Trapdoor DDH groups from pairings and isogenies

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Trapdoor DDH groups are an appealing cryptographic primitive introduced by Dent-Galbraith (ANTS 2006), where DDH instances are hard to solve unless provided with additional information (i.e., a trapdoor). In this paper, we introduce a new trapdoor DDH group construction using pairings and isogenies of supersingular elliptic curves, and present two instantiations of it. The construction solves all shortcomings of previous constructions as identified by Seurin (RSA 2013). We also present partial attacks on a previous construction due to Dent-Galbraith, and we provide a formal security definition of the related notion of "trapdoor pairings".
Original languageEnglish
Title of host publicationSelected Areas in Cryptography
Subtitle of host publication27th International Conference, Halifax, NS, Canada (Virtual Event), October 21-23, 2020, Revised Selected Papers
EditorsOrr Dunkelman, Michael J. Jacobson, Jr., Colin O’Flynn
ISBN (Electronic)9783030816520
ISBN (Print)9783030816513
Publication statusPublished - 21 Jul 2021
Event27th International Conference on Selected Areas in Cryptography, SAC 2020 - Virtual, Online
Duration: 21 Oct 202023 Oct 2020

Publication series

NameLecture Notes in Computer Science
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference27th International Conference on Selected Areas in Cryptography, SAC 2020
CityVirtual, Online

Bibliographical note

Funding Information:
Acknowledgements. We thank Jens Groth, Steven Galbraith and Frederik Ver-cauteren for discussions related to this work. In particular, some of our applications were suggested by Jens Groth. We also thank the anonymous reviewers. Work by the first and second author was supported by an EPSRC New Investigator grant (EP/S01361X/1). The third author was supported by a PhD grant from the Spanish government, co-financed by the ESF (Ayudas para contratos predoctorales para la formación de doctores 2016). This work was partially done while the third author visited the University of Birmingham.

Publisher Copyright:
© 2021, Springer Nature Switzerland AG.


  • elliptic curve cryptography
  • pairings
  • isogenies
  • trapdoor DDH

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)


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