Semi-bent Functions and Strict Uncorrelated Criterion Revisted

Abstract

In Asiacrypt’94 , Chee et al. proposed a new class of cryptographic primitive, semi-bent functions and discussed a cryptographic relationship between two Boolean functions, strict uncorrelated criterion (SUC). But their functions exist on only odd dimensional vector spaces. And SUC is a very weak condition when we guarantee S (ubstitution)-box to be resistant against and linear analysis. In this paper, we define new semi-bent functions which exist on any dimensional vector spaces. Furthermore, we extend the concept of SUC form the relation of two Boolean functions to that of m-tuples of Boolean functions, where m≧2.