An image encryption scheme employing key related skipping

Oravec, Jakub; Turán, Ján; Ovseník, L’uboš; Huszaník, Tomáš

doi:10.2478/jee-2018-0013

Abstract

This paper describes an image encryption algorithm which utilizes chaotic logistic map. Values generated by this map are used in two steps of algorithm which shuffles image pixels and then changes their intensities. Design of the encryption scheme considers possibility of various attacks, such as statistical, differential or phase space reconstruction attacks. Robustness against last mentioned type of attacks is introduced by selective skipping of values generated by the map. This skipping depends on key entered by user. The paper also verifies properties of proposed algorithm by common measures and by set of statistical tests that examine randomness of computed encrypted images. Results are compared with other approaches and they are also briefly discussed.

References

[1] ST Special Publication 800-38A: Recommendation for Block Cipher Modes of Operation: Methods and Techniques. 2001 66 p. [Online] Cited 2017-10-19.Available at: http://nvlpubs.nist.gov/nistpubs/Legacy/SP/nistspecialpublication800-38a.pdf.
Search in Google Scholar Back to article
[2] R. Matthews, “On the Derivation of a ’Chaotic’ Encryption Algorithm”, Cryptologia, 1989, vol. 8, no. 6, pp. 29-41.ISSN: 0161-1194.DOI: 10.1080/0161-118991863745.10.1080/0161-118991863745
Open DOI Search in Google Scholar Back to article
[3] J. Fridrich, “Symmetric Ciphers based on Two-Dimensional Chaotic Maps”, International Journal of Bifurcation and Chaos, 1998, vol. 8, no. 6, pp. 1259–1284.ISSN: 0218-1274. DOI: 10.1142/S021812749800098X.10.1142/S021812749800098X
Open DOI Search in Google Scholar Back to article
[4] V. I. Arnold and A. Avez, Ergodic Problems of Classical Mechanics, New Jersey: W.A.Benjamin, 1968.
Search in Google Scholar Back to article
[5] B. Chirikov, Research Concerning the Theory of Non-Linear Resonance and Stochasticity, Geneva: CERN, 1971.
Search in Google Scholar Back to article
[6] R. May, “Simple Mathematical Models with Very Complicated Dynamics”, Nature, 1976, vol. 261, no. 5560, pp. 459–467.ISSN: 0028-0836.DOI: 10.1038/261459a0.10.1038/261459a0934280
Open DOI Search in Google Scholar Back to article
[7] S. Li, G. Chen and X. Mou, “On the Dynamical Degradation of Digital Piecewise Linear Chaotic Maps”, International Journal of Bifurcation and Chaos, 2005, vol. 15, no. 10, pp. 3119-3151. ISSN: 0218-1274. DOI: 10.1142/S0218127405014052.10.1142/S0218127405014052
Search in Google Scholar Back to article
[8] F. Takens, “On the Numerical Determination of the Dimension of an Attractor, Dynamical Systems and Bifurcations”, Lecture Notes Mathematics vol. 1125, B. L. J.Braaksma, H. W. Broer, F. Takens (Eds), Berlin, Heidelberg: Springer, 1985, pp. 99–106. ISBN: 978-3-540-15233-0.DOI: 10.1007/BFb0075637.10.1007/BFb0075637
Search in Google Scholar Back to article
[9] T. Sauer, J. A. Yorke and M. Casdagli, “Embedology”, Journal of Statistical Physics, 1991, vol. 65, no. 3-4, pp. 579–616. ISSN: 0022-4715.DOI: 10.1007/BF01053745.10.1007/BF01053745
Open DOI Search in Google Scholar Back to article
[10] B. Kliková and A. Raidl, “Reconstruction of Phase Space of Dynamical Systems using Method of time Delay”, Proceedings of WDS’11. Praha (Czech Republic), 2011, pp. 83–87.ISBN: 978-8-073-78186-6.
Search in Google Scholar Back to article
[11] N. K. Pareek, V. Patidar and K. K. Sud, “Cryptography using Multiple One-Dimensional Chaotic Maps”, Communications Nonlinear Science and Numerical Simulation, 2005, vol. 10, no. 7, pp. 715–723. ISSN: 1007-5704.DOI: 10.1016/j.cnsns.2004.03.006.10.1016/j.cnsns.2004.03.006
Search in Google Scholar Back to article
