On the Construction of Boolean Functions with Optimal Algebraic Immunity and Good Other Properties by Concatenation

摘要

How to construct Boolean functions with good cryptographic characteristics is an interesting and significant problem in cryptography. Based on the properties of concatenation, two methods were proposed to construct Boolean functions with optimal or suboptimal algebraic immunity. Moreover, some other cryptographic properties, such as algebraic degree, balancedness, and nonlinearity, of the constructed function were also studied. At the end, a new idea was presented for ascertaining whether the given Boolean function had optimal algebraic immunity.