رمزنگاری تصاویر با استفاده از نظریه آشوب و اتوماتای سلولی

نوع مقاله : مقاله پژوهشی

نویسندگان

1 فردوسی مشهد/ دانشگاه آزاد

2 مربی گروه مهندسی کامپیوتر، موسسه آموزش عالی غیرانتفاعی- غیردولتی شاندیز، مشهد

3 مربی گروه مهندسی کامپیوتر، موسسه آموزش عالی فردوس، مشهد

4 دانشجوی مقطع دکتری گروه مهندسی کامپیوتر، دانشگاه شهید بهشتی

چکیده

تفاوت‌های موجود بین داده‌های متنی و داده‌های چند‌رسانه‌ای مانند تصاویر از جمله حجم زیاد تصاویر و همبستگی پیکسل‌های مجاور موجب شده که روش‌های رمزنگاری سنتی برای رمز کردن این داده‌ها کارایی لازم را نداشته باشند. در این مقاله، با به­کارگیری نگاشت‌های آشوب و اتوماتای سلولی تک بعدی حافظه‌دار، روش جدیدی برای رمزنگاری تصاویر ارائه شده است که در گام جایگشت، از نگاشت آشوب خطی Piecewise و در گام پخش از نگاشت آشوب لجستیک و اتوماتای سلولی استفاده می‌نماید. ویژگی بارز الگوریتم ارائه­شده، قابلیت بررسی صحت داده در سطح قالب است که در کاربردهایی مانند کاربردهای نظامی و پزشکی که داده‌های تصویر یا بخشی از آن بسیار حساس هستند دارای اهمیت بالایی است. نتایج بررسی‌های متفاوت از جمله بررسی حساسیت کلید و بررسی‌های آماری نشان‌دهنده‌ی حساسیت بالای روش پیشنهادی است، همچنین بررسی انواع حملات مختلف، نشان داد که روش پیشنهادی مقاومت مناسبی در برابر آنها دارد

