Abstract
The Hill cipher algorithm is one of the symmetric key algorithms that have several advantages in data encryption. However, a main drawback of this algorithm is that it encrypts identical plaintext blocks to identical ciphertext blocks and cannot encrypt images that contain large areas of a single color. Thus, it does not hide all features of the image which reveals patterns in the plaintext. Moreover, it can be easily broken with a known plaintext attack revealing weak security. This paper presents a variant of the Hill cipher that overcomes these disadvantages. The proposed technique adjusts the encryption key to form a different key for each block encryption. Visually and computationally, experimental results demonstrate that the proposed variant yields higher security and significantly superior encryption quality compared to the original one.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Barr, T.H., 2002. Invitation to Cryptography. Prentice Hall.
Chen, G., Mao, Y., Chui, C.K., 2004. A symmetric image encryption scheme based on 3D chaotic cat maps. Chaos, Soliton & Fractals, 21(3):749–761. [doi:10.1016/j.chaos.2003.12.022]
Elkamchouchi, H., Makar, M.A., 2005. Measuring Encryption Quality of Bitmap Images Encrypted with Rijndael and KAMKAR Block Ciphers. Proc. Twenty Second National Radio Science Conference (NRSC 2005), Cairo, Egypt.
Lerma, M.A., 2005. Modular Arithmetic. Http://www.math.northwestern.edu/:_mlerma/problem_solving/results/modular_arith.pdf.
Li, S., Zheng, X., 2002. On the Security of an Image Encryption Method. ICIP2002. Http://www.hooklee.com/Papers/ICIP2002.pdf.
Overbey, J., Traves, W., Wojdylo, J., 2005. On the keyspace of the Hill cipher. Cryptologia, 29(1):59–72.
Petersen, K., 2000. Notes on Number Theory and Cryptography. Http://www.math.unc.edu/Faculty/petersen/Coding/cr2.pdf.
Saeednia, S., 2000. How to make the Hill cipher secure. Cryptologia, 24(4):353–360.
Stinson, D.R., 2002. Cryptography Theory and Practice (2nd Ed.). CRC Press, Boca Raton, Florida.
Ziedan, I., Fouad, M., Salem, D.H., 2003. Application of Data Encryption Standard to Bitmap and JPEG Images. Proc. Twentieth National Radio Science Conference (NRSC 2003), Egypt. [doi:10.1109/NRSC.2003.1217349]
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ismail, I.A., Amin, M. & Diab, H. How to repair the Hill cipher. J. Zhejiang Univ. - Sci. A 7, 2022–2030 (2006). https://doi.org/10.1631/jzus.2006.A2022
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1631/jzus.2006.A2022