Ph.D. started in: 2017
Expected year of graduation: 2021
COINS consortium member: University of Bergen
Supervised by: Lilya Budaghyan
Research area: Cryptography
Project title: Properties of optimal Boolean functions
Project description: Boolean functions constitute an integral part of various encryption algorithms (such as block ciphers, in the context of which they are typically referred to as “S-boxes” or “substitution boxes” since they act as components substituting one sequence of bits for another) and as such play a central role in the design and analysis of such algorithms.
The security of the encryption depends directly on certain properties of the underlying Boolean functions, such as their non-linearity and differential uniformity whose values determine the resistance against linear and differential attacks, respectively. Different classes of Boolean functions, e.g. almost perfect non-linear (APN) functions, almost bent (AB) functions, bent functions, planar functions, etc. are defined so that the functions contained therein are optimal with respect to some given desirable quality, e.g. non-linearity. However, many questions of practical importance arise which are not answered by the definitions per se, most notably the question of how to actually construct functions of a given type (APN or AB, for example); furthermore, while many constructions are known e.g. in the case of APN functions, new ones continue to be discovered and it is thus not known whether other APN constructions exist and how they might be performed; in addition, many open questions remain pertaining to the properties of the constructions that have already been found as well. The goal of the project, therefore, is to investigate these various classes (APN, AB, bent, etc) of optimal Boolean functions with the purpose of better understanding their particular properties as well as finding new methods of constructing such functions.