International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: almost enumeration of 8-variable bent functions

Qingshu Meng
Huanguo Zhang
Jingsong Cui
Min Yang
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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.
  title={almost enumeration of 8-variable bent functions},
  booktitle={IACR Eprint archive},
  keywords={foundations / Reed-Muller code, group action, bent functions},
  note={ 13540 received 3 Apr 2005, last revised 27 Jan 2007},
  author={Qingshu Meng and Huanguo Zhang and Jingsong Cui and Min Yang},