Description
In this talk results published in European Journal of Combinatorics by E.R. van Dam and D. Fon-Der-Flaass will be presented. In particular, functions on binary vector space which are far removed from linear functions in different senses will be considered comparing three existing notions: almost perfect nonlinear (APN) functions, almost bent (AB) functions, and crooked (CR) functions. Such functions are of importance in cryptography because of their resistance to linear and differential attacks on certain cryptosystems. A combinatorial characterization of AB functions in terms of the number of solutions to a certain system of equations, and a characterization of CR in terms of the Fourier transformation, obtained by van Dam and Fon-Der-Flaass, as well as examples how these functions can be used to construct several combinatorial structures such as semi-biplanes, difference sets, distance regular graphs, symmetric association schemes and uniformly packed codes, will be presented.
Primary author
Mrs
Nastja Cepak
(University of Primorska)
