Construction of highly nonlinear resilient S-boxes with given degree

Authors:
Shaojing Fu;Kanta Matsuura;Chao Li;Longjiang Qu
Affiliations:
College of Computer, National University of Defense Technology, Changsha, People's Republic of China 410073 and Institute of Industrial Science, University of Tokyo, Tokyo, Japan 153-8505;Institute of Industrial Science, University of Tokyo, Tokyo, Japan 153-8505;College of Science, National University of Defense Technology, Changsha, People's Republic of China 410073;College of Science, National University of Defense Technology, Changsha, People's Republic of China 410073
Venue:
Designs, Codes and Cryptography
Year:
2012

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Abstract

We provide two new construction methods for nonlinear resilient S-boxes with given degree. The first method is based on the use of linear error correcting codes together with highly nonlinear S-boxes. Given a [u, m, t + 1] linear code where u = n驴d驴1, d m, we show that it is possible to construct (n, m, t, d) resilient S-boxes which have currently best known nonlinearity. Our second construction provides highly nonlinear (n, m, t, d) resilient S-boxes which do not have linear structure, then an improved version of this construction is given.