Abstract
This paper studies the security of an image encryption scheme based on the Hill cipher (Ismail et al., 2006) and reports its following problems: (1) There is a simple necessary and sufficient condition that makes a number of secret keys invalid; (2) It is insensitive to the change of the secret key; (3) It is insensitive to the change of the plain-image; (4) It can be broken with only one known/chosen plaintext; (5) It has some other minor defects. The proposed cryptanalysis discourages any use of the scheme in practice.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Alvarez, G., Li, S., 2006. Some basic cryptographic requirements for chaos-based cryptosystems. Int. J. Bifurc. Chaos, 16(8):2129–2151. [doi:10.1142/S0218127406015970]
Alvarez, G., Li, S., Hernandez, L., 2007. Analysis of security problems in a medical image encryption system. Comput. Biol. Med., 37(3):424–427. [doi:10.1016/j.compbiomed.2006.04.002]
Hill, L.S., 1929. Cryptography in an algebraic alphabet. Am. Math. Month., 36(6):306–312. [doi:10.2307/2298294]
Ismail, I.A., Amin, M., Diab, H., 2006. How to repair the Hill cipher. J. Zhejiang Univ. Sci. A, 7(12):2022–2030. [doi:10.1631/jzus.2006.A2022]
Li, C., 2005. Cryptanalyses of Some Multimedia Encryption Schemes. MS Thesis, Department of Mathematics, Zhejiang University, Hangzhou, China (in Chinese).
Li, C., Li, S., Zhang, D., Chen, G., 2004. Cryptanalysis of a chaotic neural network based multimedia encryption scheme. LNCS, 3333:418–425. [doi:10.1007/b104121]
Li, C., Li, S., Chen, G., Chen, G., Hu, L., 2005a. Cryptanalysis of a new signal security system for multimedia data transmission. EURASIP J. Appl. Signal Process., 2005(8): 1277–1288. [doi:10.1155/ASP.2005.1277]
Li, C., Li, S., Zhang, D., Chen, G., 2005b. Chosen-plaintext cryptanalysis of a clipped-neural-network-based chaotic cipher. LNCS, 3497:630–636. [doi:10.1007/11427445_103]
Li, C., Li, S., Lou, D.C., 2006. On the security of the Yen-Guo’s domino signal encryption algorithm (DSEA). J. Syst. Soft., 79(2):253–258. [doi:10.1016/j.jss.2005.04.021]
Li, C., Li, S., Alvarez, G., Chen, G., Lo, K.T., 2007a. Cryptanalysis of two chaotic encryption schemes based on circular bit shift and XOR operations. Phys. Lett. A, 369(1–2):23–30. [doi:10.1016/j.physleta.2007.04.023]
Li, C., Li, S., Asim, M., Nunez, J., Alvarez, G., Chen, G., 2007b. On the Security Defects of an Image Encryption Scheme. Cryptology ePrint Archive: Report 2007/397. Available at http://eprint.iacr.org/2007/397, Oct. 6, 2007.
Li, S., 2003. Analyses and New Designs of Digital Chaotic Ciphers. Ph.D Thesis, School of Electronic and Information Engineering, Xi’an Jiaotong University, Xi’an, China (in Chinese).
Li, S., Chen, G., Zheng, X., 2004. Chaos-based Encryption for Digital Images and Videos. In: Furht, B., Kirovski, D. (Eds.), Multimedia Security Handbook. CRC Press, LLC, p.133–167.
Li, S., Li, C., Lo, K.T., Chen, G., 2006. Cryptanalysis of an image encryption scheme. J. Electr. Imag., 15(4). [doi:10.1117/1.2360697]
Li, S., Chen, G., Cheung, A., Bhargava, B., Lo, K.T., 2007. On the design of perceptual MPEG-video encryption algorithms. IEEE Trans. on Circuits Syst. Video Technol., 17(2):214–223. [doi:10.1109/TCSVT.2006.888840]
Li, S., Li, C., Chen, G., Mou, X., 2008a. Cryptanalysis of the RCES/RSES image encryption scheme. J. Syst. Soft., 81(7):1130–1143. [doi:10.1016/j.jss.2007.07.037]
Li, S., Li, C., Lo, K.T., Chen, G., 2008b. Cryptanalysis of an image scrambling scheme without bandwidth expansion. IEEE Trans. on Circuits Syst. Video Technol., 18(3): 338–349. [doi:10.1109/TCSVT.2008.918116]
Overbey, J., Traves, W., Wojdylo, J., 2005. On the keyspace of the Hill cipher. Cryptologia, 29(1):59–72. [doi:10.1080/0161-110591893771]
Rangel-Romero, Y., Vega-García, R., Menchaca-Méndez, A., Acoltzi-Cervantes, D., Martínez-Ramos, L., Mecate-Zambrano, M., Montalvo-Lezama, F., Barrón-Vidales, J., Cortez-Duarte, N., Rodríguez-Henríquez, F., 2008. Comments on “How to repair the Hill cipher”. J. Zhejiang Univ. Sci. A, 9(2):211–214. [doi:10.1631/jzus.A072143]
Shannon, C.E., 1949. Communication theory of secrecy systems. Bell Syst. Tech. J., 28(4):656–715.
Zhou, J., Liang, Z., Chen, Y., Au, O.C., 2007. Security analysis of multimedia encryption schemes based on multiple Huffman table. IEEE Signal Process. Lett., 14(3):201–204. [doi:10.1109/LSP.2006.884012]
Author information
Authors and Affiliations
Corresponding author
Additional information
Project supported by the National Basic Research Program of China (No. 2006CB303104) and the City University of Hong Kong under the SRG Project, China (No. 7002134)
Rights and permissions
About this article
Cite this article
Li, Cq., Zhang, D. & Chen, Gr. Cryptanalysis of an image encryption scheme based on the Hill cipher. J. Zhejiang Univ. Sci. A 9, 1118–1123 (2008). https://doi.org/10.1631/jzus.A0720102
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1631/jzus.A0720102