Open Problems in Mathematics and Computational Science

pp 203-241


Open Problems on Binary Bent Functions

  • Claude CarletAffiliated withLAGA, Universities of Paris 8 and Paris 13, CNRS, UMR 7539Department of Mathematics, University of Paris 8 Email author 

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This chapter gives a survey of the recent results on Boolean bent functions and lists some open problems in this domain. It includes also new results. We recall the definitions and basic results, including known and new characterizations of bent functions; we describe the constructions (primary and secondary; known and new) and give the known infinite classes, in multivariate representation and in trace representation (univariate and bivariate). We also focus on the particular class of rotation symmetric (RS) bent functions and on the related notion of bent idempotent: we give the known infinite classes and secondary constructions of such functions, and we describe the properties of a recently introduced transformation of RS functions into idempotents.