Functions with Diffusive Properties
Information Theory
2021-02-10 v2 Cryptography and Security
math.IT
Abstract
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 -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.
Keywords
Cite
@article{arxiv.1312.4568,
title = {Functions with Diffusive Properties},
author = {Samer Seraj},
journal= {arXiv preprint arXiv:1312.4568},
year = {2021}
}
Comments
This is an update on a 2013 paper, more than 7 years after the first version. The new result is Theorem 10