@article{dbec5663d899480d90c519e33be990ca,
title = "Subsets of Groups in Public-key Cryptography",
abstract = "We suggest the use of algebraic subsets instead of subgroups in public-key cryptography. In particular, we present the subset version of two protocols introduced by Shpilrain and Ushakov with some examples in ascending HNN-extensions of free-abelian groups and discuss their resistance to length and distance based attacks. We also introduce several new group theoretic problems arising from this work.",
keywords = "Subsets of groups, Ascending HNN-extensions, Context-free languages, Key-exchange",
author = "Andr{\'e} Carvalho and Ant{\'o}nio Malheiro",
note = "info:eu-repo/grantAgreement/FCT/Concurso de avalia{\c c}{\~a}o no {\^a}mbito do Programa Plurianual de Financiamento de Unidades de I&D (2017%2F2018) - Financiamento Base/UIDB%2F00297%2F2020/PT# info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDP%2F00297%2F2020/PT# Funding Information: This work is funded by national funds through the FCT Funda\u00E7\u00E3o para a Ci\u00EAncia e a Tecnologia, I.P., under the scope of the projects UIDB/00297/2020 and UIDP/00297/2020 (Center for Mathematics and Applications). Publisher Copyright: {\textcopyright} 2025, American Institute of Mathematical Sciences. All rights reserved.",
year = "2025",
month = jun,
doi = "10.3934/amc.2024036",
language = "English",
volume = "19",
pages = "980--995",
journal = "Advances in Mathematics of Communications",
issn = "1930-5346",
publisher = "AIMS Press - American Institute of Mathematical Sciences",
number = "3",
}