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Partially-bent functions

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Abstract

We study a conjecture stated in [6] about the numbers of non-zeros of, respectively, the auto-correlation function and the Walsh transform of the function (−1)f(x), wheref(x) is any boolean function on {0, 1}n. The result that we obtain leads us to introduce the class of partially-bent functions. We study within these functions the propagation criterion. We characterize those partially-bent functions which are balanced and prove a relation between their number (which is unknown) and the number of non-balanced partially-bent functions on {0, 1}n−1. Eventually, we study their correlation immunity.

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Author notes

  1. Claude Carlet

    Present address: Université de Picardie, France

Authors and Affiliations

  1. Domaine de Voluceau, INRIA Rocquencourt, Bat 10, BP 105, 78153, Le Chesnay Cedex, France

    Claude Carlet

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  1. Claude Carlet
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Communicated by T. Beth

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Carlet, C. Partially-bent functions. Des Codes Crypt 3, 135–145 (1993). https://doi.org/10.1007/BF01388412

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  • DOI: https://doi.org/10.1007/BF01388412

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