A Characterization of Algebraic Immune Boolean Functions

doi:10.13190/jbupt.200705.55.344

JOURNAL OF BEIJING UNIVERSITY OF POSTS AND TELECOM ›› 2007, Vol. 30 ›› Issue (5): 55-57.doi: 10.13190/jbupt.200705.55.344

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A Characterization of Algebraic Immune Boolean Functions

ZHANG Wei-guo1, DING Yong2, ZHANG Ning1， XIAO Guo-zhen1

(1. State Key laboratory of Integrated Service Networks, Xidian University, Xi’an 710071, China;
2. Schoole of Mathematics and Computational Science, Guilin University of Electronic Technology, Guilin 541004, China)

Received:2006-12-22 Revised:2007-05-20 Online:2007-10-30 Published:2007-10-30
Contact: ZHANG Wei-guo

Abstract

Abstract:

A characterization of the algebraic immune Boolean functions is presented by means of the covering vectors. A sufficient and necessary condition is given that the algebraic immunity of a Boolean function is not more than a fixed value. This result is used to describe a characterization of the algebraic immune of normal Boolean functions. It is also shown that the upper bound of the algebraic immunity of -normal Boolean functions is .

Key words: Cryptography, Boolean function, algebraic immunity, normality

CLC Number:

TN918.1

ZHANG Wei-guo1, DING Yong2, ZHANG Ning1， XIAO Guo-zhen1. A Characterization of Algebraic Immune Boolean Functions[J]. JOURNAL OF BEIJING UNIVERSITY OF POSTS AND TELECOM, 2007, 30(5): 55-57.

References

[1] Chlamtac I, Conti M, Liu J J N. Mobile Ad hoc networking: imperatives and challenges[J]. Ad Hoc Networks, 2003, 1(1): 13-64.
[2] Kelly F P, Maulloo A, Tan D. Rate control for communication networks: shadow prices, proportional fairness and stability[J]. Journal of Operations Research Society, 1998, 49(3): 237-252.
[3] Han H, Shakkottai S. Overlay TCP for multi-path routing and congestion control//The IMA Workshop on Measurements and Modeling of the Internet. Urbana-Champaign, Illinois: , 2004.
[4] Kar K, Sarkar S, Tassiulas L. Optimization based rate control for multipath sessions//The 17th International Teletraffic Congress (ITC 2001). Salvador da Bahia, Brazil: , 2001.
[5] Low S H. Multipath optimization flow control//8th IEEE International Conference on Networks (ICON 2000). Singapore: , 2000.
[6] Wang W, Palaniswami M, Low S H. Optimal flow control and routing in multi-path networks[J]. Performance Evaluation, 2003, 52(2-3): 119-132.
[7] Lin X, Shroff N B. The multi-path utility maximization problem//41st Annual Allerton Conference on Communication, Control, and Computing. Monticello: , 2003.
[8] Lin X, Shroff N B. Utility maximization for communication networks with multi-path routing[J]. IEEE Transactions on Automatic Control, 2006, 51(5): 766-781.
[9] Srinivasan V, Chiasserini C F, Nuggehalli P S, et al. Optimal rate allocation for energy-efficient multipath routing in wireless Ad hoc networks. IEEE Transactions on Wireless Communications, 2004, 3(3): 891-899.
[10] Xu W Q, Wu T J. Optimal congestion control algorithm for Ad hoc networks: penalty function-based approach[J]. Zhejiang University, Science A, 2006, 7(12): 2110-2117.
[11] Kar K, Sarkar S, Tassiulas L. A scalable, low-overhead rate control algorithm for multirate multicast sessions[J]. IEEE Journal on Selected Areas in Communications, 2002, 20(8): 1541-1557.
[12] Xu W Q, Wu T J. TCP issues in mobile Ad hoc networks: challenges and solutions[J]. Journal of Computer Science and Technology, 2006, 21(1): 72-81.

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A Characterization of Algebraic Immune Boolean Functions

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