A database for boolean functions and constructions of generalized pairs

Abstract

In this thesis, we study spectral measures of Boolean functions. In the first half of thesis, we study the Walsh spectrum and the periodic autocorrelation spectrum of a Boolean function. A database of Boolean functions is implemented and described, and a survey is presented of cryptographic criteria, most of which are included within the database. In the second half of the thesis, we study the aperiodic autocorrelation spectrum of a Boolean function and some more spectral measures with respect to certain types of unitary matrix. We investigate the Turyn construction for Golay complementary pairs. We show how to convert this construction so as to realize three distinct types of complementary construction. We focus, in particular, on the construction of Boolean function pairs which are Type-I, Type-II or Type-III complementary or near-complementary.