Hybrid strategy of particle swarm optimization and simulated annealing for optimizing orthomorphisms

Orthomorphism on F₂ⁿ is a kind of elementary permutation with good cryptographic properties. This paper proposes a hybrid strategy of Particle Swarm Optimization (PSO) and Simulated Annealing (SA) for finding orthomorphisms with good cryptographic properties. By experiment based on this strategy, we get some orthomorphisms on F₂ⁿ (n = 5, 6, 7, 9, 10) with good cryptographic properties in the open document for the first time, and the optimal orthomorphism on F⁸₂ found in this paper also does better than the one proposed by Feng Dengguo et al. in stream cipher Loiss in difference uniformity, algebraic degree, algebraic immunity and corresponding permutation polynomial degree. The PSOSA hybrid strategy for optimizing orthomorphism in this paper makes design of orthomorphisms with good cryptographic properties automated, efficient and convenient, which proposes a new approach to design orthomorphisms.