On bent functions associated to AB functions
Lilya Budaghyan, Claude Carlet, Tor Helleseth · 2011
In 1998, the second author, Charpin and Zinoviev characterized APN and AB (n, n)-functions by means of associated 2n-variable Boolean functions. In particular, they proved that a function F is AB if and only if the associated Boolean function γFis bent. This observation leads to potentially new bent functions associated to the known AB functions, or at least gives new insight on known bent functions. However, up to now, representations of γFare known only for Gold AB power functions and determining γFfor the rest of AB functions is an open problem. In the present paper we determine γFfor most of the known families of APN and AB functions.