Title: Generalised linear orthomorphic permutations

Authors: Haiqing Han; Siru Zhu; Yanqing Dai; Qili Mao; Qin Li; Kang Shi

Addresses: School of Mathematics and Physics, Hubei Polytechnic University, Huangshi City, 435003, Hubei Province, China ' Air Force Early Warning Academy of PLA, Wuhan City, 430072, Hubei Province, China ' School of Mathematics and Physics, Hubei Polytechnic University, Huangshi City, 435003, Hubei Province, China ' School of Mathematics and Physics, Hubei Polytechnic University, Huangshi City, 435003, Hubei Province, China ' Normal Department, Hubei Polytechnic University, Huangshi City, 435003, Hubei Province, China ' School of Mathematics and Physics, Hubei Polytechnic University, Huangshi City, 435003, Hubei Province, China

Abstract: The concept of generalised orthomorphic permutations over the Galois field Fⁿ_q is proposed on the basis of the original concept with regard to orthomorphic permutations over the Galois field Fⁿ₂ in this scientific research paper. At the same time, the enumeration formula of the total generalised linear orthomorphic permutations over the Galois field Fⁿ_q is given. It is worth noting that the Galois field Fⁿ_q possesses the prime subfield F_p with an arbitrary prime number as the characteristic. The local creating algorithm is obtained and generates the partial generalised linear orthomorphic permutations over the Galois general field Fⁿ_q. Consequently the existing and innovative enumeration formula involved linear orthomorphic permutations over a Galois field with characteristic two happens to be a special case to contain in our novel fruits over the general field. In the field of information security, the generalised linear orthomorphic permutations have been thoroughly discussed and generated far and wide for the design of the p-permutation in the diffusion layer of iterative round function involving an unbreakable cryptosystem. Finally we can obtain some generalised linear orthomorphic permutations with the greatest branch number in this research paper.

Keywords: p-permutation; block cipher; the b-number; generalised orthomorphic permutation.

DOI: 10.1504/IJRIS.2021.117073

International Journal of Reasoning-based Intelligent Systems, 2021 Vol.13 No.3, pp.115 - 122

Received: 16 Feb 2019
Accepted: 26 Jul 2019
Published online: 16 Aug 2021 *

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