Further Results on Autocorrelation of Vectorial Boolean Functions

Abstract

In this paper, we study the properties of the sum-of-squares indicator of vectorial Boolean functions. Firstly, we give the upper bound ofSecondly, based on the Walsh-Hadamard transform, we give a secondary construction of vectorial bent functions. Further, three kinds of sum-of-squares indicators of vectorial Boolean functions are defined by autocorrelation function and the lower and upper bounds of the sum-of-squares indicators are derived. Finally, we study the sum-ofsquares indicators with respect to several equivalence relations, and get the sum-of-squares indicator which have the best cryptographic properties.