有限域上低差分置换的计算与构造

Calculation and Construction of Permutations with Low Differential Uniformity over Finite Fields

低差分置换是对称密码算法的重要组件，最近屈等先后提出了优先函数、优先布尔函数的概念，并用之构造4-差分置换．构造了一些具有较少项数的优先布尔函数，将交换法中的布尔函数推广为F2n到F4的映射，进一步研究了广义的交换构造，构造了三类新的4-差分置换，并计算了它们的非线性度．

Permutations with low differential uniformity is an important component of the cipher algorithm. Recently, Qu et al. has put forward the concepts of preferred function（PF） and preferred Boolean function（PBF） one after another, and constructed differentially 4-uniform permutations. In this thesis, we construct some new PBFs with few items, and further study the generalized switching method, that is, to replace the Boolean function in the switching method by a mapping from F2n to F4. Finally, three new differentially 4-uniform permutations are constructed and their nonlinearity are also computed.