摘要
To protect against algebraic attacks, a high algebraic immunity is now an important criterion for Boolean functions used in stream ciphers. In this paper, a new method based on a univariate polynomial representation of Boolean functions is proposed. The proposed method is used to constmct Boolean functions with an odd number of variables and with maximum algebraic immunity. We also discuss the nonlinearity of the constructed functions. Moreover, a lower bound is deter- mined for the number of Boolean functions with rmximum algebraic immunity.
To protect against algebraic attacks, a high algebraic immunity is now an important criterion for Boolean functions used in stream ciphers. In this paper, a new method based on a univariate polynomial representation of Boolean functions is proposed. The proposed method is used to construct Boolean functions with an odd number of variables and with maximum algebraic immunity. We also discuss the nonlinearity of the constructed functions. Moreover, a lower bound is determined for the number of Boolean functions with maximum algebraic immunity.
基金
This work was supported by the National Natural Science Foundation of China under Grants No. 61103191, No. 61070215
the Funds of Key Lab of Fujian Province University Network Security and Cryptology under Crant No. 2011003
and the Open Research Fund of State Key Laboratory of Inforrmtion Security.
作者简介
Zhao Wentao, received the Ph.D. degree in computer science in 2007 from the National University of Defense Technology of China. He is now an associate professor with College of Computer, Na- tional University of Defense Technology. His research fields include cryptography and Network security. Email： bmce_zhao@ tom.comFu Shaofing, received the Ph.D degree in applied mathematics from National University of Defense Technology in 2010. He is now a lecturer with the College of Computer, National University of Defense Technology of China. His research fields include cryptography and inforrmtion security. Fxnail： shaojing 1984@ yahoo.cnLi Chao, received the Ph.D. degree in engineering in 2002 from the National University of Defense Technology of China. Since December 2001, he has been a professor with the Department of Mathermtics and System Science, National University of Defense Technology. His research fields include coding theory and cryptography.
