具有高非线性度和最优代数次数的弹性函数的构造

Construction of Resilient Functions with High Nonlinearity and Optimal Algebraic Degree

摘要:

具有良好的非线性度和最优代数次数的弹性布尔函数在流密码和分组密码设计和分析中起着至关重要的作用。在本文中，通过修改Maiorana-McFarland(M-M)类Bent函数，利用不同的低阶弹性函数，给出构造高非线性度弹性布尔函数的一种新方法,所构造的函数具有严格几乎最优的非线性度和最优的代数次数。

Abstract:

Resilient Boolean functions with good nonlinearity and optimal algebraic degree play an important role in the design and analysis of stream cipher and block ciphers. In this paper, based on different lower resilient functions, a new construction method to obtain high nonlinearity resilient Boolean function is given via modifying Maiorana-McFarland (M-M) class bent functions. It is shown that the constructed functions have the strictly almost optimal nonlinearity and the optimal algebraic degree.