### On Time-Lock Cryptographic Assumptions in Abelian Hidden-Order Groups

Aron van Baarsen and Marc Stevens

##### Abstract

In this paper we study cryptographic finite abelian groups of unknown order and hardness assumptions in these groups. Abelian groups necessitate multiple group generators, which may be chosen at random. We formalize this setting and hardness assumptions therein. Furthermore, we generalize the algebraic group model and strong algebraic group model from cyclic groups to arbitrary finite abelian groups of unknown order. Building on these formalizations, we present techniques to deal with this new setting, and prove new reductions. These results are relevant for class groups of imaginary quadratic number fields and time-lock cryptography build upon them.

Available format(s)
Category
Foundations
Publication info
A minor revision of an IACR publication in Asiacrypt 2021
DOI
10.1007/978-3-030-92075-3_13
Keywords
cryptographic abelian groupshidden order groupsalgebraic group modeltime-lock cryptography
Contact author(s)
aron van baarsen @ cwi nl
History
2021-12-03: revised
See all versions
Short URL
https://ia.cr/2021/1184

CC BY

BibTeX

@misc{cryptoeprint:2021/1184,
author = {Aron van Baarsen and Marc Stevens},
title = {On Time-Lock Cryptographic Assumptions in Abelian Hidden-Order Groups},
howpublished = {Cryptology ePrint Archive, Paper 2021/1184},
year = {2021},
doi = {10.1007/978-3-030-92075-3_13},
note = {\url{https://eprint.iacr.org/2021/1184}},
url = {https://eprint.iacr.org/2021/1184}
}

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