Abstract
In this paper, we propose a new method to construct cryptographically significant (vectorial) Boolean functions over by using the decomposition of the multiplicative group of , and give a generalized description for constructing a class of vectorial Boolean functions with high algebraic immunity. Moreover, for even n, we introduce two special classes of vectorial Boolean functions with high algebraic immunity: one is hyper-bent and the other is balanced with optimal algebraic degree.
Acknowledgements
The authors thank the reviewers for their helpful advice and comments. This work is supported by the Science and Technology on Information Assurance Laboratory under Grant No.KJ-11-02 and National Natural Science Foundation of China under Grants No. 61272499, No. 10990011.