基于毗连的几乎最优弹性布尔函数的构造

Construction of almost optimal resilient Boolean functions via concatenation

近年来,几乎最优弹性布尔函数的研究应用快速发展,提高几乎最优函数的非线性度有着重要的意义。针对一种性能较好的几乎最优函数进行分析和改进,结合毗连的构造方法,来构造偶数元几乎最优函数。在保持其弹性和代数次数的前提下,得到非线性度更高的几乎最优函数,使其性能得到一定提高,并给出了一种构造高非线性度弹性布尔函数的构造方法。分析表明,所提出的方案构造方法简单,容易实现,非线性度得到进一步提高,具有m阶弹性,且代数次数保持不变。

In recent years, research of almost optimal resilient Boolean functions develops rapidly, and it is important to improve the nonlinearity degree of almost optimal functions. Analysis and improvement of an almost optimal function with good performance was given, and an almost optimal function with even variables was constructed using concatenating construction method. A nonlinear optimal function with higher nonlinearity was got while maintaining its resilience and algebraic degree, which improved the performance of the function. And the construction method was also given to construct an elastic Boolean function with high nonlinearity. Analysis shows that the proposed construction method is simple and easy to implement, the nonlinearity is improved with m resilience and unchanged algebraic de~＇ee.