Cryptographic analysis and construction of complete permutations using a recursive approach
by Shuang Xiang; Yingqi Tang; Yan Tong; Jinzhou Huang
International Journal of Ad Hoc and Ubiquitous Computing (IJAHUC), Vol. 45, No. 2, 2024

Abstract: This paper proposes a novel recursive approach for constructing generalised complete permutations over finite fields and analyses their cryptographic properties. The method can generate complete, strong complete, K-strong complete, and S-complete permutations by recursively combining component permutations and arbitrary mappings. Compared to prior recursive techniques, the approach provides larger classes of permutations with superior cryptographic strengths like higher algebraic degree, etc. Algebraic degree, nonlinearity, differential/boomerang uniformity, and other properties are investigated. For instance, constructed complete permutations can achieve optimal algebraic degrees to resist structural attacks. The analysis also derives tight lower and upper bounds on (c-)differential uniformity, (c-)boomerang uniformity and nonlinearity. Results demonstrate improved algebraic degree, differential and boomerang uniformities over previous recursive methods. Overall, this work makes significant contributions around complete permutation generation and analysis in cryptography.

Online publication date: Thu, 22-Feb-2024

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