Rolando Flores-Carapia1, Víctor Manuel Silva-García2, Benjamín Luna-Benoso2 and Carlos Rentería-Márquez2
1 Department of Security, CIDETEC, Instituto Politécnico Nacional, D.F., 07700, México (e-mail: rfloresca@ipn.mx).
2 Instituto Politécnico Nacional, México.
Manuscript received on May 11, 2015
Accepted for publication on July 22, 2015 ]]>
Published on October 15, 2015
Abstract
In this paper, color images are encrypted and subsequently damage occlusion is made to the encrypted figures, with different sizes; the intention is to simulate an attack. In this research, two aspects are discussed, namely: the first is to encrypt images with quality; that is, the figures encrypted pass randomness tests proposed in this paper. The second aspect deals with the problem of recovering the encrypted figure information when it has been damaged. To retrieve information from encrypted images, the enryption of images is carried out in two steps: in the first a permutation is applied to the entire image and the second uses the AES cryptosystem with variable permutations. To perform this task an algorithm is used that utilizes the pi number to generate the permutations. To improve the sharpness of the deciphered figures with damage two filters are applied; median and average. To measure the degree of improvement in the damaged images two tests are proposed; the first is the correlation coefficient between adjacent pixels in the horizontal, vertical and diagonal directions. The second is based on the information entropy.
Key words: AES with variable permutations, goodness-of-fit test, fourier transform, correlation, entropy of information, median and mean filters.
DESCARGAR ARTÍCULO EN FORMATO PDF
REFERENCES
[1] S. Baruah, V. Bonifaci, G. D'Angelo, H. Li, A. Marchetti-Spaccamela, N. Megow, and L. Stougie, "Scheduling real-time mixed-criticality jobs," IEEE Transactions on Computers, vol. 61, no. 8, pp. 1140-1152, 2012. [ Links ]
[2] L. Xuemei, X. Tong, and L. Dai, "A novel scheme reality preserving image encryption," in 2011 Third International Conference Measuring Technology and Mechatronics Automation. IEEE, 2011, pp. 218-221. [ Links ]
[3] J. Li and L. Gan, "Study on chaotic cryptosystem for digital image encryption," in 2011 Third International Conference Measuring Technology and Mechatronics Automation. IEEE, 2011, pp. 426-430. [ Links ]
[4] C. Fu, J. Chen, H. Zou, W. Meng, Y. Zhan, and Y. Yu, "A chaos-based digital image encryption scheme with an improved diffusion strategy," Optics Express, vol. 20, no. 3, pp. 2363-78, 2012. [ Links ]
[5] H. Zhu, C. Zhao, and X. Zhang, "A novel image encryption-compression scheme using hyper-chaos and chinese remainder theorem," Signal Processing: Image Communication, vol. 28, no. 6, pp. 670-680, 2013. [ Links ]
[6] "Advanced encryption standard (AES)," 2001, FIPS PUB 197. [ Links ]
[7] D. R. Stinson, Cryptography: Theory and Practice. Chapman & Hall/ CRC Press, 2005. [ Links ]
[8] M. Matsui, "Linear cryptanalysis method for DES cipher," Lecture Notes in Computer Science, vol. 765, pp. 386-397, 1994. [ Links ]
[9] E. Biham and A. Shamir, "Differential cryptanalysis of the full 16-round DES," Lecture Notes in Computer Science, vol. 740, pp. 487-496, 1993. [ Links ]
[10] S. Keshari and S. G. Modani, "Color image encryption scheme based on 4-weighted fractional fourier transform," Journal of Electronic Imaging, vol. 21, no. 3, pp. 033 018-1-6, 2012. [ Links ]
[11] W. Chen, X. Chen, and C. Sheppard, "Optical color-image encryption and synthesis using coherent diffractive imaging in the fresnel domain," Optics Express, vol. 20, no. 4, pp. 3853-65, 2012. [ Links ]
[12] P. Refregier and B. Javidi, "Optical image encryption based on input plane and fourier plane random encoding," Optical Letters, vol. 20, no. 7, pp. 767-769, 1995. [ Links ]
[13] W. Chen and X. Chen, "Double random phase encoding using phase reservation and compression," Journal of Optics, vol. 16, no. 2, pp. 025 402-7, 2014. [ Links ]
