Title :
On the Construction of Boolean Functions With Optimal Algebraic Immunity
Author :
Li, Na ; Qu, LongJiang ; Qi, Wen-Feng ; Feng, GuoZhu ; Li, Chao ; Xie, DuanQiang
Author_Institution :
Dept. of Appl. Math., Zhengzhou Inf. Eng. Univ., Zhengzhou
fDate :
3/1/2008 12:00:00 AM
Abstract :
In this correspondence, we introduce a method to construct Boolean functions in any number of variables, with optimal algebraic immunity. Remarkably, all functions of this type with an odd number of variables can be obtained in this way. We study some cryptographic properties, such as balancedness, algebraic degree of the constructed functions. Moreover, a lower bound of the number of Boolean functions with optimal algebraic immunity is given.
Keywords :
Boolean functions; cryptography; Boolean functions; cryptographic properties; optimal algebraic immunity; Artificial intelligence; Boolean functions; Chaos; Computer simulation; Cryptography; Equations; H infinity control; Information security; Mathematics; National security; Algebraic attacks; Boolean functions; algebraic degree; algebraic immunity; balancedness;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2007.915914
