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Orthomorphism on F n2 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 F n2(n=5, 6, 7, 9, 10) with good cryptographic properties in the open document for the first time, and the optimal orthomorphism on F 82 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.
Orthomorphism on F n2 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 F n2 (n = 5, 6, 7, 9, 10) with good cryptographic properties in the open document for the first time, and the optimal orthomorphism on F 82 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 Proposition a new approach to design orthomorphisms.