Research On Cryptographic Properties Of Boolean Function By Concatenation

Nowadays,the information age is approaching.It is of great signifi-cance to ensure information security.Boolean functions play a vital role in the field of information security.This paper studies on some important cryptographic properties of Boolean functions,and mainly achieves the following results:1.A special kind of concatenated Boolean function f=f1?f2?f3?f1 is giv-en.The relationship between the Walsh spectrum of the newly constructed Boolean functionf=ff1?f2?f3?f1 and functionsf1,f2,f3 is present.With the help of the Walsh spectrum,this dissertation discusses the cryptography properties of the con-catenated Boolean function,such as the correlation immunity,algebraic immunity and other cryptographic properties,drawing some related conclusions.A sufficient and necessary condition about the correlation immunity of the concatenated Boolean functions is given.The upper and lower bounds of algebraic immunity of concatenated Boolean functions are given.2.This dissertation gives the relations of auto-correlation and cross-correlation functions about the concatenated Boolean function f=f1?f2?f3?f1,discusses the cryptography properties,such as the propagation criterion,the global avalanche characteristic and the linear structure of the concatenated Boolean functions f=f1?f2?f3?f1.We give a condition that the concatenated Boolean functions satisfy propagation criterion,and show the relationship about the sum of squares indicator of the concatenated Boolean functions,the condition that there is no linear structure for the concatenated Boolean functions.3.With the relations of auto-correlation and cross-correlation functions about concatenated Boolean functions f=f1?f2?f3?f1,this dissertation discusses some conclusions of the new construction of Bent function,and gives a new construction of Bent function.We present a characterization of bent-negabent functions,which is related to the second-order derivatives.