Title: On the construction of bent vectorial functions

Authors: Claude Carlet, Sihem Mesnager

Addresses: LAGA, Department of Mathematics, Universities of Paris 8 and Paris 13 and CNRS, 2 rue de la liberte, Saint-Denis Cedex 93526, France. ' LAGA, Department of Mathematics, Universities of Paris 8 and Paris 13 and CNRS, 2 rue de la liberte, Saint-Denis Cedex 93526, France

Abstract: This paper is devoted to the constructions of bent vectorial functions, that is, maximally non-linear multi-output Boolean functions. Such functions contribute to an optimal resistance to both linear and differential attacks of those cryptosystems in which they are involved as substitution boxes (S-boxes). We survey, study more in details and generalise the known primary and secondary constructions of bent functions, and we introduce new ones.

Keywords: block ciphers; S-box; vectorial functions; bent functions; Walsh-Hadamard transform; nonlinear Boolean functions; multi-output Boolean functions; linear attacks; differential attacks; cryptosystems; substitution boxes; cryptography; security.

DOI: 10.1504/IJICOT.2010.032131

International Journal of Information and Coding Theory, 2010 Vol.1 No.2, pp.133 - 148

Published online: 10 Mar 2010 *

Full-text access for editors Access for subscribers Purchase this article Comment on this article