@inproceedings{d40d6817ec8c4c629165710cbbd9aa3d,
title = "On the symmetric property of homogeneous boolean functions",
abstract = "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{\textquoteright}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.",
keywords = "Cryptographically Strong Boolean Functions, Homogeneous Functions, S-box Theory, Symmetric Functions",
author = "Chengxin Qu and Jennifer Seberry and Josef Pieprzyk",
year = "1999",
doi = "10.1007/3-540-48970-3_3",
language = "English",
isbn = "3540657568",
volume = "1587",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer, Springer Nature",
pages = "26--35",
editor = "Josef Pieprzyk and Rei Safavi-Naini and Jennifer Seberry",
booktitle = "Information Security and Privacy",
address = "United States",
note = "4th Australasian Conference on Information Security and Privacy, ACISP - 1999 ; Conference date: 07-04-1999 Through 09-04-1999",
}