While exploring desirable properties of hash functions in cryptography, the author was led to investigate three notions of functions with scattering or "diffusive" properties, where the functions map between binary strings of fixed finite length. These notions of diffusion ask for some property to be fulfilled by the Hamming distances between outputs corresponding to pairs of inputs that lie on the endpoints of edges of an $n$-dimensional hypercube. Given the dimension of the input space, we explicitly construct such functions for every dimension of the output space that allows for the functions to exist.

翻译：作者在探索加密中散列函数的适当特性时,被引导调查了三种功能概念,即散射或“难以”特性,即固定长度的二进制字符串之间的功能分布图。这些扩散概念要求通过输出在一元元超立方体边缘端端对投入的对数之间拉长距离来达到某些属性。鉴于输入空间的维度,我们明确为允许功能存在的输出空间的每个层面构建了这些功能。