Construction of t-resilient functions over a finite alphabet


Paul Camion

INRIA, projet CODES
BP 105
78153 Le Chesnay Cedex, France
Paul.Camion@inria.fr

Anne Canteaut
INRIA, projet CODES
BP 105
78153 Le Chesnay Cedex, France
Anne.Canteaut@inria.fr

In Advances in Cryptology - EUROCRYPT'96 , LNCS 1070, pages 283-293
Springer-Verlag, 1996.
(Also as Research Report RR-2789, INRIA, February 1996.)


Abstract

We extend the notions of correlation-immune functions and resilient functions to functions over any finite alphabet endowed with the structure of an Abelian group. Thus we generalize the results of Gopalakrishnan and Stinson as we give an orthogonal array characterization and a Fourier transform characterization for resilient functions over any finite alphabet. This leads to a generalization of some related cryptographic objects as perfect local randomizers. It also enables us to construct new resilient functions by composition of resilient functions of smaller order.

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