An Improvement of Image Encryption Based on Continued Fractions of Quartic Irrationals
Abstract
In this paper, we propose a symmetric-key image encryption scheme using an infinite simple continued fraction derived from a quartic irrational number of the form , where , as the secret key. Efficiency of encryption is measured in terms of correlation coefficients, deviation from ideality, the avalanche effect, and peak signal-to-noise ratios. After encrypting five standard test images, namely, Airplane, Baboon, Fruits, Lena, and Peppers, our scheme is compared with the schemes of Hamad et al. (2013) and Pareek (2012). The results show that our scheme is more effective than the scheme of Pareek (2012). Moreover, except for the correlation coefficients, our scheme is slightly more effective than the scheme of Hamad et al. (2013). Keywords : image encryption, RGB image, continued fraction, quartic irrational numberReferences
Abd El-Samie, F.E., Ahmed, H.E.H., Elashry, I.F., Shahieen, M.H., Faragallah, O.S., El-Rabaie, E.-S.M., & Alshebeili, S.A. (2014). Image Encryption: A Communication Perspective. Boca Raton: CRC Press.
Burton, D.M. (2007). Elementary Number Theory. (6th ed.). New York: McGraw-Hill.
Goldberg, S. (1960). Probability: An Introduction. Englewood Cliffs: Prentice-Hall.
Hamad, S., Khalifa, A., Elhadad, A., & Rida, S.Z. (2013). A modified Playfair cipher for encrypting digital images. Journal of Communication and Computer Engineering, 3(2), 1-9.
Havil, J. (2012). The Irrationals: A Story of the Numbers You Can’t Count on. Princeton: Princeton University Press.
Liu, Z., Xu, L., Liu, T., Chen, H., Li, P., Lin, C., Liu, S. (2011). Color image encryption by using Arnold transform and color-blend operation in discrete cosine transform domains. Optics Communications, 284, 123-128.
Özdemir, A.S., & Yaprakdal, A.B. (2010). Using the relationship between periodic continued fraction and quadratic irrationals: ASAB-II cipher. Istanbul Aydın Üniversitesi Dergisi, 2, 131-149.
Pareek, N.K. (2012). Design and analysis of a novel digital image encryption scheme. International Journal of Network Security & Its Applications, 4(2), 95-108.
Peat, J., Barton, B., & Elliott, E. (2008). Statistics Workbook for Evidence-based Health Care. Chichester: Wiley.
University of Wisconsin-Madison. (2012). Public-domain Test Images for Homework and Projects. Retrieved June 11, 2018, from http://homepages.cae.wisc.edu/~ece533/images/index.html
Young, C.Y. (2010). Precalculus. Hoboken: Wiley.
Burton, D.M. (2007). Elementary Number Theory. (6th ed.). New York: McGraw-Hill.
Goldberg, S. (1960). Probability: An Introduction. Englewood Cliffs: Prentice-Hall.
Hamad, S., Khalifa, A., Elhadad, A., & Rida, S.Z. (2013). A modified Playfair cipher for encrypting digital images. Journal of Communication and Computer Engineering, 3(2), 1-9.
Havil, J. (2012). The Irrationals: A Story of the Numbers You Can’t Count on. Princeton: Princeton University Press.
Liu, Z., Xu, L., Liu, T., Chen, H., Li, P., Lin, C., Liu, S. (2011). Color image encryption by using Arnold transform and color-blend operation in discrete cosine transform domains. Optics Communications, 284, 123-128.
Özdemir, A.S., & Yaprakdal, A.B. (2010). Using the relationship between periodic continued fraction and quadratic irrationals: ASAB-II cipher. Istanbul Aydın Üniversitesi Dergisi, 2, 131-149.
Pareek, N.K. (2012). Design and analysis of a novel digital image encryption scheme. International Journal of Network Security & Its Applications, 4(2), 95-108.
Peat, J., Barton, B., & Elliott, E. (2008). Statistics Workbook for Evidence-based Health Care. Chichester: Wiley.
University of Wisconsin-Madison. (2012). Public-domain Test Images for Homework and Projects. Retrieved June 11, 2018, from http://homepages.cae.wisc.edu/~ece533/images/index.html
Young, C.Y. (2010). Precalculus. Hoboken: Wiley.
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Published
2020-05-01
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Research Article
