Construction of bent functions of 2k variables from a basis of

Abstract

In this paper, starting with a basis of , we define some sets in that are the supports of bent functions of 2k variables. We also establish some results in order to count the number of bent functions we can construct and we provide a complete classification of all bases of (for k=2) providing the same supports of bent functions.

Keywords:

• Boolean function
• bent function
• support of a Boolean function
• Gauss–Jordan basis
• cryptography

2010 AMS Subject Classifications::

• 06E30
• 94A60
• 94C10

Acknowledgements

This work was partially supported by Spanish grants MTM2008-06674-C02-01 and MTM2011-24858 of the Ministerio de Ciencia e Innovación of the Gobierno de España and ACOMP/2010/039 and ACOMP/2011/005 of the Generalitat Valenciana.