A construction of Boolean functions with good cryptographic properties

Abstract

The two important qualities of a cipher are security and speed. Frequently, to satisfy the security of a Boolean function primitive, speed may be traded-off. In this paper, we present a general construction that addresses both qualities. The idea of our construction is to manipulate a cryptographically strong base function and one of its affine equivalent functions, using concatenation and negation. We achieve security from the inherent qualities of the base function, which are preserved (or increased), and obtain speed by the simple Boolean operations. We present two applications of the construction to demonstrate the flexibility and efficiency of the construction.

Keywords:

• cryptographic Boolean functions
• avalanche characteristics
• resiliency
• algebraic immunity
• nonlinearity
• hidden weighted bit function

2010 AMS Subject Classifications::

• 94C10
• 94A60
• 11T71

Acknowledgements

The authors express their appreciation for the insightful and constructive comments of the referees and the editor, which improved the quality of the paper.