[12] H. Liu and X. Wang, “Colour Image Encryption based on One-Time Keys and Robust Chaotic Maps”, Computers & Mathematics with Applications, 2010, vol. 59, no. 10, pp. 3320–3327. ISSN: 0898-1221.DOI: 10.1016/j.camwa.2010.03.017.10.1016/j.camwa.2010.03.017
Search in Google Scholar Back to article
[13] X. Wang, L. Teng and X. Qin, “A Novel Colour Image Encryption Algorithm based on Chaos”, Signal Processing, 2012, vol. 92, no. 4, pp. 1101–1108. ISSN: 0165-1684. DOI: 10.1016/j.sigpro.2011.10.023.10.1016/j.sigpro.2011.10.023
Open DOI Search in Google Scholar Back to article
[14] X. Wang and K. Guo, “A New Image Alternate Encryption Algorithm based on Chaotic Map”, Nonlinear Dynamics, 2014, vol. 76, no. 4, pp. 1943–1950. ISSN: 0924-090X.DOI: 10.1007/s11071-014-1259-7.10.1007/s11071-014-1259-7
Open DOI Search in Google Scholar Back to article
[15] C. Zhu, “A Novel Image Encryption Scheme based on Improved Hyper-Chaotic Sequences”, Optics Communications, 2012, vol. 285, no. 1, pp. 29–37.ISSN: 0030-4018. DOI: 10.1016/j.optcom.2011.08.079.10.1016/j.optcom.2011.08.079
Open DOI Search in Google Scholar Back to article
[16] M. A. Murillo-Escobar, C. Cruz-Hernández, F. Abundiz-Pérez et al , “A RGB Image Encryption Algorithm based on Total Plain Image Characteristics and Chaos”, Signal Processing, 2015, vol. 109, no. C, pp. 119–131. ISSN: 0165-1684. DOI: 10.1016/j.sigpro.2014.10.033.10.1016/j.sigpro.2014.10.033
Open DOI Search in Google Scholar Back to article
[17] X. J. Tong, Z. Wang, M. Zhang et al, “An Image Encryption Algorithm based on the Perturbed High-Dimensional Chaotic Map”, Nonlinear Dynamics, 2015, vol. 80, no. 3, pp. 1493–1508. ISSN: 0924-090X. DOI: 10.1007/s11071-015-1957-9.10.1007/s11071-015-1957-9
Open DOI Search in Google Scholar Back to article
[18] C. E. Shannon, “A Mathematical Theory of Communication”, The Bell System Technical Journal, 1948, vol. 27, no. 3, pp. 379–423. ISSN: 0005-8580. DOI: 10.1002/j.1538-7305.1948.tb01338.x.10.1002/j.1538-7305.1948.tb01338.x
Open DOI Search in Google Scholar Back to article
[19] Y. Wu, J. Noonan and S. Agaian, “NPCR and UACI Randomness Tests for Image Encryption”, Journal of Selected Areas Telecommunications, 2011, vol. 2, no. 4, pp. 31–38. ISSN: 1925-2676.
Search in Google Scholar Back to article
[20] ST Internal Report 6483: Randomness Testing of the Advanced Encryption Standard Finalist Candidates, 2000 15 p. [Online] Cited 2017-11-02. Available at: http://ws680.nist.gov/publication/get_pdf.cf?pub_id/alpha151216.
Search in Google Scholar Back to article
[21] ST Special Publication 800-22 Rev.1a: A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications. 2001 131 p. [Online] Cited 2017-11-02. Available at: http:http://nvlpubs.nist.gov/nistpubs/Legacy/SP/nistspecialpublication800-22r1a.pdf.
Search in Google Scholar Back to article
[22] High Resolution Images used for an Experiment with NIST 800-22 Suite, [Online] Cited 2017-11-13. Available at: http://imagedb.wz.sk/sets/flowerandtarn.zip.
Search in Google Scholar Back to article
[23] J. Oravec and J. Turán, “Substitution Steganography with Security Improved by Chaotic Image Encryption”, Proceedings of Informatics 2017. Poprad (Slovakia), pp. 284–288. ISBN: 978-1-538-60888-3 DOI: 10.1109/Informatics.2017.8327261.10.1109/Informatics.2017.8327261
Open DOI Search in Google Scholar Back to article
[24] V. Hajduk, M. Broda, O. Kováč and D. Levický, “Image Steganography with QR Code and Cryptography”, Proceedings of Radioelektronika 2016. Košice (Slovakia), pp. 350–353. ISBN: 978-15-0901-673-0. DOI: 10.1109/RADIOELEK.2016.7477370.10.1109/RADIOELEK.2016.7477370
Search in Google Scholar Back to article

An image encryption scheme employing key related skipping

Abstract

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