کلیدواژه‌ها


   [1]      P. H. Bardell, “Analysis of cellular automata used as pseudorandom pattern generators,” in Proceedings. International Test Conference 1990, 1990, pp. 762–768.##
   [2]      K. Cattell and J. C. Muzio, “An Explicit Similarity Transform between Cellular Automata and LFSR Matrices,” Finite Fields Their Appl., vol. 4, no. 3,            pp.   239–251, 1998.##
   [3]      R. Díaz Len et al., “Wolfram cellular automata and their cryptographic use as pseudorandom bit generators,” Int. J. Pure Appl. Math., vol. 4, 2003.##
   [4]      C. Fraile Rubio, L. Hernandez Encinas, S. White, Á. Rey, and G. Sánchez, “The Use of Linear Hybrid Cellular Automata as Pseudo Random Bit Generators in Cryptography.,” Neural Parallel Sci. Comp., vol. 12, pp. 175–192, 2004.##
   [5]      P. Guan, “Cellular automaton public-key cryptosystem,” Complex Syst., vol. 1, 1987.##
   [6]      H. Gutowitz, “Cryptography with Dynamical Systems,” Cellular Automata and Cooperative Systems. Springer, Dordrecht, 1993. 237-274.##
   [7]      W. Meier and O. Staffelbach, “Analysis of Pseudo Random Sequences Generated by Cellular Automata,” in Proceedings of the 10th Annual International Conference on Theory and Application of Cryptographic Techniques, 1991, pp. 186–199.##
   [8]      S. Nandi, B. K. Kar, and P. P. Chaudhuri, “Theory and Applications of Cellular Automata in Cryptography,” IEEE Trans. Comput., vol. 43, no. 12, pp. 1346–1357, Dec. 1994.##
   [9]      S. Wolfram, “Cryptography with Cellular Automata,” in Advances in Cryptology, 1986, pp. 429–432.##
[10]      I. Ingemarsson, D. Tang, and C. Wong, “A Conference Key Distribution System,” IEEE Trans. Inf. Theor., vol. 28, no. 5, pp. 714–720, Sep. 2006.##
[11]      K. Bogart, “Basic Algebra,” Am. Math. Mon., vol. 92, no. 10, 1985.##
[12]      A. Joux, “A One Round Protocol for Tripartite Diffie--Hellman,” in Algorithmic Number Theory, 2000, pp. 385–393.
[13]      M. Just and S. Vaudenay, “Authenticated multi-party key agreement,” in Advances in Cryptology --- ASIACRYPT ’96, 1996, pp. 36–49.##
[14]      G. Marañón, L. H. Encinas, A. H. Encinas, Á. M. del Rey, and G. R. Sánchez, “Graphic Cryptography with Pseudorandom Bit Generators and Cellular Automata,” in Knowledge-Based Intelligent Information and Engineering Systems, 2003, pp. 1207–1214.##
[15]      L. Hernandez Encinas, Á. Rey, and A. Encinas, “Encryption of Images with 2-dimensional Cellular Automata,” Proc. of 6-th Multiconference on Systemics, Cybernetics and Informatics, 2002, pp. 471-476.##
[16]      T. Toffoli and N. H. Margolus, “Invertible cellular automata: A review,” Phys. D Nonlinear Phenom., vol. 45, no. 1, pp. 229–253, 1990.##
[17]      C. Schwartz, “A NEW GRAPHICAL METHOD FOR ENCRYPTION OF COMPUTER DATA,” Cryptologia, vol. 15, no. 1, pp. 43–46, 1991.##
[18]      I. N. Herstein, “Topics in Algebra,” 1975.##
[19]      D. Xiao, X. Liao, and P. Wei, “Analysis and improvement of a chaos-based image encryption algorithm,” Chaos, Solitons & Fractals, vol. 40, no. 5, pp. 2191–2199, 2009.##
[20]      C. Çokal and E. Solak, “Cryptanalysis of a chaos-based image encryption algorithm,” Phys. Lett. A, vol. 373, no. 15, pp. 1357–1360, 2009.##
[21]      D. Arroyo, G. Alvarez, S. Li, C. Li, and J. Nunez, “Cryptanalysis of a discrete-time synchronous chaotic encryption system,” Phys. Lett. A, vol. 372, no. 7, pp. 1034–1039, 2008.##
[22]      G. Álvarez, F. Montoya, M. Romera, and G. Pastor, “Cryptanalysis of a discrete chaotic cryptosystem using external key,” Phys. Lett. A, vol. 319, no. 3, pp. 334–339, 2003.##
[23]      C. Li, S. Li, G. Chen, and W. A. Halang, “Cryptanalysis of an image encryption scheme based on a compound chaotic sequence,” Image Vis. Comput., vol. 27, no. 8, pp. 1035–1039, 2009.##
[24]      C. Li, S. Li, M. Asim, J. Nunez, G. Alvarez, and G. Chen, “On the security defects of an image encryption scheme,” Image Vis. Comput., vol. 27, no. 9, pp. 1371–1381, 2009.##
[25]      R. Alonso-Sanz, “Reversible cellular automata with memory: two-dimensional patterns from a single site seed,” Phys. D Nonlinear Phenom., vol. 175, no. 1, pp. 1–30, 2003.##
[26]      R. Alonso-Sanz and M. Martín, “Elementary Cellular Automata with Memory,” Complex Syst., vol. 14, no. 2, p. ‎99–126, 2003.##
[27]      Z.-H. Guan, F. Huang, and W. Guan, “Chaos-based image encryption algorithm,” Phys. Lett. A, vol. 346, no. 1, pp. 153–157, 2005.##
[28]      C. Li and G. Chen, “On the security of a class of image encryption schemes,” in 2008 IEEE International Symposium on Circuits and Systems, 2008, pp. 3290–3293.##
[29]      G. Chen, Y. Mao, and C. K. Chui, “A symmetric image encryption scheme based on 3D chaotic cat maps,” Chaos, Solitons & Fractals, vol. 21, no. 3, pp. 749–761, 2004.##
[30]      Yaobinmao, Guanrongchen, and Shiguolian, “A NOVEL FAST IMAGE ENCRYPTION SCHEME BASED ON 3D CHAOTIC BAKER MAPS,” Int. J. Bifurc. Chaos, vol. 14, 2011.##
[31]      J. Shen, X. Jin, and C. Zhou, “A Color Image Encryption Algorithm Based on Magic Cube Transformation and Modular Arithmetic Operation,” in Advances in Multimedia Information Processing - PCM 2005, 2005, pp. 270–280.##
[32]      X. He, Q. Zhu, and P. Gu, “A New Chaos-Based Encryption Method for Color Image,” in Rough Sets and Knowledge Technology, 2006, pp. 671–678.##
 
