Boolean functions are important cryptographic primitives with extensive use in symmetric cryptography. These functions need to possess various properties, such as nonlinearity to be useful. The main limiting factor of the quality of a Boolean function is the number of its input variables, which has to be sufficiently large. The contemporary design methods either scale poorly or are able to create only a small subset of all functions with the desired properties. This necessitates the development of new and more efficient ways of Boolean function design. In this paper, we propose a new semantic mutation operator for the design of bent Boolean functions via genetic programming. The principle of the proposed operator lies in evaluating the function’s nonlinearity in detail to purposely avoid mutations that could be disruptive and taking advantage of the fact that the nonlinearity of a Boolean function is invariant under all affine transformations. To assess the efficiency of this operator, we experiment with three distinct variants of genetic programming and compare its performance to three other commonly used non-semantic mutation operators. The detailed experimental evaluation proved that the proposed semantic mutation operator is not only significantly more efficient in terms of evaluations required by genetic programming but also nearly three times faster than the second-best operator when designing bent functions with 12 inputs and almost six times faster for functions with 20 inputs.

布尔函数是重要的密码原语，在对称密码学中广泛使用。这些函数需要具有各种属性，例如非线性才能发挥作用。布尔函数质量的主要限制因素是其输入变量的数量，该数量必须足够大。现代设计方法要么扩展性差，要么只能创建具有所需属性的所有功能的一小部分。这就需要开发新的、更有效的布尔函数设计方法。在本文中，我们提出了一种新的语义变异算子，用于通过遗传编程设计弯曲布尔函数。所提出的算子的原理在于详细评估函数的非线性，以故意避免可能具有破坏性的突变，并利用布尔函数的非线性在所有仿射变换下不变的事实。为了评估该算子的效率，我们对遗传编程的三种不同变体进行了实验，并将其性能与其他三种常用的非语义变异算子进行了比较。详细的实验评估证明，所提出的语义变异算子不仅在遗传编程所需的评估方面显着提高了效率，而且在设计具有 12 个输入的弯曲函数时比第二最佳算子快了近三倍，并且比第二最佳算子快了近六倍。具有 20 个输入的功能。