Classification of All $t$-Resilient Boolean Functions with $t+4$ Variables

Shahram Rasoolzadeh

Paper 2023/638

Classification of All $t$ -Resilient Boolean Functions with $t + 4$ Variables

Shahram Rasoolzadeh

, Radboud University, Nijmegen, The Netherlands

Abstract

We apply Siegenthaler's construction, along with several techniques, to classify all $(n - 4)$ -resilient Boolean functions with $n$ variables, for all values of $n \geq 4$ , up to extended variable-permutation equivalence. We show that, up to this equivalence, there are only 761 functions for any $n$ larger than or equal to 10, and for smaller values of $n$ , i.e., for $n$ increasing from 4 to 9, there are 58, 256, 578, 720, 754, and 760 functions, respectively. Furthermore, we classify all 1-resilient 6-variable Boolean functions and show that there are 1035596784 such functions up to extended variable-permutation equivalence.

Metadata

Available format(s): PDF
Category: Secret-key cryptography
Publication info: Published by the IACR in TOSC 2023
Keywords: correlation immunity resilient functions boolean functions
Contact author(s): shahram rasoolzadeh @ ru nl
History: 2023-08-15: revised; 2023-05-04: received; See all versions
Short URL: https://ia.cr/2023/638
License: CC BY-NC

BibTeX

@misc{cryptoeprint:2023/638,
      author = {Shahram Rasoolzadeh},
      title = {Classification of All $t$-Resilient Boolean Functions with $t+4$ Variables},
      howpublished = {Cryptology {ePrint} Archive, Paper 2023/638},
      year = {2023},
      url = {https://eprint.iacr.org/2023/638}
}

Paper 2023/638

Classification of All t-Resilient Boolean Functions with t+4 Variables

Abstract

Metadata

Classification of All $t$ -Resilient Boolean Functions with $t + 4$ Variables