[33]      Q. Zhang, L. Guo, and X. Wei, “Image encryption using DNA addition combining with chaotic maps,” Math. Comput. Model., vol. 52, no. 11, pp. 2028–2035, 2010.##
[34]      J. W. Yoon and H. Kim, “An image encryption scheme with a pseudorandom permutation based on chaotic maps,” Commun. Nonlinear Sci. Numer. Simul., vol. 15, no. 12, pp. 3998–4006, 2010.##
[35]      I. Amr Ismail, A. Mohammed, and H. Diab, “A Digital Image Encryption Algorithm Based A Composition of Two Chaotic logestic Maps[J],” Int. J. Netw. Secur., vol. 11, 2010.##
[36]      F. Maleki, A. Mohades, S. M. Hashemi, and M. E. Shiri, “An Image Encryption System by Cellular Automata with Memory.” 2008 Third International Conference on Availability, Reliability and Security, Barcelona, pp. 1266–1271, 2008.##
[37]      R.-J. Chen and J.-L. Lai, “Image security system using recursive cellular automata substitution,” Pattern Recognit., vol. 40, no. 5, pp. 1621–1631, 2007.##
[38]      D. R. Stinson, “Cryptography: Theory and Practice, Third Edition,” 2001.##
[39]      C. Z. S. Y. Q. Zhang Xiaoyan; Wang, “Image Encryption Scheme Based on Balanced Two-Dimensional Cellular Automata,” Math. Probl. Eng., pp. 229–253, 2013.##
[40]      Á. Rey and G. Sánchez, “An image encryption algorithm based on 3D cellular automata and chaotic maps,” Int. J. Mod. Phys. C, vol. 26, 2015.##
[41]      X. Wang and D. Luan, “A novel image encryption algorithm using chaos and reversible cellular automata,” Commun. Nonlinear Sci. Numer. Simul., vol. 18, no. 11, pp. 3075–3085, 2013.##
[42]      A. A. Abdo, S. Lian, I. A. Ismail, M. Amin, and H. Diab, “A cryptosystem based on elementary cellular automata,” Commun. Nonlinear Sci. Numer. Simul., vol. 18, no. 1, pp. 136–147, 2013.##
[43]      X. Chai, Z. Gan, K. Yang, Y. Chen, and X. Liu, “An image encryption algorithm based on the memristive hyperchaotic system, cellular automata and DNA sequence operations,” Signal Process. Image Commun., vol. 52, pp. 6–19, 2017.##
[44]      X. Chai, X. Zheng, Z. Gan, D. Han, and Y. Chen, “An image encryption algorithm based on chaotic system and compressive sensing,” Signal Processing, vol. 148, pp. 124–144, 2018.##
[45]      R. Enayatifar, A. H. Abdullah, I. F. Isnin, A. Altameem, and M. Lee, “Image encryption using a synchronous permutation-diffusion technique,” Opt. Lasers Eng., vol. 90, pp. 146–154, 2017.##