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Designs, Codes and Cryptography

, Volume 37, Issue 2, pp 319–346 | Cite as

Highly Nonlinear Resilient Functions Through Disjoint Codes in Projective Spaces

  • Pascale CharpinEmail author
  • Enes Pasalic
Article

Abstract

Functions which map n-bits to m-bits are important cryptographic sub-primitives in the design of additive stream ciphers. We construct highly nonlinear t-resilient such functions ((n, m, t) functions) by using a class of binary disjoint codes, a construction which was introduced in IEEE Trans. Inform. Theory, Vol. IT-49 (2) (2003). Our main contribution concerns the generation of suitable sets of such disjoint codes. We propose a deterministic method for finding disjoint codes of length ν m by considering the points of PG\((v-1, \mathbb{F}_{2^{m}}\)). We then obtain some lower bounds on the number of disjoint codes, by fixing some parameters. Through these sets, we deduce in certain cases the existence of resilient functions with very high nonlinearity values. We show how, thanks to our method, the degree and the differential properties of (n, m, t) functions can be improved.

Keywords

Boolean function n-input m-output function resilient function nonlinearity propagation characteristic symmetric cryptography stream cipher linear code projective space complete weight enumerator 

AMS Classification:

11T71 

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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  1. 1.INRIA, project CODESDomaine de Voluceau, RocquencourtCedexFrance

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