标题： 度的重要性：关于演化同质布尔函数 显示英文标题

标题： Degree is Important: On Evolving Homogeneous Boolean Functions

摘要： 布尔函数具有良好的密码学性质，如高非线性和代数次数，在流密码和分组密码的安全性中起着重要作用。 此类函数可以通过代数构造或元启发式方法进行设计。 本文研究了使用进化算法（EAs）来设计同次弯布尔函数，即那些具有最大非线性且代数正规形式中仅包含相同次数的单项式的函数。 在我们的工作中，我们评估了三种基因型编码和四种适应度函数。 我们的结果表明，虽然EAs能够找到二次同次弯函数（最佳方法是利用限制编码的遗传算法），但没有任何方法能产生三次同次弯函数。 显示英文摘要

摘要： Boolean functions with good cryptographic properties like high nonlinearity and algebraic degree play an important in the security of stream and block ciphers. Such functions may be designed, for instance, by algebraic constructions or metaheuristics. This paper investigates the use of Evolutionary Algorithms (EAs) to design homogeneous bent Boolean functions, i.e., functions that are maximally nonlinear and whose algebraic normal form contains only monomials of the same degree. In our work, we evaluate three genotype encodings and four fitness functions. Our results show that while EAs manage to find quadratic homogeneous bent functions (with the best method being a GA leveraging a restricted encoding), none of the approaches result in cubic homogeneous bent functions.