关键词: Plateaued函数, 真值序列, Q-learning, 深度Q网络, 遗传算法, Walsh谱, 非线性度

Abstract: Plateaued functions,as an important generalization of Bent functions,inherit many of the desirable cryptographic pro-perties of Bent functions and hold significant application value.However,traditional methods for constructing plateaued functions suffer from issues such as high computational complexity and limited flexibility.To address these challenges,this paper proposes an adaptive genetic algorithm enhanced by a deep Q-Network(DQN).This algorithm deeply integrates DQN with the genetic algorithm,constructing a multi-dimensional state space to perceive population evolutionary characteristics.Through a group consensus mechanism,it intelligently selects from six combinations of crossover and mutation strategies,enabling adaptive control of genetic parameters.Experimental results demonstrate that the proposed algorithm achieves a fitness improvement of 0.20~0.35,exhibits faster convergence speed and higher stability,and can generate an average of 230~300 valid Plateaued function truth sequences,significantly outperforming both the standard genetic algorithm and the basic Q-learning-enhanced genetic algorithm.The algorithm intelligently adjusts the mutation rate within the range of 0.235~0.276 and maintains the crossover operation usage rate between 70% and 90%,effectively optimizing the Walsh spectrum distribution while preserving population diversity.Although computational overhead increases slightly,its significant advantages in solution quality,convergence performance,and strategic adaptability validate the effectiveness of deep reinforcement learning in the construction of cryptographic functions,providing a novel approach for the intelligent design of Boolean functions.

Key words: Plateaued function, Truth sequence, Q-learning, Deep Q-Network, Genetic algorithm, Walsh spectrum, Nonlinearity