Generic-group identity-based encryption: A tight impossibility result

Gili Schul-Ganz*, Gil Segev*

*Corresponding author for this work

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

5 Scopus citations

Abstract

Following the pioneering work of Boneh and Franklin (CRYPTO'01), the challenge of constructing an identity-based encryption scheme based on the Diffie-Hellman assumption remained unresolved for more than 15 years. Evidence supporting this lack of success was provided by Papakonstantinou, Rackoff and Vahlis (ePrint'12), who ruled out the existence of generic-group identity-based encryption schemes supporting an identity space of sufficiently large polynomial size. Nevertheless, the breakthrough result of Döttling and Garg (CRYPTO'17) settled this long-standing challenge via a non-generic construction. We prove a tight impossibility result for generic-group identity-based encryption, ruling out the existence of any non-trivial construction: We show that any scheme whose public parameters include npp group elements may support at most npp identities. This threshold is trivially met by any generic-group public-key encryption scheme whose public keys consist of a single group element (e.g., ElGamal encryption). In the context of algebraic constructions, generic realizations are often both conceptually simpler and more efficient than non-generic ones. Thus, identifying exact thresholds for the limitations of generic groups is not only of theoretical significance but may in fact have practical implications when considering concrete security parameters.

Original languageAmerican English
Title of host publication2nd Conference on Information-Theoretic Cryptography, ITC 2021
EditorsStefano Tessaro
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Pages26:1-26:23
Number of pages23
ISBN (Electronic)9783959771979
DOIs
StatePublished - 1 Jul 2021
Event2nd Conference on Information-Theoretic Cryptography, ITC 2021 - Virtual, Bertinoro, Italy
Duration: 23 Jul 202126 Jul 2021

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume199
ISSN (Print)1868-8969

Conference

Conference2nd Conference on Information-Theoretic Cryptography, ITC 2021
Country/TerritoryItaly
CityVirtual, Bertinoro
Period23/07/2126/07/21

Bibliographical note

Publisher Copyright:
© 2021 Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. All rights reserved.

Keywords

  • Generic-group model
  • Identity-based encryption

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