Abstract
Boolean functions with good cryptographic properties act as important nonlinear components in symmetric cryptography which is often used to encrypt stored data for cloud computing. In this paper, we develop a new class of Boolean functions with optimal algebraic immunity by utilizing the Reed-Muller code. In addition, our new functions are balanced and have good nonlinearity.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Ding C, Xiao G, Shan W. The Stability Theory of Stream Ciphers[M]. Springer Berlin Heidelberg, 1991.
Nicolas T. Courtois, Willi Meier. Algebraic Attacks on Stream Ciphers with Linear Feedback.[ C]. Advances in Cryptology - EUROCRYPT 2003, International Conference on the Theory and Applications of Cryptographic Techniques, Warsaw, Poland, May 4-8, 2003, Proceedings. 2003:345-359.
Nicolas T. Courtois,Willi Meier. Fast Algebraic Attacks on Stream Ciphers with Linear Feedback.[C]. Advances in Cryptology - EUROCRYPT 2003, Lecture Notes in Computer Science. 2003:176-194.
Carlet C, Gaborit P. On the construction of balanced boolean functions with a good algebraic immunity.[C]// Information Theory, 2005. ISIT 2005. Proceedings. International Symposium on. 2005:1101-1105.
Carlet C. A Method of Construction of Balanced Functions with Optimum Algebraic Immunity[J]. Iacr Cryptology Eprint Archive, 2006, 2006(2):131-6.
Carlet C. Vectorial Boolean functions for cryptography[J]. Boolean Models & Methods in Mathematics, 2006.
Carlet C. Constructing balanced functions with optimum algebraic immunity[C]// IEEE International Symposium on Information Theory. 2007:451-455.
8. Carlet C, Feng K. An Infinite Class of Balanced Functions with Optimal Algebraic Immunity, Good Immunity to Fast Algebraic Attacks and Good Nonlinearity.[C]// Advances in Cryptology - ASIACRYPT 2008, International Conference on the Theory and Application of Cryptology and Information Security, Melbourne, Australia, December 7-11, 2008. Proceedings. 2008:425-440.
Carlet C, Zeng X, Li C, et al. Further properties of several classes of Boolean functions with optimum algebraic immunity[J]. Designs Codes & Cryptography, 2009, 52(3):303-338.
Dalai D K, Maitra S, Sarkar S. Basic Theory in Construction of Boolean Functions with Maximum Possible Annihilator Immunity[J]. Designs Codes & Cryptography, 2006, 40(1):41-58.
Su S, Tang X, Zeng X. A systematic method of constructing Boolean functions with optimal algebraic immunity based on the generator matrix of the Reed-Muller code[J]. Designs Codes & Cryptography, 2014, 72(3):653-673.
Su S. Construction of balanced even-variable Boolean functions with optimal algebraic immunity[J]. International Journal of Computer Mathematics, 2014, 92(11):1-14.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
Liu, H., Zheng, D., Zhao, Q. (2017). Construction of Boolean Functions with Optimal Algebraic Immunity. In: Barolli, L., Xhafa, F., Yim, K. (eds) Advances on Broad-Band Wireless Computing, Communication and Applications. BWCCA 2016. Lecture Notes on Data Engineering and Communications Technologies, vol 2. Springer, Cham. https://doi.org/10.1007/978-3-319-49106-6_80
Download citation
DOI: https://doi.org/10.1007/978-3-319-49106-6_80
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-49105-9
Online ISBN: 978-3-319-49106-6
eBook Packages: EngineeringEngineering (R0)