Generic-group delay functions require hidden-order groups

Lior Rotem, Gil Segev*, Ido Shahaf

*Corresponding author for this work

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

4 Scopus citations


Despite the fundamental importance of delay functions, underlying both the classic notion of a time-lock puzzle and the more recent notion of a verifiable delay function, the only known delay function that offers both sufficient structure for realizing these two notions and a realistic level of practicality is the “iterated squaring” construction of Rivest, Shamir and Wagner. This construction, however, is based on rather strong assumptions in groups of hidden orders, such as the RSA group (which requires a trusted setup) or the class group of an imaginary quadratic number field (which is still somewhat insufficiently explored from the cryptographic perspective). For more than two decades, the challenge of constructing delay functions in groups of known orders, admitting a variety of well-studied instantiations, has eluded the cryptography community. In this work we prove that there are no constructions of generic-group delay functions in cyclic groups of known orders: We show that for any delay function that does not exploit any particular property of the representation of the underlying group, there exists an attacker that completely breaks the function’s sequentiality when given the group’s order. As any time-lock puzzle and verifiable delay function give rise to a delay function, our result holds for these two notions we well, and explains the lack of success in resolving the above-mentioned long-standing challenge. Moreover, our result holds even if the underlying group is equipped with a d-linear map, for any constant d ≥ 2 (and even for super-constant values of d under certain conditions).

Original languageAmerican English
Title of host publicationAdvances in Cryptology – EUROCRYPT 2020 - 39th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings
EditorsAnne Canteaut, Yuval Ishai
Number of pages26
ISBN (Print)9783030457266
StatePublished - 2020
Event39th Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2020 - Zagreb, Croatia
Duration: 10 May 202014 May 2020

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12107 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference39th Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2020

Bibliographical note

Funding Information:
Supported by the European Union’s Horizon 2020 Framework Program (H2020) via an ERC Grant (Grant No. 714253). L. Rotem—Supported by the Adams Fellowship Program of the Israel Academy of Sciences and Humanities. I. Shahaf—Supported by the Clore Israel Foundation via the Clore Scholars Programme.

Publisher Copyright:
© International Association for Cryptologic Research 2020.


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