Vectrix: A Proposed Mathematical Structure and Its Application in Cryptography
DOI:
https://doi.org/10.54117/w5x30d53Keywords:
Encryption, Decryption, Cipher, Cryptography, VectorixAbstract
This paper studies the security of the Hill cipher through its key space and the entropy of the keys, the analysis was extended to a proposed structure called Vectrix (plural, Vectrices). The key space of the existing cipher is defined by the space of non-singular matrices, and for the proposed algorithm it is define by the space of non-sigular Vectrices. In each case, Shannon entropy was used to measure the associated uncertainty. The results show that, the entropy associated with Vectrix key is triple of the entropy of the traditional Hill Cipher key and the key space is cubic power of the key space of the respective Matrix key space.
References
Shannon, C. E. (1949). Communication theory of secrecy systems. Bell System Technical Journal, 28(4), 656–715. https://doi.org/10.1002/j.1538-7305.1949.tb00928.x
Mfungo, D. E., Fu, X., Wang, X., & Xian, Y. (2023). Enhancing image encryption with the Kronecker XOR product, the Hill cipher, and the sigmoid logistic map. Applied Sciences, 13(6), 4034. https://doi.org/10.3390/app13064034
Ismail, I. A., Amin, M., & Diab, H. (2006). How to repair the Hill cipher. Journal of Zhejiang University Science A, 7(12), 2022–2030. https://doi.org/10.1631/jzus.2006.A2022
Overbey, J., Traves, W., & Wojdylo, J. (2005). On the keyspace of the Hill cipher. Cryptologia, 29(1), 59–72. https://doi.org/10.1080/0161-110591893771
Hassan, K. A., Garko, A., Sani, S., Abdullahi, U., & Sahalu, S. (2022). Combined techniques of Hill cipher and transposition cipher. Journal of Mathematical Letters, 1(1), 57–64. https://doi.org/10.31586/jml.2023.822
Ameen, K. A., Abdulwahab, W. K., & Taher, Y. N. A. (2025). Encryption technique using a mixture of Hill cipher and modified DNA for secure data transmission. International Journal of Computing and Digital Systems, 17(2), 1–9. https://doi.org/10.12785/ijcds/1571016767
Prerna, Urooj, M., Kumari, M., & Shrivastava, J. N. (2014). Image encryption and decryption using modified Hill cipher technique. International Journal of Information and Computation Technology, 4(17), 1895–1901. https://www.ripublication.com/ijictv4n17spl_20.pdf
Jain, S., & Arya, K. (2022). A neoteric strategy of Hill cipher for analysis of degenerate matrices. Journal of Algebraic Statistics, 13(1), 194–198. https://www.publishoa.com/index.php/journal/article/view/74
Saeednia, S. (2000). How to make the Hill cipher secure. Cryptologia, 24(4), 307–317. https://doi.org/10.1080/0161-110090896000
Santoso, Y. S. (2021). Message security using a combination of Hill cipher and RSA algorithms. Jurnal Matematika dan Ilmu Pengetahuan Alam LLDikti Wilayah 1 (JUMPA), 1(1), 20–28. https://doi.org/10.31294/jumpa.v1i1.10417
Qowi, Z., & Hudallah, N. (2021). Combining Caesar cipher and Hill cipher in generating encryption key on the Vigenère cipher algorithm. Journal of Physics: Conference Series, 1918(4), 042004. https://doi.org/10.1088/1742-6596/1918/4/042004
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