S-boxes with Controllable Nonlinearity

Abstract. In this paper, we give some relationship between the nonlinearity of rational functions over F2n and the number of points of associated hyperelliptic curve. Using this, we get a lower bound on nonlinearity of rational-typed vector Boolean functions over F2n . While the previous works give us a lower bound on nonlinearity only for special-typed monomials, our result gives us general bound applicable for all rational fuctions defined over F2n . As an application of our results, we get a lower bound on nonlinearity of n × kn S-boxes.

• Type: Conference
• Year: 1999
• Where: EUROCRYPT
• Authors: Jung Hee Cheon, Seongtaek Chee, Choonsik Park
• Keywords: Associated Hyperelliptic Curve, Cryptology, EUROCRYPT 1999, Lower Bound, Nonlinearity