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2011•International Journal of Foundations of Computer ScienceRequires access

ON THE NONEXISTENCE of BENT FUNCTIONS

Yin Zhang, Meicheng Liu, Dongdai Lin

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Abstract

In this paper, we study the nonexistence of bent functions in the class of Boolean functions without monomials of degree less than d in their algebraic normal forms (ANF). We prove that n-variable Boolean functions in such class are not bent when there are not more than n + d - 3 monomials in their ANFs. We also show that an n-variable Boolean function is not bent if it has no monomial of degree less than ⌈3n/8 + 3/4⌉ in its ANF.

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What this paper is about

In this paper, we study the nonexistence of bent functions in the class of Boolean functions without monomials of degree less than d in their algebraic normal forms (ANF). We prove that n-variable Boolean functions in such class are not bent when there are not more than n + d - 3 monomials in their ANFs. We also show that an n-variable Boolean function is not bent if it has no monomial of degree less than ⌈3n/8 + 3/4⌉ in its ANF.

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Available abstract

In this paper, we study the nonexistence of bent functions in the class of Boolean functions without monomials of degree less than d in their algebraic normal forms (ANF). We prove that n-variable Boolean functions in such class are not bent when there are not more than n + d - 3 monomials in their ANFs. We also show that an n-variable Boolean function is not bent if it has no monomial of degree less than ⌈3n/8 + 3/4⌉ in its ANF.

Key concepts: Monomial, Bent molecular geometry, Boolean function, Mathematics, Class (philosophy), Bent function, Degree (music), Combinatorics

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