Generation of high-order random key matrix for Hill Cipher encryption using the modular multiplicative inverse of triangular matrices

• Published in: Wireless networks Vol. 30; no. 6; pp. 5697 - 5707
• Main Authors: Chen, Yuehong, Xie, Rong, Zhang, Haotong, Li, Dongdong, Lin, Weiwei
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.08.2024; Springer Nature B.V
• Subjects: Algorithms; Communications Engineering; Complexity; Computer Communication Networks; Constraints; Cryptography; Electrical Engineering; Encryption; Engineering; Fields (mathematics); Genetic algorithms; IT in Business; Linear algebra; Mathematics; Methods; Networks; Number theory; Systems science; Wireless networks; Hill key generation; Hill Cipher; Cloud data security; Modular multiplicative inverse
• ISSN: 1022-0038; 1572-8196
• DOI: 10.1007/s11276-023-03330-8

Hill Cipher is one of the classic symmetric encryption algorithms widely used in cloud data security. Although the hill cipher principle is relatively simple, its key matrix must be invertible, and all elements must be integers. However, the inverses of randomly generated matrix does not always exist and it is time-consuming to test whether the higher-order matrix is reversible. In this paper, we propose Random Key Matrix Generation Method (RKMGM), a novel algorithm to randomly generate a high order hill key matrix based on the modular multiplicative inverse of a triangular matrix. We prove that RKMGM extends the selection of key matrices from finite field to the rational number field and has no constraints on matrix order, and then analyze the time complexity of RKMGM. Compared to alternative hill key generation methods based on the involutory matrix, self-inversion matrix, and single mode, RKMGM has the advantages of simplicity, fewer constraints, one-time random generation, and high key space complexity.