STUDYING THE PROPERTIES OF PIXELS PERMUTATIONS BASED ON DISCRETIZED STANDARD MAP
Serhii Haliuk
s.haliuk@chnu.edu.uaChernivtsi National University, Department of Radio Engineering and Information Security (Ukraine)
http://orcid.org/0000-0003-3836-2675
Oleh Krulikovskyi
Chernivtsi National University, Department of Radio Engineering and Information Security (Ukraine)
http://orcid.org/0000-0001-5995-6857
Vitalii Vlasenko
Chernivtsi National University, Department of Radio Engineering and Information Security (Ukraine)
http://orcid.org/0000-0002-9085-5787
Abstract
In this article, we described specifics of pixels permutations based on the discretized, two-dimensional Chirikov standard map. Some properties of the discretized Chirikov map can be used by an attacker to recover the original images that are studied. For images with dimensions N ´ N the vulnerability of permutations allows for brute force attacks, and shown is the ability of an intruder to restore the original image without setting the value of keys permutations. Presented is also, successful cryptographic attack on the encrypted image through permutation of pixels. It is found that for images with dimension N ´ N the maximum number of combinations is equal to NN-1. A modified Chirikov map was proposed with improved permutation properties, due to the use of two nonlinearities, that increase the keys space to N2!.
Keywords:
discretized standard map, permutation of pixels, key space, precision of computingReferences
Alvarez, G., Li, S. J.: Some Basic Cryptographic Requirements for Chaos-Based Cryptosystems. Inter. Journal of Bif. and Chaos 16(8)/2006, 2129–2151.
DOI: https://doi.org/10.1142/S0218127406015970
Google Scholar
Argyris A., Syvridis D., Larger L., Annovazzi-Lodi V., Colet P., Fischer I., García-Ojalvo J., Mirasso C.R., Pesquera L., Shore K.A.: Chaos-based communications at high bit rates using commercial fibre-optic links. Nature 438(7066)/2005, 343–346.
DOI: https://doi.org/10.1038/nature04275
Google Scholar
Arroyo D., Alvarez G., Fernandez V.: A basic framework for the cryptanalysis of digital chaos-based cryptography. Proc. of the 6th International Multi-Conference on Systems, Signals and Devices, Djerba 2009, 58–63.
DOI: https://doi.org/10.1109/SSD.2009.4956652
Google Scholar
Chirikov B. V.: Research concerning the theory of nonlinear resonance and stochasticity Preprint 267, Institute of Nuclear Physics, Novosibirsk, 1969, (Engl. Trans., CERN Trans. 1971, 71–40).
Google Scholar
Fridrich J.: Symmetric Ciphers Based on Two-Dimensional Chaotic Maps. Inter. Journal of Bif. and Chaos 8(6)/1998, 1259–284.
DOI: https://doi.org/10.1142/S021812749800098X
Google Scholar
Hussain I., Shah T.: Literature survey on nonlinear components and chaotic nonlinear components of block ciphers. Nonlinear Dynamics 74/2013, 869–904.
DOI: https://doi.org/10.1007/s11071-013-1011-8
Google Scholar
Jolfaei A., Mirghadri A.: An image encryption approach using chaos and stream cipher. Journal of Theoretical and Applied Information Technology 19(2)/2010, 117–125.
Google Scholar
Kocarev L., Lian S. (Eds.): Chaos-Based Cryptography Theory, Algorithms and Applications. Springer-Verlag Berlin Heidelberg, 2011.
DOI: https://doi.org/10.1007/978-3-642-20542-2
Google Scholar
Lian S. G., Sun J., Wang Z.: A block cipher based on a suitable use of chaotic standard map. Chaos, Solitons and Fractals 26(1)/2005, 117–29.
DOI: https://doi.org/10.1016/j.chaos.2004.11.096
Google Scholar
Lian S., Sun J., Wang Z.: Security analysis of a chaos-based image encryption algorithm. Phisyca A 351(2)/2005, 645–661.
DOI: https://doi.org/10.1016/j.physa.2005.01.001
Google Scholar
National Institute of Standards and Technology (May 11, 2010). NIST Digital Library of Mathematical Functions. Section 26.4. Retrieved August 30, 2010.
Google Scholar
Solak, E., Cokal, C., Yildiz, O.T., Biyikoglu, T.: Cryptanalysis of fridrich’s chaotic image encryption. Int. J. Bifurcation Chaos 20(5), 1405–1413.
DOI: https://doi.org/10.1142/S0218127410026563
Google Scholar
von Bremen H. F., Udwadia F. E., Proskurowski W.: An efficient QR based method for the computation of Lyapunov exponents. Physica D 101/1997, 1–16.
DOI: https://doi.org/10.1016/S0167-2789(96)00216-3
Google Scholar
Warren H. S. .: Hacker’s Delight. Addison-Wesley Professional. 2012.
Google Scholar
Yuan G., Yorke J. A.: Collapsing of chaos in one dimensional maps. Physica D: Nonlinear Phenomena 136/2000, 18–30.
DOI: https://doi.org/10.1016/S0167-2789(99)00147-5
Google Scholar
Authors
Serhii Haliuks.haliuk@chnu.edu.ua
Chernivtsi National University, Department of Radio Engineering and Information Security Ukraine
http://orcid.org/0000-0003-3836-2675
Authors
Oleh KrulikovskyiChernivtsi National University, Department of Radio Engineering and Information Security Ukraine
http://orcid.org/0000-0001-5995-6857
Authors
Vitalii VlasenkoChernivtsi National University, Department of Radio Engineering and Information Security Ukraine
http://orcid.org/0000-0002-9085-5787
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