Algebraic construction of near-bent function with application to cryptography

Abstract

Near-bent functions that occur in odd dimensions are the important class of Boolean functions, which are useful functions for cryptography. In this paper, we construct near-bent function with trace term using well known Welch function exponent in polynomial form and various other forms of near-bent functions. We have also investigated some important cryptographical properties of near-bent functions.

Subject Classification: (2020):

• 06E30
• 94D10

Keywords:

• Near-bent functions
• Boolean functions
• Trace
• Walsh coefficient
• Cryptography