Cryptology ePrint Archive: Report 2005/100

almost enumeration of 8-variable bent functions

Qingshu Meng and Huanguo Zhang and Jingsong Cui and Min Yang

Abstract: Bent functions are important cryptographic Boolean functions. In order to enumerate eight-variable bent functions, we solve the following three key problems. Firstly, under the action of $AGL(7,2)$, we almost completely classify $R(4,7)/R(2,7)$. Secondly, we construct all seven-variable \emph{plateaued} functions from the orbits of $R(4,7)/R(2,7)$. Thirdly, we present a fast algorithm to expand \emph{plateaued} function into bent functions. Based on the results above, it is feasible to enumerate eight-variable bent functions in practice.

Category / Keywords: foundations / Reed-Muller code, group action, bent functions

Date: received 3 Apr 2005, last revised 27 Jan 2007

Contact author: mqseagle at sohu com

Available formats: PDF | BibTeX Citation

Note: one reference is added and several spelling mistakes are corrected

Version: 20070127:114651 (All versions of this report)

Discussion forum: Show discussion | Start new discussion