers”, arXiv preprint arXiv: 1705.00975
  • Segal S. (1978). "Riemann's example of a continuous 'nondifferentiable' function continued". The Mathematical Intelligencer. 1 (2): 81–82
  • Soni A, Acharya A,(2012) A Novel Image Encryption Approach using an Index based Chaos and DNA Encoding and its Performance; International Journal of Computer Applications 47(23):1-6
  • Trochet H. (2009). "A History of Fractal Geometry". MacTutor History of Mathematics
  • Wade M., Chouikha M., Gill T.; Patterson W., Washington T,(2019) “A Dual Layer Image Encryption using Polymerase Chain Reaction Amplification and DNA Encryption”, IEEE 10th Annual Ubiquitous Computing, Electronics & Mobile Communication Conference (UEMCON).
  • Wang L, Ye Q, Xiao Y, Zou Y, Zhang B. (2008), An image encryption scheme based on cross chaotic map. Congress onImage and Signal Processing; 3: 22-26.
  • Wang T., Song L., Wang M., Zhuang, Z. (2020). A novel image encryption algorithm based on parameter-control scroll chaotic attractors. IEEE Access, 8, 36281–36292.
  • Wang W, Si M, Pang Y, Ran P, Wang H, Jiang X, Liu Y, Wu J, Wu W, Chilamkurti N, et al(2018). An encryption algorithm based on combined chaos in body area networks. Comput Electr Eng;65:282–91.
  • Wang X, Wang Q, Zhang Y (2015). A fast image algorithm based on rows and columns switch. Nonlinear Dynam;79(2):1141–9
  • Wang X., Liu L. (2020). Image Encryption Based on Hash Table Scrambling and DNA Substitution. IEEE Access, 8, 68533–68547.
  • Xua Q, Suna K., Caoa C., Zhub C.(2019) A fast image encryption algorithm based on compressive sensing and hyperchaotic map. Optics and Lasers in Engineering (121) 203–214
  • Yin Q, Wang C. (2018) A New Chaotic Image Encryption Scheme Using Breadth-First Search and Dynamic Diffusion, International Journal of Bifurcation and Chaos, Vol. 28, No. 4
  • https://geoffboeing.com/2015/03/chaos-theory-logistic-map/

IMAGE ENCRYPTION USING JULIA SETS AND LOGISTIC MAP

Year 2023, Volume: 5 Issue: 2, 65 - 78, 28.02.2023
https://doi.org/10.56809/icujtas.1150308

Abstract

As data exchange over open networks and the internet is growing rapidly, data vulnerability is becoming a major issue to examine. As a possible solution to this problem, the method of encrypting data such as text, images, audio, and video is recommended. When doing this, classical encryption algorithms such as Advanced Encryption Standard (AES) are always the primary choice, but when it comes to image or video encryption, when looking at many studies in the literature, it is often seen that the authors recommend chaos-based encryption techniques due to computational efficiency. Looking at the main features of chaos encryption, the randomness of the keys, sensitivity to initial conditions and more efficient results are obtained when working with larger keys. A new cryptographic approach to image processing is proposed in this research paper. In this approach, an encryption algorithm is presented by using the logistic map, which is one of the chaotic maps, and the julia fractal sets together. The reason for using the fractal-based set in the approach is to increase the strength of the key and ensure that the encryption is more successful. This algorithm has emerged with the use of the new key, which is created by processing two keys, in image encryption. In addition, studies have been carried out to increase the success rate of the algorithm. With the new approach presented, there are quantitative values obtained as a result of the analysis and analysis of the encrypted images together with the original images. In order to improve these values, various changes were made in the algorithm and tests were carried out. As a result of these tests, the success of the method was measured by comparing the encrypted image with the original image. To measure this success, Pixel Count Rate of Change (NPCR), Peak Signal to Noise Ratio (PSNR), Signal to Noise Ratio (SNR), Correlation Coefficient, Combined Average Variable Intensity (UACI), Structural Similarity Index Measure (SSIM), Entropy, and Local Shannon Entropy, Mean Squared Error (MSE), Histogram Analysis metrics were used.

