Properties of the full class of quaternary bent-functions of two variables

Abstract

The development of modern cryptography methods is related in many respects to the research of perfect algebraic constructions which are characterized by the highest level of cryptographic strength indicators. The most important among these structures are bent-sequences, which have a maximum level of nonlinearity. This paper is devoted to the actual issue of research of such perfect algebraic constructions as quaternary bent-sequences. It is shown that in the quaternary case the complete class of affine functions and Vilenkin-Chrestenson functions are different algebraic constructions. The degeneracy of the full class of quaternary bent-functions of one variable is established, and the algorithm for the synthesis of the full class of quaternary bent-functions of two variables is proposed. The structural properties of the full class of quaternary bent-sequences were discovered, on the basis of which the 4428 different IV-sets were found that can be used to construct pseudorandom key sequence generators. The algebraic degrees of nonlinearity of all existing quaternary bent-functions of two variables are determined.

Subject Classification: (2010):

• 94A60

Keywords:

• Many-valued logic function
• Bent-sequence
• Pseudo-random key sequence generator