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2021•Journal of Mathematical CryptologyOpen access

Using Inclusion / Exclusion to find Bent and Balanced Monomial Rotation Symmetric Functions

Elizabeth M. Reid

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Abstract

Abstract There are many cryptographic applications of Boolean functions. Recently, research has been done on monomial rotation symmetric (MRS) functions which have useful cryptographic properties. In this paper we use the inclusion/exclusion principle to construct formulas for the weights of two subclasses of MRS functions: degree d short MRS functions and d -functions. From these results we classify bent and balanced functions of these forms.

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Abstract There are many cryptographic applications of Boolean functions. Recently, research has been done on monomial rotation symmetric (MRS) functions which have useful cryptographic properties. In this paper we use the inclusion/exclusion principle to construct formulas for the weights of two subclasses of MRS functions: degree d short MRS functions and d -functions. From these results we classify bent and balanced functions of these forms.

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Available abstract

Abstract There are many cryptographic applications of Boolean functions. Recently, research has been done on monomial rotation symmetric (MRS) functions which have useful cryptographic properties. In this paper we use the inclusion/exclusion principle to construct formulas for the weights of two subclasses of MRS functions: degree d short MRS functions and d -functions. From these results we classify bent and balanced functions of these forms.

Key concepts: Monomial, Boolean function, Bent molecular geometry, Mathematics, Bent function, Cryptography, Inclusion–exclusion principle, Symmetric function

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