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Abstract
In this paper, for an integer n≥10, two classes of n-variable Boolean functions with optimum algebraic immunity (AI) are constructed, and their nonlinearities are also determined. Based on non-degenerate linear transforms to the proposed functions, we can obtain 1-resilient n-variable Boolean functions with optimum AI and high nonlinearity if n−1 is never equal to any power of 2.
Acknowledgements
The authors would like to thank the anonymous referees for their helpful comments, which have significantly improved the presentation of the paper. The work of W. Su and X. Zeng was supported in part by Chenguang plan of Wuhan City (200850731340) and the National Science Foundation of China (NSFC) under Grant 60973130. The work of L. Hu was supported in part by NSFC under Grants 60773134 and 10990011 and National Basic Research (973) Program of China (2007CB311201).