Propagation characteristics and correlation-immunity of highly nonlinear boolean functions

  • Authors:
  • Anne Canteaut;Claude Carlet;Pascale Charpin;Caroline Fontaine

  • Affiliations:
  • INRIA projet CODES, Le Chesnay Cedex, France;GREYC, Université de Caen, Caen Cedex, France;INRIA projet CODES, Le Chesnay Cedex, France;LIFL, Université des Sciences et Technologies de Lille, Villeneuve d'Ascq Cedex, France

  • Venue:
  • EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
  • Year:
  • 2000

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Abstract

We investigate the link between the nonlinearity of a Boolean function and its propagation characteristics. We prove that highly nonlinear functions usually have good propagation properties regarding different criteria. Conversely, any Boolean function satisfying the propagation criterion with respect to a linear subspace of codimension 1 or 2 has a high nonlinearity. We also point out that most highly nonlinear functions with a three-valued Walsh spectrum can be transformed into 1-resilient functions.