Some Studys On Bent Functions And Correlation Immune Functions

Nowadays, as the information revolution is propelled onto a unprecedented level, the theory of information safety, which is based on cryptography, attacts far more attention than before.Since the birth of cryptography, the safety of cryptographic systems have been the focus of research. Besides, the safety of cryptographic system depends on the properties of the logical functions related to the systems, such as, nonlinearity, correlation immunity, balance, propagation criteria, stability and so on. So the research into the properties of logical function is academically indispensable for analysising and designing the cryptographic systems.This thesis attempts to have a close study of correlation immunity, propagation criteria and bent functions on boolean functions. The main results are as follows:(1) We give the necessary and sufficient conditions when the sum function of several bent functions is still bent function;(2) Several equal conditions about correlation immune functions and a new method of generate correlation immune functions are obtained. These results generalize predecessor's correlation corresponding results.(3) The determination theorem about the correlation immune functions which satisfies propagation criteria is given.