Construction of Boolean functions with optimal algebraic immunity based on the maximal linear orthomorphic permutations

Abstract

How to construct Boolean functions with good cryptographic characteristics is an interesting and significant problem in cryptography. Based on the maximal linear orthomorphic permutations, a method is proposed in this paper to construct a large class of Boolean functions with optimal algebraic immunity. Moreover, we demonstrate that the Boolean functions construct by Wang are contained in ours. The Boolean functions constructed in this paper can be balanced. At the end, based on the examples, we also give two conjectures on the construction of Boolean functions with optimal algebraic immunity.

Cite this paper

@article{Du2011ConstructionOB, title={Construction of Boolean functions with optimal algebraic immunity based on the maximal linear orthomorphic permutations}, author={Jiao Du and Qiao-yan Wen and Jie Zhang and Shan-qi Pang and Rui Wang}, journal={Proceedings of 2011 International Conference on Computer Science and Network Technology}, year={2011}, volume={3}, pages={1571-1575} }