Title :
Two Classes of Symmetric Boolean Functions With Optimum Algebraic Immunity: Construction and Analysis
Author :
Chen, Yindong ; Lu, Peizhong
Author_Institution :
Dept. of Comput. Sci., Shantou Univ. (STU), Shantou, China
fDate :
4/1/2011 12:00:00 AM
Abstract :
This paper discusses two classes of symmetric Boolean functions. For each class, a necessary and sufficient condition for having optimum algebraic immunity is proposed. The algebraic degree and nonlinearity of the Boolean functions are also completely determined. And then we prove several of Braeken´s conjectures about the algebraic degree and nonlinearity of the Boolean functions with optimum algebraic immunity in the two classes.
Keywords :
Boolean functions; cryptography; algebraic degree; nonlinearity; optimum algebraic immunity; stream cipher; symmetric Boolean functions; Artificial intelligence; Boolean functions; Computer science; Cryptography; Equations; Hamming weight; Resists; Algebraic attacks; algebraic immunity; stream cipher; symmetric Boolean function;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2011.2111810
