Hill Cipher Cryptosystem over Complex Numbers

Maxrizal Maxrizal

doi:10.31002/ijome.v2i1.1217

Hill Cipher Cryptosystem over Complex Numbers

Maxrizal Maxrizal

Abstract

The Hill Cipher cryptosystem is a symmetry key cryptosystem. This cryptosystem uses the concept of integer over modulo p. This cryptosystem uses a matrix K as a secret key. We must choose the key matrix K which has an inverse in modulo p. This secret key matrix will be used by the sender and recipient of the message to encrypt and descript the message. For this reason, this paper will discuss the generalization of Hill Cipher using matrices over complex numbers. Calculation of determinants and inverses of the matrix K will adopt a system of determinant and inverse calculations on Hill Cipher. The results show that the proposed cryptosystem scrambles the plaintext.

Keywords

complex numbers; cryptosystem over complex numbers; Hill Cipher cryptosystem

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References

Acharya, B., Sharma, M. D., Tiwari, S., & Minz, V. K. (2010). Privacy Protection of Biometric Traits Using Modified Hill Cipher with Involutory Key and Robust Cryptosystem. Procedia Computer Science, 2, 242–247. https://doi.org/10.1016/j.procs.2010.11.031

Anton, H., & Rorres, C. (2004). Elementary Linear Algebra: Applications Version. Wiley eGrade.

Dummit, D. S., & Foote, R. M. (2004). Abstract Algebra (3rd ed.). John Wiley & Sons Inc.

Khalaf, A. A. M., El-Karim, M. S. A., & Hamed, H. F. A. (2016). A Triple Hill Cipher Algorithm Proposed to Increase The Security of Encrypted Binary Data and its Implementation Using FPGA. ICACT Transactions on Advanced Communications Technology (TACT), 5(1), 752–759. https://doi.org/10.1109/ICACT.2016.7423615

Krishna, A. V. ., & Madhuravani, K. (2012). A Modified Hill Cipher Using Randomized Approach. International Journal of Computer Network and Information Security, 5, 56–62. https://doi.org/10.5815/ijcnis.2012.05.07

L, G. (2017). Modified Hill Cipher Based Image Encryption Technique. International Journal for Research in Applied Science and Engineering Technology (IJRASET), 5(4), 342–345. https://doi.org/10.22214/ijraset.2017.4063

Lang, S. (1993). Linear Algebra. New York: Springer.

Reddy, K. A., Vishnuvardhan, B., Madhuviswanatham, & Krishna, A. V. N. (2012). A Modified Hill Cipher Based on Circulant Matrices. Procedia Technology, 4, 114–118. https://doi.org/10.1016/j.protcy.2012.05.016

Sastry, V. U. K., & Ravi, S. N. (2008). Modified Hill Cipher for a Large Block of Plaintext with Interlacing and Iteration. Journal of Computer Science, 4(1), 15–20. https://doi.org/10.3844/jcssp.2008.15.20

DOI: https://doi.org/10.31002/ijome.v2i1.1217