TY - JOUR TT - Grayscale Image Encryption Based on Theory of Finite Fields AU - Kurt Pehlivan, Meltem AU - Duru, Nevcihan AU - Sakallı, Muharrem Tolga PY - 2016 DA - December JF - Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi PB - Bilecik Şeyh Edebali Üniversitesi WT - DergiPark SN - 2458-7575 SP - 10 EP - 17 VL - 3 IS - 2 KW - Görüntü Şifreleme KW - Sonlu Cisimler KW - Gri Seviye Görüntü Şifreleme KW - Deşifreleme N2 - With the development of technology, studies to ensure privacy and security have gained importance. Fortransmitting information between sender and recipient sides without getting third parts many methods have beendeveloped. In this study, according to irreducible polynomial that is determined between the parties (sender andrecipient), the pixel values of grayscale images which are of size 128x128 that are expressed by finite field elementsover Galois Field (28) (GF(28)). Polynomial coefficients of each finite field element considered as 8-bit binary number,than this number is converted to decimal number. These decimal numbers are replaced with the original grayscalepixel values than encrypted image is sent to the recipient. In this study Matlab is used to getting finite field elements,encryption and decryption process. Thanks to improved method encrypted grayscale images are decrypted as lossless. CR - Güvenoğlu, E. ve Suçsuz, N., "Yer DeğiĢtirme ve Değer DönüĢtürme Özelliğine Sahip Görüntü ġifreleme Algoritmalarının Analizi," Akademik Bilişim Konferansları 2007-AB2007, Kütahya, Türkiye, Ocak 2007. CR - Yen, J. C. and Guo, J. I., "A new chaotic image encryption algorithm," National Lien-Ho College of Technology and Commerce, Taiwan, China, 1998. CR - Guo, J. I. and Yen, J. C., "A new mirrorlike image encryption algorithm and its VLSI architecture," 10 th. VLSI Design/CAD Symposium, Taiwan, China, 1999. CR - Chang, C. , Hwang, M. and Chen, T., "A new encryption algorithm for image cryptosystems," The Journal of Systems and Software, vol. 58, pp. 83-91, 2000. CR - Maniccam, S. S. and Bourbakis, N. G., Lossless image compression and encryption using SCAN,"International Journal of Pattern Recognition, vol. 34, 2001. CR - Scripcariu, L. and Frunza, M. D., "New Image Encryption Algorithm Based on Inversable Functions Defined on Galois Fields",In Proc. of the Intern. Symposium on Signals, Circuits and Systems ISSCS 2005, vol 1., pp. 243-246, 2005. CR - ġahin, A., BuluĢ, E. ve Sakallı, M. T., "Gri Seviye Resimler Üzerinde Rasgele Lsb Yöntemini ve Sayi Teorisini Kullanarak Bilgi Gizleme Ve Steganaliz," Akademik BiliĢim Konferansları 2006-AB2006, Denizli, Türkiye, ġubat 2006. CR - Lin, Y. and Wang, P., "Improved Invertible Secret Image Sharing with Steganography," 2011 Seventh International Conference on Intelligent Information Hiding and Multimedia Signal Processing, Dalian, China, 2011. CR - Srividya, B. V. and Akhila, S., "A Heuristic Approach for Secured Transfer of Image Based on Bezier Curve over Galois Field GF(pm)," Proceedings of International Conference on Circuits, Communication, Control and Computing (I4C 2014), MSRIT, BANGALORE, India, November 2014. CR - Chhotaray, S. K., Chhotaray, A. and Rath, G. S., "A New Method of Generating Public Key Matrix and Using It for Image Encryption," 2015 2nd International Conference on Signal Processing and Integrated Networks (SPIN), Noida, Delhi-NCR, India, 2015. CR - Danacıoğlu, N. ve Muluk, F. Z., Galois cisimleri ve en yüksek çözümlü 2k-1 tasarımlarının oluĢturulması, Ġstatistikçiler Dergisi,vol. 3,2010. CR - Yavuzer Aslan, F. "Blok Ģifrelerde kullanılan doğrusal dönüĢüm yapılarının incelenmesi," Yüksek Lisans Tezi, Trakya Üniversitesi Fen Bilimleri Enstitüsü, Edirne, 21, 2012. CR - Vikipedi BMP. [Online]. Available: https://tr.wikipedia.org/wiki/BMP, 2016. CR - Wang, Z., Bovik, A.C., Sheikh, H.R. and Simoncelli, E.P. Image Quality Assessment: From Error Visibility to Structural Similarity, IEEE Transactions On Image Processing,vol. 13, April 2004,. CR - Kaya, Y. ve Kayci, L., "Kelebek Görüntülerinin Sınıflandırılması Ġçin Bir Ġçerik Bazlı Görüntü EriĢim Sistemi," Akademik Bilişim, Mersin, Türkiye, ġubat 2014. UR - https://dergipark.org.tr/tr/pub/bseufbd/issue//354837 L1 - https://dergipark.org.tr/tr/download/article-file/366420 ER -