Construction of Boolean Functions with Optimal Algebraic Immunity
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.
KeywordsBoolean Function Generator Matrix Stream Cipher Balance Function Algebraic Degree
Unable to display preview. Download preview PDF.
- 1.Ding C, Xiao G, Shan W. The Stability Theory of Stream Ciphers[M]. Springer Berlin Heidelberg, 1991.Google Scholar
- 2.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.Google Scholar
- 3.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.Google Scholar
- 4.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.Google Scholar
- 5.Carlet C. A Method of Construction of Balanced Functions with Optimum Algebraic Immunity[J]. Iacr Cryptology Eprint Archive, 2006, 2006(2):131-6.Google Scholar
- 6.Carlet C. Vectorial Boolean functions for cryptography[J]. Boolean Models & Methods in Mathematics, 2006.Google Scholar
- 7.Carlet C. Constructing balanced functions with optimum algebraic immunity[C]// IEEE International Symposium on Information Theory. 2007:451-455.Google Scholar
- 8.8. 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.Google Scholar
- 9.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.Google Scholar
- 10.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.Google Scholar
- 11.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.Google Scholar
- 12.Su S. Construction of balanced even-variable Boolean functions with optimal algebraic immunity[J]. International Journal of Computer Mathematics, 2014, 92(11):1-14.Google Scholar