Nearly bent functions

Abstract

In this paper, we define a large class of almost balanced Boolean functions called nearly bent functions. These functions lie at large Hamming distance to all affine functions and preserve a high level of algebraic degree. Then a construction of nearly bent functions is described. It is shown that the constructed functions have good global avalanche characteristic properties. In the concluding remarks, we show that nearly bent functions have good stability.

Keywords:

• cryptography
• Boolean function
• bent function
• GAC
• stream cipher

2000 AMS Subject Classifications :

• 94A60
• 06E30

Acknowledgements

The authors would like to thank the anonymous reviewers for their comments that improved the technical and the editorial quality of this paper. This work was supported by the Natural Science Foundations of China (No. 61003299), the Natural Science Basic Research Plan in Shaanxi Province of China (No. SJ08-ZT14), the Fundamental Research Funds for the Central Universities, and the 111 Project (No. B08038).