Çeşmelioğlu, AyçaMeidl, WilfriedTopuzoğlu, Alev2021-05-152021-05-152014978-1-107-07400-2https://hdl.handle.net/20.500.12939/688Cesmelioglu, Ayca/0000-0001-5049-9135A function f : F-p(n) -> F-p is called partially bent if for all a is an element of F-p(n) the derivative D(a)f(x) = f(x + a) - f(x) is constant or balanced, i.e., every value in F-p is taken on p(n-1) times. Bent functions have balanced derivatives D(a)f for all nonzero a is an element of F-p(n), hence are partially bent. Partially bent functions may be balanced and highly nonlinear, and thus have favorable properties for cryptographic applications in stream and block ciphers. Hence they are of independent interest. Partially bent functions are also used to construct new bent functions. The aim of this article is to provide a deeper understanding of partially bent functions. We collect their properties and describe partially bent functions with appropriate generalizations of relative difference sets and difference sets. The descriptions of bent functions as relative difference sets and of Hadamard difference sets in characteristic 2, follow from our result as special cases. We describe Hermitian matrices related to partially bent functions and interpret a secondary construction of bent functions from partially bent functions in terms of relative difference sets.eninfo:eu-repo/semantics/closedAccessBent FunctionsEngineeringDualsBook Part22382-s2.0-84953638310N/AWOS:000356958200003N/A