On the symmetric property of homogeneous boolean functions

Chengxin Qu, Jennifer Seberry, Josef Pieprzyk

Research output: Chapter in Book/Report/Conference proceedingConference proceeding contributionpeer-review

19 Citations (Scopus)


We use combinatorial methods and permutation groups to classify homogeneous boolean functions. The property of symmetry of a boolean function limits the size of the function’s class. We exhaustively searched for all boolean functions on V6. We found two interesting classes of degree 3 homogeneous boolean functions: the first class is degree 3 homogeneous bent boolean functions; and the second is degree 3 homogeneous balanced boolean functions. Both the bent and balanced functions discovered have nice algebraic and combinatorial structures. We note that some structures can be extended to a large boolean space. The application of homogeneous boolean functions for fast implementation on parallel architectures is mooted.

Original languageEnglish
Title of host publicationInformation Security and Privacy
Subtitle of host publication4th Australasian Conference, ACISP’99 Wollongong, NSW, Australia, April 7–9, 1999 Proceedings
EditorsJosef Pieprzyk, Rei Safavi-Naini, Jennifer Seberry
Place of PublicationBerlin
PublisherSpringer, Springer Nature
Number of pages10
ISBN (Electronic)9783540489702
ISBN (Print)3540657568, 9783540657569
Publication statusPublished - 1999
Externally publishedYes
Event4th Australasian Conference on Information Security and Privacy, ACISP - 1999 - Wollongong, Australia
Duration: 7 Apr 19999 Apr 1999

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
ISSN (Print)03029743
ISSN (Electronic)16113349


Other4th Australasian Conference on Information Security and Privacy, ACISP - 1999


  • Cryptographically Strong Boolean Functions
  • Homogeneous Functions
  • S-box Theory
  • Symmetric Functions


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