AIRCC's International Journal of Computer Science and Information Technology

Open Access Open Access  Restricted Access Subscription Access

Method for a Simple Encryption of Images Based on The Chaotic Map of Bernoulli


Affiliations
1 Department of Electric-Electronic Engineering, TecNM-Instituto Tecnologico de Veracruz, Veracruz, Mexico
 

In this document, we propose a simple algorithm for the encryption of gray-scale images, although the scheme is perfectly usable in color images. Prior to encryption, the proposed algorithm includes a pair of permutation processes, inspired by the Bernoulli mapping. The permutation disperses the image information to hinder the unauthorized recovery of the original image. The image is encrypted using the XOR function between a sequence generated from the same Bernoulli mapping and the image data, obtained after two permutation processes. Finally, for the verification of the algorithm, the gray-scale Lena pattern image was used; calculating histograms for each stage alongside of the encryption process. The histograms prove dispersion evolution for pattern image during whole algorithm.

Keywords

Algorithm of Image Encryption, Bernoulli Mapping, Permutation.
User
Notifications
Font Size

  • Lagarde, K. C., & Rogers, R. M. (1998). U.S. Patent No. 5,721,908. Washington, Dc: U.S. Patent And Trademark Office.

  • Jorquera, D. M., Iglesias, V. G., Gimeno, F. J. M., & Pérez, F. M. Mecanismos De Difusiónmasivaenaplicacionesdistribuidas.

  • Tsai, C. L., & Lin, U. C. (2011). Information Security Of Cloud Computing For Enterprises. Advances In Information Sciences And Service Sciences, 3(1), 132.

  • Dutta, S., Das, T., Jash, S., Patra, D., & Paul, P. (2014). A Cryptography Algorithm Using The Operations Of Genetic Algorithm & Pseudo Random Sequence Generating Functions. International Journal, 3(5).

  • Melander, B., Björkman, M., &Gunningberg, P. (2000). A New End-To-End Probing And Analysis Method For Estimating Bandwidth Bottlenecks. In Global Telecommunications Conference, 2000.

  • Globecom'00. Ieee (Vol. 1, Pp. 415-420). Ieee.

  • Ammar, A., El-Kabbany, A. S. S., Youssef, M. I., &Emam, A. A Novel Secure Image Ciphering Technique Based On Chaos. In 4th Wseas Int. Conf. On Information Science, Communications, And Applications (Pp. 21-23).

  • Alvarez, G., & Li, S. (2006). Some Basic Cryptographic Requirements For Chaos-Based Cryptosystems. International Journal Of Bifurcation And Chaos, 16(08), 2129-2151.

  • Nasri, M., Helali, A., Sghaier, H., &Maaref, H. (2010, March). Adaptive Image Transfer For Wireless Sensor Networks (Wsns). In Design And Technology Of Integrated Systems In Nanoscale Era (Dtis), 2010 5th International Conference On (Pp. 1-7). Ieee.

  • Saleski, A. (1973). On Induced Transformations Of Bernoulli Shifts. Theory Of Computing Systems, 7(1), 83-96.

  • Li, S., Chen, G., &Mou, X. (2005). On The Dynamical Degradation Of Digital Piecewise Linear Chaotic Maps. International Journal Of Bifurcation And Chaos, 15(10), 3119-3151.

  • Biswas, H. R. (2013). One Dimensional Chaotic Dynamical Systems. Journal Of Pure And Applied Mathematics: Advances And Applications, 10(1), 69-101.

  • Persohn, K. J., &Povinelli, R. J. (2012). Analyzing Logistic Map Pseudorandom Number Generators For Periodicity Induced By Finite Precision Floating-Point Representation. Chaos, Solitons & Fractals, 45(3), 238-245.

  • Agiza, H. N. (1999). On The Analysis Of Stability, Bifurcation, Chaos And Chaos Control Of Kopel Map. Chaos, Solitons & Fractals, 10(11), 1909-1916.

  • Fu, C., Lin, B. B., Miao, Y. S., Liu, X., & Chen, J. J. (2011). A Novel Chaos-Based Bit-Level Permutation Scheme For Digital Image Encryption. Optics Communications, 284(23), 5415-5423.

  • Abarbanel, H. (2012). Analysis Of Observed Chaotic Data. Springer Science & Business Media.

  • Ahmed, H. E. D. H., Kalash, H. M., & Allah, O. S. F. (2007). An Efficient Chaos-Based Feedback Stream Cipher (Ecbfsc) For Image Encryption And Decryption. Informatica, 31(1).

  • Behnia, S., Akhshani, A., Mahmodi, H., &Akhavan, A. (2008). A Novel Algorithm For Image Encryption Based On Mixture Of Chaotic Maps. Chaos, Solitons & Fractals, 35(2), 408-419.

  • Wong, K. W., Kwok, B. S. H., & Law, W. S. (2008). A Fast Image Encryption Scheme Based On Chaotic Standard Map. Physics Letters A, 372(15), 2645-2652.


Abstract Views: 357

PDF Views: 158




  • Method for a Simple Encryption of Images Based on The Chaotic Map of Bernoulli

Abstract Views: 357  |  PDF Views: 158

Authors

Luis Alfredo Crisanto Baez
Department of Electric-Electronic Engineering, TecNM-Instituto Tecnologico de Veracruz, Veracruz, Mexico
Ricardo Francisco Martinez Gonzalez
Department of Electric-Electronic Engineering, TecNM-Instituto Tecnologico de Veracruz, Veracruz, Mexico
Yesenia Isabel Moreno Pavan
Department of Electric-Electronic Engineering, TecNM-Instituto Tecnologico de Veracruz, Veracruz, Mexico
Marcos Alonso Mendez Gamboa
Department of Electric-Electronic Engineering, TecNM-Instituto Tecnologico de Veracruz, Veracruz, Mexico

Abstract


In this document, we propose a simple algorithm for the encryption of gray-scale images, although the scheme is perfectly usable in color images. Prior to encryption, the proposed algorithm includes a pair of permutation processes, inspired by the Bernoulli mapping. The permutation disperses the image information to hinder the unauthorized recovery of the original image. The image is encrypted using the XOR function between a sequence generated from the same Bernoulli mapping and the image data, obtained after two permutation processes. Finally, for the verification of the algorithm, the gray-scale Lena pattern image was used; calculating histograms for each stage alongside of the encryption process. The histograms prove dispersion evolution for pattern image during whole algorithm.

Keywords


Algorithm of Image Encryption, Bernoulli Mapping, Permutation.

References