Hyperchaotic Sbox design based on genetic particle swarm algorithm
LU Yawen, LI Zhengquan, TAN Lirong, GU Bin, XING Song
1. School of Internet of Things Engineering, Jiangnan University, Wuxi, Jiangsu 214122, China; 2. Jiangsu Future Networks Innovation Institute, Nanjing, Jiangsu 211111, China; 3. School of Electronic Information, Nanjing Vocational College of Information Technology, Nanjing, Jiangsu 210023, China; 4. Information Systems Department, California State University, Los Angeles, CA 90032, USA
Abstract：To solve the problem that the previously constructed Sboxes based on chaotic systems were difficult to achieve good cryptographic performance, the design scheme for Sboxes was proposed based on hyperchaotic system and genetic particle swarm optimization algorithm. Introducing sine and cosine functions and exponential factors, the twodimensional hyperchaotic system was constructed based on the onedimensional chaotic mapping. The performance analysis was conducted by system bifurcation diagram, phase diagram and Lyapunov exponent diagram to reveal that the chaotic system exhibited continuous hyperchaotic intervals in the parameter range with complex chaotic behavior. By varying initial values, parameters and iteration times of the chaotic system, Sboxes were dynamically generated. Combining particle swarm optimization algorithm and genetic algorithm, the genetic particle swarm optimization algorithm for Sboxes was proposed, and the Sboxes generated by chaotic system were used as initial population. The particle swarm optimization algorithm was leveraged to enhance the crossover operation in the genetic algorithm, and a new mutation strategy was introduced in conjunction with hillclimbing algorithm. To verify the performance of the generated Sbox, the simulation tests were conducted on bijective property, nonlinearity, strict avalanche criterion, differential probability and bit independence criterion. The simulation results show that the proposed optimization algorithm can generate Sboxes with good performance in terms of nonlinearity, differential uniformity and bit independence criterion.
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