CHAOS-BASED DATA ENCRYPTION USING ARNOLD’S CAT MAP

  • Atila Bostan Atılım University
  • Murat Karakaya Atılım University
  • Gökhan Şengül Atılım University
Keywords: Chaos-based encryption, Arnold’s CAT Map, Chaotic maps verification

Abstract

Continuous Automorphism of the Torus (CAT) is a group of algebraic functions and are typically used in chaos-based encryption applications. Arnold’s CAT Map is one of the known CAT calculations. The most charming property of Arnold’s CAT Map is a number of repetitions of permutations eventually returns the array into the initial state. The number of repetition to return to the initial state is a function of array dimensions and mapping parameter, unquestionably it is chaotic as well. Utilization of Arnold’s CAT Map in encryption is common especially in image encryption and it is generally preferred for its time efficiency when compared with classical block cipher alternatives. Although substitution and permutation are two essential properties of an encryption algorithm, CAT maps are criticized for conducting permutation only. In this study an encryption algorithm that makes use of Arnold’s CAT Map calculation is proposed and its cryptographic properties are presented.

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References

Kocarev, Ljupco, and Shiguo Lian, eds. Chaos-based cryptography: Theory, algorithms and applications. Vol. 354. Springer, 2011.

Stallings, William, and Mohit P. Tahiliani. Cryptography and network security: principles and practice. Vol. 6. London: Pearson, 2014.

Borel, Armand, and Nolan R. Wallach. Continuous cohomology, discrete subgroups, and representations of reductive groups. Vol. 67. American Mathematical Soc., 2013.

L. Shujun, M. Xuanqin, and C. Yuanlong, “Pseudo-random bit generator based on couple chaotic systems and its applications in stream-cipher cryptography,” in Progress in Cryptology —INDOCRYPT 2001, vol. 2247 of Lecture Notes in Computer Science, pp. 316–329, 2001.

Soleymani, Ali, Md Jan Nordin, and Elankovan Sundararajan. "A chaotic cryptosystem for images based on Henon and Arnold cat map." The Scientific World Journal 2014 (2014).

Z. Zhu, W. Zhang, K. Wong, and H. Yu, “A chaos-based symmetric image encryption scheme using a bit-level permutation”, Information Sciences, vol. 181, no. 6, pp. 1171–1186, 2011.

S.-J. Xu, X.-B. Chen, R. Zhang, Y.-X. Yang, and Y.-C. Guo, “An improved chaotic cryptosystem based on circular bit shift and XOR operations,” Physics Letters A, vol. 376, no. 10-11, pp. 1003–1010, 2012.

Z. Zhang and T. Cao, “A chaos-based image encryption scheme with confusion- diffusion architecture,” Communications in Computer and Information Science, vol. 152, no. 1, pp. 258–263, 2011.

C. Fu, B. Lin,Y.Miao, X. Liu, and J.Chen, “Anovel chaos-based bit-level permutation scheme for digital image encryption”, Optics Communications, vol. 284, no. 23, pp. 5415–5423, 2011.

Y. Zhang, P. Xu, and L. Xiang, “Research of image encryption algorithm based on chaotic magic square,” Advances in Intelligent and Soft Computing, vol. 149, no. 2, pp. 103–109, 2012.

M. Ghebleh, A. Kanso, and H. Noura, “An image encryption scheme based on irregularly decimated chaotic maps,” Signal Processing: Image Communication, vol. 29, no. 5, pp. 618–627, 2014.

A. M. Elshamy, A. N. Z. Rashed, A. E. A. Mohamed et al., “Optical image encryption based on chaotic baker map and double random phase encoding,” Journal of Lightwave Technology, vol. 31, no. 15, pp. 2533–2539, 2013.

R. Ye and W. Zhou, “An image encryption scheme based on 2D tent map and coupled map lattice,” International Journal of Information and Communication Technology Research, vol. 1, pp. 344–348, 2011.

R. Ye and W. Zhou, “A chaos-based image encryption scheme using 3D skew tent map and coupledmap lattice,” International Journal of Computer Network and Information Security, vol. 4, pp. 38–44, 2012.

X. Wang, F. Chen, and T. Wang, “A new compound mode of confusion and diffusion for block encryption of image based on chaos,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 9, pp. 2479–2485, 2010.

S. Al-Maadeed, A. Al-Ali, and T. Abdalla, “A new chaos based image-encryption and compression algorithm,” Journal of Electrical and Computer Engineering, vol. 2012, Article ID 179693, 11 pages, 2012.

V. Patidar, N. K. Pareek, and K. K. Sud, “A new substitution diffusion based image cipher using chaotic standard and logistic maps,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 7, pp. 3056–3075, 2009.

K. Wong, B. S. Kwok, and W. Law, “A fast image encryption scheme based on chaotic standard map,” Physics Letters, Section A: General, Atomic and Solid State Physics, vol. 372, no. 15, pp. 2645–2652, 2008.

C. Guanghuia, H. Kai, Z. Yizhi, Z. Jun, and Z. Xing, “Chaotic image encryption based on running-key related to plaintext”, The Scientific World Journal, vol. 2014, Article ID 490179, 9 pages, 2014.

Q. Zhang, X. Xue, and X. Wei, “A novel image encryption algorithm based on DNA subsequence operation”, The Scientific World Journal, vol. 2012,Article ID 286741, 10 pages, 2012.

H. Liu, Z. Zhu, H. Jiang, and B. Wang, “A novel image encryption algorithm based on improved 3D chaotic cat map”, in Proceedings of the 9th International Conference for Young Computer Scientists (ICYCS ’08), pp. 3016–3021, November 2008.

Z.Guan, F. Huang, andW.Guan, “Chaos-based image encryption algorithm”, Physics Letters A: General, Atomic and Solid State Physics, vol. 346, no. 1–3, pp. 153–157, 2005.

D. Xiao, X. Liao, and P. Wei, “Analysis and improvement of a chaos-based image encryption algorithm,” Chaos, Solitons and Fractals, vol. 40, no. 5, pp. 2191–2199, 2009.

J. Chen, Z. Zhu, C. Fu, H. Yu, and L. Zhang, “A fast chaos based image encryption scheme with a dynamic state variables selection mechanism,” Communications in Nonlinear Science and Numerical Simulation, 2014.

J.P. Keating. Asymptotic properties of the periodic orbits of the cat. Nonlinearity, 4:277–307, 1991.

Published
2018-06-29
How to Cite
Bostan, A., Karakaya, M., & Şengül, G. (2018). CHAOS-BASED DATA ENCRYPTION USING ARNOLD’S CAT MAP. International Journal of Scientific Research in Information Systems and Engineering (IJSRISE), 4(1), 25-30. Retrieved from http://ijsrise.com/index.php/IJSRISE/article/view/5
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