References

  • Agarwal S.(2018) Secure Image Transmission Using Fractal and 2D-Chaotic Map. Journal of Imaging, 4, 17.
  • Akhshani A ,Akhavan A ,Lim S, Hassan Z (2012) An image encryption scheme based on quantum logistic map; Communications in Nonlinear Science and Numerical Simulation Volume 17, Issue 12, Pages 4653-4661
  • Al-Maadeed S, Al-Ali A, Abdalla T (2012) A New Chaos-Based Image-Encryption and Compression Algorithm”,Hindawi Publishing Corporation, Journal of Electrical and Computer Engineering, Article ID 179693.
  • Al-Najjar H., AL-Najjar A.,(2011) ”Image Encryption Algorithm Based on Logistic Map and Pixel Mapping Table”
  • Alsafasfeh Q, Arfoa A(2011). Image encryption based on the general approach for multiple chaotic systems. Journal of Intelligent Learning Systems and Applications.; 3(3): 238-244.
  • Anchal J, Navin R (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.
  • 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.
  • Askar S.; Karawia A.; Al-Khedhairi A.; Al-Ammar F.(2018) “An Algorithm Of Image Encryption Using Logistic and Two-Dimensional Chaotic Economic Maps”, Entropy, MDPI,Vol.20, Issue 1.
  • Baker G, Gollub J .(1996) Chaotic dynamics: an introduction. Cambridge University Press; second ed.
  • Barnsley, M.F., Demko S.(1985) ‘Iterated function systems and the global construction of fractals’, Proc. R. Soc. Lond. A, Math. Phys. Sci., 399, pp. 243–275
  • Brahim A., Pacha A., Said H. (2020) Image encryption based on compressive sensing and chaos systems, Optics & Laser Technology Volume 132, 106489
  • Diab H. (2018) An efficient chaotic image cryptosystem based on simultaneous permutation and diffusion operations. IEEE Access;6:42227–44.
  • Edgar G.(2004). Classics on Fractals. Boulder, CO: Westview Press. ISBN 978-0-8133-4153-8.
  • El-Latif A., El-Atty B., Talha M,(2018) “Robust Encryption of Quantum Medical Images”, IEEE Access, vol. 6, pp. 1073 – 1081
  • Hua Z, Zhou Y, Huang H. (2019)Cosine-transform-based chaotic system for image encryption. Inform Sci;480:403–19.
  • Kaur G, Agarwal R, Patidar V. (2020) Chaos based multiple order optical transform for 2D image encryption, Engineering Science and Technology, an International Journal 23, 998–1014
  • Khanzadi H, Eshghi M, Borujeni S (2014). Image encryption using random bit sequence based on chaotic maps. Arabian Journal for Science and engineering; 39(2): 1039-1047.
  • 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.
  • Kumar M., Chahal A.(2014) Effect of Encryption Technique and Size of Image on Correlation Coefficient in Encrypted Image, International Journal of Computer Applications (0975 – 8887), Volume 97– No.12
  • Li T., Du B., Liang X. (2020). Image Encryption Algorithm Based on Logistic and Two-Dimensional Lorenz. IEEE Access, 8, 13792–13805.
  • Liu H, Zhao B, Huang L,(2019) “A RemoteSensing Image Encryption Scheme Using DNA Bases Probability and Two-Dimensional Logistic Map”, IEEE Access, vol. 7, pp. 65450–65459.
  • Liu J, Zhang L,Yue G (2003). "Fractal Dimension in Human Cerebellum Measured by Magnetic Resonance Imaging". Biophysical Journal. 85 (6): 4041–4046
  • Liu L., Lei Y., Wang D. (2020). A Fast Chaotic Image Encryption Scheme with Simultaneous Permutation-Diffusion Operation. IEEE Access, 8, 27361–27374.
  • Liu L., Wang D., Lei Y. (2020). An Image Encryption Scheme Based on Hyper Chaotic System and DNA with Fixed Secret Keys. IEEE Access, 8, 46400–46416.
  • Lu Q., Zhu C., Deng X. (2020). An Efficient Image Encryption Scheme Based on the LSS Chaotic Map and Single S-Box. IEEE Access, 8, 25664–2567
  • Roy A., Misra A. P., Banerjee S.(2017) “Chaos-based image encryption using vertical-cavity surface-emitting lasers”, arXiv preprint arXiv: 1705.00975
  • Segal S. (1978). "Riemann's example of a continuous 'nondifferentiable' function continued". The Mathematical Intelligencer. 1 (2): 81–82
  • Soni A, Acharya A,(2012) A Novel Image Encryption Approach using an Index based Chaos and DNA Encoding and its Performance; International Journal of Computer Applications 47(23):1-6
  • Trochet H. (2009). "A History of Fractal Geometry". MacTutor History of Mathematics
  • Wade M., Chouikha M., Gill T.; Patterson W., Washington T,(2019) “A Dual Layer Image Encryption using Polymerase Chain Reaction Amplification and DNA Encryption”, IEEE 10th Annual Ubiquitous Computing, Electronics & Mobile Communication Conference (UEMCON).
  • Wang L, Ye Q, Xiao Y, Zou Y, Zhang B. (2008), An image encryption scheme based on cross chaotic map. Congress onImage and Signal Processing; 3: 22-26.
  • Wang T., Song L., Wang M., Zhuang, Z. (2020). A novel image encryption algorithm based on parameter-control scroll chaotic attractors. IEEE Access, 8, 36281–36292.
  • Wang W, Si M, Pang Y, Ran P, Wang H, Jiang X, Liu Y, Wu J, Wu W, Chilamkurti N, et al(2018). An encryption algorithm based on combined chaos in body area networks. Comput Electr Eng;65:282–91.
  • Wang X, Wang Q, Zhang Y (2015). A fast image algorithm based on rows and columns switch. Nonlinear Dynam;79(2):1141–9
  • Wang X., Liu L. (2020). Image Encryption Based on Hash Table Scrambling and DNA Substitution. IEEE Access, 8, 68533–68547.
  • Xua Q, Suna K., Caoa C., Zhub C.(2019) A fast image encryption algorithm based on compressive sensing and hyperchaotic map. Optics and Lasers in Engineering (121) 203–214
  • Yin Q, Wang C. (2018) A New Chaotic Image Encryption Scheme Using Breadth-First Search and Dynamic Diffusion, International Journal of Bifurcation and Chaos, Vol. 28, No. 4
  • https://geoffboeing.com/2015/03/chaos-theory-logistic-map/
There are 38 citations in total.

Details

Primary Language Turkish
Subjects Computer Software
Journal Section Research Articles
Authors

Bahar Arıtürk 0000-0001-5972-401X

Mustafa Cem Kasapbaşı 0000-0001-6444-6659

Publication Date February 28, 2023
Submission Date July 28, 2022
Published in Issue Year 2023 Volume: 5 Issue: 2

Cite

APA Arıtürk, B., & Kasapbaşı, M. C. (2023). JULİA SETLERİ VE LOJİSTİK HARİTA KULLANILARAK GÖRÜNTÜ ŞİFRELEME. İstanbul Ticaret Üniversitesi Teknoloji Ve Uygulamalı Bilimler Dergisi, 5(2), 65-78. https://doi.org/10.56809/icujtas.1150308