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

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Abstract

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.

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Acknowledgements

This work is supported by Key-Area Research and Development Program of Guangdong Province (2021B0101420002), Guangdong Marine Economic Development Special Fund Project (GDNRC[2022]17), 2022 Basic and Applied Basic Research Project from Guangzhou Science and Technology (20220101185), and Guangzhou Development Zone Science and Technology (2021GH10, 2020GH10).

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Authors and Affiliations

  1. School of Mathematics and Systems Science, Guangdong Polytechnic Normal University, Guangzhou, 510665, China

    Yuehong Chen

  2. Guangdong University of Foreign Studies South China Business College, Guangzhou, 510545, China

    Rong **e

  3. School of Mathematics and Systems Science, Guangdong University of Finance and Economics, Guangzhou, 510320, China

    Rong **e & Haotong Zhang

  4. School of Computer Science and Engineering, South China University of Technology, Guangzhou, 510006, China

    Haotong Zhang, Dongdong Li & Weiwei Lin

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  1. Yuehong Chen
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Correspondence to Rong **e or Weiwei Lin.

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Chen, Y., **e, R., Zhang, H. et al. Generation of high-order random key matrix for Hill Cipher encryption using the modular multiplicative inverse of triangular matrices. Wireless Netw (2023). https://doi.org/10.1007/s11276-023-03330-8

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