One-Round Authenticated Group Key Exchange from Isogenies

Atsushi Fujioka, Katsuyuki Takashima, Kazuki Yoneyama*

*Corresponding author for this work

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

9 Citations (Scopus)


This paper proposes two one-round authenticated group key exchange protocols from newly employed cryptographic invariant maps (CIMs): one is secure in the quantum random oracle model and the other resists against maximum exposure where a non-trivial combination of secret keys is revealed. The security of the former (resp. latter) is proved under the n-way decisional (resp. n-way gap) Diffie–Hellman assumption on the CIMs in the quantum random (resp. random) oracle model. We instantiate the proposed protocols on the hard homogeneous spaces with limitation where the number of the user group is two. In particular, the protocols instantiated by using the CSIDH, commutative supersingular isogeny Diffie–Hellman, key exchange are currently more realistic than the general n-party CIM-based ones due to its realizability. Our two-party one-round protocols are secure against quantum adversaries.

Original languageEnglish
Title of host publicationProvable Security - 13th International Conference, ProvSec 2019, Proceedings
EditorsRon Steinfeld, Tsz Hon Yuen
Number of pages9
ISBN (Print)9783030319182
Publication statusPublished - 2019
Externally publishedYes
Event13th International Conference on Provable and Practical Security, ProvSec 2019 - Cairns, Australia
Duration: 2019 Oct 12019 Oct 4

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11821 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference13th International Conference on Provable and Practical Security, ProvSec 2019


  • Commutative supersingular isogeny Diffie–Hellman
  • Cryptographic invariant maps
  • G-CK model
  • G-CK model
  • Hard homogeneous spaces
  • One-round authenticated group key exchange
  • Quantum adversary

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)


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