Loughborough University
Browse

On the algebraic degree stability of Boolean functions when restricted to affine spaces

conference contribution
posted on 2025-02-04, 16:57 authored by Claude Carlet, Serge FEUKOUA JONZOSerge FEUKOUA JONZO, Ana SalageanAna Salagean

We study the n-variable Boolean functions which keep their algebraic degree unchanged when they are restricted to any (affine) hyperplane, or more generally to any affine space of a given co-dimension k. For cryptographic applications it is of interest to determine functions f which have a relatively high degree and also maintain this degree when restricted to affine spaces of co-dimension k for k ranging from 1 to as high a value as possible. This highest value will be called the restriction degree stability of f, denoted by deg stab(f). We give several necessary and/or sufficient conditions for f to maintain its degree on spaces of co-dimension k. The value of deg stab(f) is determined for functions which are direct sums of monomial as well as for functions of degrees r ∈ {1, 2, n − 2, n − 1, n}; we also determine the symmetric functions which maintain their degree on any hyperplane. Finally, using our previous results and some computer assistance, we determine the behaviour of all the functions in 8 variables, therefore determining the optimal ones (i.e. with highest value of deg stab(f)) for each degree.

Funding

Boolean functions with optimal stability of their cryptographic indicators under restriction of the inputs

Engineering and Physical Sciences Research Council

Find out more...

History

School

  • Science

Department

  • Computer Science

Published in

Designs, Codes and Cryptography

Source

13th International Workshop of Coding and Cryptography

Publisher

Springer

Version

  • AM (Accepted Manuscript)

Publisher statement

This version of the contribution has been accepted for publication, after peer review (when applicable) but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/xxxxx. Use of this Accepted Version is subject to the publisher’s Accepted Manuscript terms of use https://www.springernature.com/gp/open-research/policies/accepted-manuscript-terms

Publication date

2024-07-10

ISSN

0925-1022

eISSN

1573-7586

Language

  • en

Location

Perugia, Italy

Event dates

17th June 2024 - 21st June 2024

Depositor

Dr Serge FEUKOUA JONZO. Deposit date: 1 February 2025

Usage metrics

    Loughborough Publications

    Categories

    No categories selected

    Exports

    RefWorks
    BibTeX
    Ref. manager
    Endnote
    DataCite
    NLM
    DC