Cryptology ePrint Archive: Report 2021/1184

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.

Category / Keywords: foundations / cryptographic abelian groups, hidden order groups, algebraic group model, time-lock cryptography

Original Publication (with minor differences): IACR-ASIACRYPT-2021

Date: received 14 Sep 2021, last revised 3 Dec 2021

Contact author: aron van baarsen at cwi nl

Available format(s): PDF | BibTeX Citation

Version: 20211203:151346 (All versions of this report)

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