Spectral Domain Analysis of Correlation Immune and Resilient Boolean Functions

Authors:
Claude Carlet;Palash Sarkar
Affiliations:
GREYC and University Paris 8/ and INRIA, Project CODES, 105-78153, Le Chesnay Cedex, Francef1claude.carlet@inria.frf1;Centre for Applied Cryptographic Research, Department of Combinatorics and Optimization, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, Canada, N2L 3G1f2psarkar@cacr.math.u ...
Venue:
Finite Fields and Their Applications
Year:
2002

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Abstract

We use a general property of Fourier transform to obtain direct proofs of recent divisibility results on the Walsh transform of correlation immune and resilient functions. Improved upper bounds on the nonlinearity of these functions are obtained from the divisibility results. We deduce further information on correlation immune and resilient functions. In particular, we obtain a necessary condition on the algebraic normal form of correlation immune functions attaining the maximum possible nonlinearity.