Plateaued Functions

The focus of this paper is on nonlinear characteristics of cryptographic Boolean functions First we introduce the notion of plateaued functions that have many cryptographically desirable properties Second we establish a sequence of strengthened inequalities on some of the most important nonlinearity criteria including nonlinearity propagation and correlation immunity and prove that critical cases of the inequalities co incide with characterizations of plateaued functions We then proceed to prove that plateaued functions include as a proper subset all partially bent functions that were introduced earlier by Carlet This settles an open question that arises from previously known results on partially bent functions In addition we construct plateaued but not partially bent functions that have many properties useful in cryptography