摘要
作为Bent函数的重要推广,Plateaued函数继承了很多Bent函数的优良密码学性质,具有重要的应用价值。由于传统构造Plateaued函数的方法存在计算复杂度高、灵活性不足等问题,因此提出一种基于深度Q网络(Deep Q-Network,DQN)增强的自适应遗传算法。该算法深度融合DQN与遗传算法,构建多维状态空间感知种群进化特征,通过群体共识机制智能选择6种交叉与变异策略组合,实现遗传参数的自适应调控。实验结果表明,该算法的适应度提升幅度达0.20~0.35,收敛速度更快,稳定性更高,平均可生成230~300个有效Plateaued函数真值序列,显著优于标准遗传算法和基础Q-learning遗传算法。算法能智能调节变异率(0.235~0.276)与交叉操作使用率(70%~90%),在优化Walsh谱分布的同时保持种群多样性。尽管计算开销略有增加,但所提算法在解的质量、收敛性能和策略自适应能力上具有显著优势,验证了深度强化学习在密码学函数构造中的有效性,为布尔函数智能化设计提供了新方案。
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.
作者
吴严生
曹心怡
樊卫北
WU Yansheng;CAO Xinyi;FAN Weibei(College of Computer Science,Nanjing University of Posts and Telecommunications,Nanjing 210023,China)
出处
《计算机科学》
北大核心
2026年第4期57-65,共9页
Computer Science
基金
国家自然科学基金(62372247)
江苏省研究生科研与实践创新计划项目(SJCX24_0326)。
