Explicit constructions of ternary plateaued functions with maximal algebraic degree

Plateaued functions with high algebraic degree play a significant role in cryptosystems. We find nine explicit construction methods for ternary plateaued functions with (almost) maximal algebraic degree . To obtain the methods, we first consider a framework for constructing ternary functions, which are good candidates for plateaued functions. Then we obtain three explicit criteria for input values of the framework for the ternary functions to be s ′ -plateaued functions, where s ′ = s − 1 , s , or s + 1 . Consequently, we find nine explicit construction methods for ternary s ′ -plateaued functions, which arise from s -plateaued functions, where s ′ = s − 1 , s or s + 1 . The connection with the degree bound is also given. Using our construction methods, we find three infinite families of ternary 1-plateaued functions with (almost) maximal algebraic degree; this is done by selecting out input functions from partial spread bent functions. We emphasize that eight of our construction methods are new and that these three infinite families are also new to the literature.