On values of vectorial Boolean functions and related problems in APN functions

George Shushuev

Paper 2015/1244

On values of vectorial Boolean functions and related problems in APN functions

George Shushuev

Abstract

In this paper we prove that there are only differential 4-uniform functions which are on distance 1 from an APN function. Also we prove that there are no APN functions of distance 1 from another APN functions up to dimension 5. We determine some properties of the set of values of an arbitrary vectorial Boolean function from F_n^2 to F_n^2 in connection to the set of values of its derivatives. These results are connected to several open question concerning metric properties of APN functions.

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Preprint. MINOR revision.
Keywords: Vectorial Boolean function APN function differentially &#948 -uniform function
Contact author(s): shushuev @ math nsc ru
History: 2015-12-31: received
Short URL: https://ia.cr/2015/1244
License: CC BY

BibTeX

@misc{cryptoeprint:2015/1244,
      author = {George Shushuev},
      title = {On values of vectorial Boolean functions and related problems in APN functions},
      howpublished = {Cryptology ePrint Archive, Paper 2015/1244},
      year = {2015},
      note = {\url{https://eprint.iacr.org/2015/1244}},
      url = {https://eprint.iacr.org/2015/1244}
}