To Label, or Not To Label (in Generic Groups)

Mark Zhandry

Research output: Chapter in Book/Report/Conference proceedingConference contribution

6 Scopus citations


Generic groups are an important tool for analyzing the feasibility and in-feasibility of group-based cryptosystems. There are two distinct wide-spread versions of generic groups, Shoup’s and Maurer’s, the main difference being whether or not group elements are given explicit labels. The two models are often treated as equivalent. In this work, however, we demonstrate that the models are in fact quite different, and care is needed when stating generic group results: We show that numerous textbook constructions are not captured by Maurer, but are captured by Shoup. In the other direction, any construction captured by Maurer is captured by Shoup.For constructions that exist in both models, we show that security is equivalent for “single stage” games, but Shoup security is strictly stronger than Maurer security for some “multi-stage” games.The existing generic group un-instantiability results do not apply to Maurer. We fill this gap with a new un-instantiability result.We explain how the known black box separations between generic groups and identity-based encryption do not fully apply to Shoup, and resolve this by providing such a separation.We give a new un-instantiability result for the algebraic group model.

Original languageEnglish (US)
Title of host publicationAdvances in Cryptology – CRYPTO 2022 - 42nd Annual International Cryptology Conference, CRYPTO 2022, Proceedings
EditorsYevgeniy Dodis, Thomas Shrimpton
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages31
ISBN (Print)9783031159817
StatePublished - 2022
Event42nd Annual International Cryptology Conference, CRYPTO 2022 - Santa Barbara, United States
Duration: Aug 15 2022Aug 18 2022

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume13509 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference42nd Annual International Cryptology Conference, CRYPTO 2022
Country/TerritoryUnited States
CitySanta Barbara

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science


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