Quaternion Feistel Cipher with an Infinite Key Space Based on Quaternion Julia Sets

• Autorzy: Dzwonkowski M. , Rykaczewski R.
• Języki publikacji: EN

Abstrakty

EN

In this paper Quaternion Feistel Cipher (QFC) with an infinite key space based on quaternion Julia sets is proposed. The basic structure of the algorithm is based on the scheme proposed in 2012 by Sastry and Kumar. The proposed algorithm uses special properties of quaternions to perform rotations of data sequences in 3D space for each of the cipher rounds. It also uses Julia sets to form an infinite key space. The plaintext is divided into two square matrices of equal size and written using Lipschitz quaternions. A modular arithmetic was implemented for operations with quaternions. A computer-based analysis has been carried out and obtained results are shown at the end of this paper.

Słowa kluczowe

EN

cryptography; lossless scheme; multimedia encryption; security

• Wydawca: Instytut Łączności - Państwowy Instytut Badawczy
• Czasopismo: Journal of Telecommunications and Information Technology
• Rocznik: 2015
• Tom: nr 4
• Strony: 15--21
• Opis fizyczny: Bibliogr. 20 poz., rys., tab.

Twórcy

autor

Dzwonkowski M.

• Faculty of Electronics, Telecommunications and Informatics, Department of Teleinformation Networks, Gdańsk University of Technology, Gdańsk, Poland

autor

Rykaczewski R.

• Department of Radiological Informatics and Statistics, Medical University of Gdańsk, Gdańsk, Poland

Bibliografia

• [1] T. Nagase, M. Komata, and T. Araki, "Secure signals transmission based on quaternion encryption scheme", in Proc. 18th Int. Conf. Adv. Inform. Netw. Appl. AINA 2004, Fukuoka, Japan, 2004, vol. 2, pp. 35-38.
• [2] T. Nagase, R. Koide, T. Araki, and Y. Hasegawa, "A new quadripartite public-key cryptosystem", in Proc. Int. Symp. on Commun. and Inform. Technol. ISCIT 2004, Sapporo, Japan, 2004, pp. 74-79.
• [3] T. Nagase, R. Koide, T. Araki, and Y. Hasegawa, "Dispersion of sequences for generating a robust enciphering system", Trans. Commun. Inform. Technol. (ECTI-CIT 2005), vol. 1, no. 2, pp. 9-14, 2005.
• [4] M. Dzwonkowski and R. Rykaczewski, "A new quaternion encryption scheme for image transmission", ICT Young 2012 Conf., Gdańsk, 2012, pp. 21-27.
• [5] M. Dzwonkowski and R. Rykaczewski, "Quaternion encryption method for image and video transmission", Przegl. Telekom. + Wiad. Telekom., vol. 8-9, pp. 1216-1220, 2013.
• [6] B. Czaplewski, M. Dzwonkowski, and R. Rykaczewski, "Digital fingerprinting based on quaternion encryption for image transmission", Przegl. Telekom. + Wiad. Telekom., vol. 8-9, pp. 792-798, 2013.
• [7] B. Czaplewski, M. Dzwonkowski, and R. Rykaczewski, "Digital fingerprinting for color images based on the quaternion encryption scheme", Pattern Recogn. Lett., vol. 46, pp. 11-19, 2014.
• [8] M. Dzwonkowski and R. Rykaczewski, "A quaternion-based modified feistel cipher for multimedia transmission", Przegl. Telekom. + Wiad. Telekom., vol. 8-9, pp. 1177-1181, 2014.
• [9] V. U. K. Sastry and K. A. Kumar, "A modified feistel cipher involving modular arithmetic addition and modular arithmetic inverse of a key matrix", Int. J. Adv. Comp. Sci. Appl. (IJACSA 2012), vol. 3, no. 7, pp. 40-43, 2012.
• [10] R. Goldman, "Understanding quaternions", Graphical Models, vol. 73, no. 2, pp. 21-49, 2011.
• [11] R. Goldman, An Integrated Introduction to Computer Graphics and Geometric Modeling. New York: CRC Press, 2009.
• [12] F. Zhang, "Quaternion and matrices of quaternions", Linear Algebra and its Applications, vol. 251, pp. 21-57, 1997.
• [13] D. Eberly, "Quaternion Algebra and Calculus", Geometric Tools, LLC, 2010 [Online]. Available: http://www.geometrictools.com/Documentation/Documentation.html
• [14] G. M. Julia, "Memoir on iterations of rational functions", J. de Mathématiques pures et appliquées, 4th tome (83th volume of the collection), pp. 47-246, 1918.
• [15] A. Douady, "Julia Sets and the Mandelbrot Set", in The Beauty of Fractals: Images of Complex Dynamical Systems, H.-O. Peitgen and P. H. Richter, Eds. Berlin: Springer, 1986, p. 161.
• [16] C. Corrales-Rodrigáñez, "Rotations and units in quaternion algebras", J. Number Theory, vol. 132, no. 5, pp. 888-895, 2012.
• [17] Quat - A 3D-Fractal-Generator, Version 1.20 [Online]. Available: http://www.physcip.uni-stuttgart.de/phy11733/quat e.html
• [18] Robert G. Brown's General Tools Page [Online]. Available: http://www.phy.duke.edu/~rgb/General/dieharder.php
• [19] Cryptool Portal [Online]. Available: http://www.cryptool.org/en/
• [20] P. Armitage, G. Berry, and J. N. S. Matthews, Statistical Methods in Medical Research, 4th ed. (revised). Chichester: Wiley - Blackwell, 2001.