A complete characterization of plateaued Boolean functions in terms of their Cayley graphs

In this paper we find a complete characterization of plateaued Boolean functions in terms of the associated Cayley graphs. Precisely, we show that a Boolean function $f$ is $s$-plateaued (of weight $=2^{(n+s-2)/2}$) if and only if the associated Cayley graph is a complete bipartite graph between the support of $f$ and its complement (hence the graph is strongly regular of parameters $e=0,d=2^{(n+s-2)/2}$). Moreover, a Boolean function $f$ is $s$-plateaued (of weight $\neq 2^{(n+s-2)/2}$) if and only if the associated Cayley graph is strongly $3$-walk-regular (and also strongly $\ell$-walk-regular, for all odd $\ell\geq 3$) with some explicitly given parameters.Comment: 7 pages, 1 figure, Proceedings of Africacrypt 201

LIPIcs, Volume 274, ESA 2023, Complete Volume

LIPIcs, Volume 274, ESA 2023, Complete Volum

A complete characterization of plateaued Boolean functions in terms of their Cayley graphs

The article of record as published may be found at http://dx.doi.org/10.In this paper we find a complete characterization of plateaued Boolean functions in terms of the associated Cayley graphs. Precisely, we show that a Boolean function f is s-plateaued (of weight = 2(n+s−2)/2) if and only if the associated Cayley graph is a complete bipartite graph between the support of f and its com- plement (hence the graph is strongly regular of parameters e = 0, d = 2(n+s−2)/2 ). Moreover, a Boolean function f is s-plateaued (of weight ̸= 2(n+s−2)/2) if and only if the associated Cayley graph is 3-walk-regular (and also l-walk-regular, for all odd l ≥ 3) with some explicitly given parameters