An Efficient Authenticated Key Exchange from Random Self-reducibility on CSIDH

Tomoki Kawashima*, Katsuyuki Takashima, Yusuke Aikawa, Tsuyoshi Takagi

*Corresponding author for this work

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

5 Citations (Scopus)


SIDH and CSIDH are key exchange protocols based on isogenies and conjectured to be quantum-resistant. Since the protocols are similar to the classical Diffie–Hellman, they are vulnerable to the man-in-the-middle attack. A key exchange which is resistant to such an attack is called an authenticated key exchange (AKE), and many isogeny-based AKEs have been proposed. However, the parameter sizes of the existing schemes should be large since they all have relatively large security losses in security proofs. This is partially because the random self-reducibility of isogeny-based decisional problems has not been proved yet. In this paper, we show that the computational problem and the gap problem of CSIDH are random self-reducible. A gap problem is a computational problem given access to the corresponding decision oracle. Moreover, we propose a CSIDH-based AKE with small security loss, following the construction of Cohn-Gordon et al. in CRYPTO 2019, as an application of the random self-reducibility of the gap problem of CSIDH. Our AKE is proved to be the fastest CSIDH-based AKE when we aim at 110-bit security level.

Original languageEnglish
Title of host publication23rd International Conference, 2020, Proceedings
EditorsDeukjo Hong
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages27
ISBN (Print)9783030688899
Publication statusPublished - 2021
Externally publishedYes
Event23rd International Conference on Information Security and Cryptology, ICISC 2020 - Seoul, Korea, Republic of
Duration: 2020 Dec 22020 Dec 4

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12593 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference23rd International Conference on Information Security and Cryptology, ICISC 2020
Country/TerritoryKorea, Republic of


  • Authenticated key exchange
  • Isogeny-based cryptography
  • Post-quantum
  • Tight security

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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