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Bent functions from a finite abelian group into a finite abelian group. (English. Russian original) Zbl 1047.94011
Discrete Math. Appl. 12, No. 2, 111-126 (2002); translation from Diskretn. Mat. 14, No. 1, 99-113 (2002).
Summary: We introduce the notions of an absolutely non-homomorphic function, a minimal function (farthest from homomorphisms) and a bent function, and prove that the class of bent functions coincides with the class of absolutely non-homomorphic functions, that a function is uniquely determined by the distances to homomorphisms with shifts, and that in the primary case the bent functions are absolutely minimal.

94A60 Cryptography
06E30 Boolean functions
20K01 Finite abelian groups
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