[14] W. Chen, B. Javidi, and X. Chen, "Advances in optical security system," Advances in Optics and Photonics, vol. 6, no. 2, pp. 120-155, 2014. [ Links ]
[15] Y. Wu, G. Yang, H. Jin, and J. P. Noonan, "Image encryption using the two-dimensional logistic chaotic map," Journal of Electronic Imaging, vol. 21, no. 1, p. 013014, 2012. [ Links ]
[16] V. M. Silva-García, R. Flores-Carapia, C. Rentería-Marquez, B. Luna-Benoso, C. A. Jimenez-Vazquez, and M. D. Gonzalez Ramírez, "Cipher image damage and decisions in real time," Journal of Electronic Imaging, vol. 24, no. 1, pp. 013 012-1-13, 2015. [ Links ]
[17] R. Gonzalez and R. Woods, Digital Image Processing. Prentice Hall, 2008. [ Links ]
[18] P. Soille, Morphological Image Analysis. Springer-Verlag, 2004. [ Links ]
[19] R. Wolpe and R. Myers, Probability and Statistics for Engineers and Scientists. Prentice Hall, 2007. [ Links ]
[20] A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Vangel, D. Banks, A. Heckert, J. Dray, and S. Vo, A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications. NIST 800-22, 2010. [ Links ]
[21] J. Peters, D. Janzing, and B. Scholkopf, "Causal inference on discrete data using additive noise models," IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 33, no. 12, pp. 2436-2450, 2011. [ Links ]
[22] Y. Yao and S.-S. Chen, "Multiplicative noise enhances spatial reciprocity," Physica A: Statistical Mechanics and its Applications, vol. 413, no. 1, pp. 432-437, 2014. [ Links ]
[23] "Practicas comerciales - requisitos que deben observarse para la conservación de mensajes de datos," 2002, Nom-151. Norma Oficial Mexicana NOM-151-SCFI-2002. [ Links ]
[24] P. Dymora, M. Mazurek, and D. Strzalka, "Long-range dependencies in quick-sort algorithm," Przeglad Elektrotechniczny, vol. 90, no. 1, pp. 149-152, 2014. [ Links ]
[25] J. Daemen and V. Rijmen, "AES proposal: Rijndael," 1998. [ Links ]
[26] D. A. Osvik, A. Shamir, and E. Tromer, "Cache attacks and countermeasures: The case of AES," Lecture Notes in Computer Science, vol. 3860, pp. 1-20, 2006. [ Links ]
[27] "Data encryption standard (DES)," 1999, FIPS PUB 46-3. [ Links ]
[28] S. Michael, Calculus: cálculo infinitesimal. Barcelona, Spain: Reverte, 1993. [ Links ]
[29] "Jaohxv. pi world," http://ja0hxv.calico.jp/pai/estart.html, accessed: 2010-09-30. [ Links ]
[30] J. Gallian, Contemporary abstract algebra. Brooks/Cole, 2011. [ Links ]
[31] E. Shannon, "A mathematical theory of communication," Bell Systems Technical Journal, vol. 27, no. 3, pp. 379-423, 1948. [ Links ]
[32] M. Abramowitz and I. Stegun, Handbook of Mathematical Functions. Washington: National Bureau of Standards, 1968. [ Links ]
[33] T. M. Apostol, Analisis Matematico. Barcelona: Reverte, 1994. [ Links ]
[34] V. M. Silva-García, R. Flores-Carapia, C. Rentería-Marquez, and B. Luna-Benoso, "Triple-DES-96 cryptographic system," International Journal of Contemporary Mathematical Sciences, vol. 8, no. 19, pp. 925-934, 2013. [ Links ]
[35] A. Gomez, Enciclopedia de la Seguridad Informatica. Mexico: Alfaomega, 2007. [ Links ]
[36] T. ElGamal, "A public key cryptosystem and a signature scheme based on discrete logarithms," IEEE Transaction on Information Theory, vol. 31, no. 4, pp. 469-472, 1985. [ Links ]
[37] R. L. Rivest, A. Shamir, and L. Adleman, "A method for obtaining digital signatures and public key cryptosystems," Communications of the ACM, vol. 21, no. 2, pp. 120-126, 1978. [ Links ]
[38] R. Azarderakhsh and A. Reyhani-Masoleh, "Parallel and high-speed computations of elliptic curve crytography using hybrid-double multipliers," Transactions on Parallel and Distributed Systems, vol. 26, no. 6, pp. 1668-1677, 2015. [ Links ]
[39] D. Jay, Probabilidad y Estadística: para ingeniería y ciencias. International Thompson, 2005. [ Links ]
[40] J. D. Argüelles, Antología general de la poesía mexicana. Mexico: Océano, 2012. [ Links ]
]]>