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Covering Sequences of Boolean Functions and Their Cryptographic Significance

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Abstract

We introduce the notion of covering sequence of a Boolean function, related to the derivatives of the function. We give complete characterizations of balancedness, correlation immunity and resiliency of Boolean functions by means of their covering sequences. By considering particular covering sequences, we define subclasses of (correlation-immune) resilient functions. We derive upper bounds on their algebraic degrees and on their nonlinearities. We give constructions of resilient functions belonging to these classes. We show that they achieve the best known trade-off between order of resiliency, nonlinearity and algebraic degree.

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Authors and Affiliations

  1. INRIA projet CODES, Domaine de Voluceau, Rocquencourt, BP 105-78153, Le Chesnay Cedex, France;

    C. Carlet

  2. Université, Paris 8, France

    C. Carlet

  3. Mech. & Math. Department, Moscow State University, 119899, Moscow, Russia

    Yu. Tarannikov

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  1. C. Carlet
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  2. Yu. Tarannikov
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Carlet, C., Tarannikov, Y. Covering Sequences of Boolean Functions and Their Cryptographic Significance. Designs, Codes and Cryptography 25, 263–279 (2002). https://doi.org/10.1023/A:1014935513734

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