CONSTRUCTION OF SUBSETS OF BENT FUNCTIONS SATISFYING RESTRICTIONS IN THE REED-MULLER DOMAIN

摘要

Bent functionsare Booleanfunctionswith highestnonlinearitywhich makes them interesting for cryptography. Determination of bent functions is an importantbut hard problem, since the general structure of bent functions is still unknown. Various constructions methods for bent functions are based on certain deterministic procedures, which might result in some regularitythat is a feature undesired for applications in cryptography. Random generation of bent functions is an alternative, however, the search space is very large and the related procedures are time consuming. A solution is to restrict the search space by imposing some conditions that should be satis?ed by the produced bent functions. In this paper, we propose three ways of imposing such restrictions to construct subsets of Boolean functions within which the bent functions are searched. We estimate experimentally the number of bent functions in the corresponding subsets of Boolean functions.