SimS: a simplification of SiGamal

Tako Boris Fouotsa*, Christophe Petit

*Corresponding author for this work

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

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At Asiacrypt 2020, Moriya et al. introduced two new IND-CPA secure supersingular isogeny based Public Key Encryption (PKE) protocols: SiGamal and C-SiGamal. Unlike the PKEs canonically derived from SIDH and CSIDH, the new protocols provide IND-CPA security without the use of hash functions. SiGamal and C-SiGamal are however not IND-CCA secure. Moriya et al. suggested a variant of SiGamal that could be IND-CCA secure, but left its study as an open problem. In this paper, we revisit the protocols introduced by Moriya et al. First, we show that the SiGamal variant suggested by Moriya et al. for IND-CCA security is, in fact, not IND-CCA secure. Secondly, we propose a new isogeny-based PKE protocol named SimS, obtained by simplifying SiGamal. SimS has smaller public keys and ciphertexts than (C-)SiGamal and it is more efficient. We prove that SimS is IND-CCA secure under CSIDH security assumptions and one Knowledge of Exponent-type assumption we introduce. Interestingly, SimS is also much closer to the CSIDH protocol, facilitating a comparison between SiGamal and CSIDH.

Original languageEnglish
Title of host publicationPost-Quantum Cryptography
Subtitle of host publication12th International Workshop, PQCrypto 2021, Daejeon, South Korea, July 20–22, 2021, Proceedings
EditorsJung Hee Cheon, Jean-Pierre Tillich
Number of pages19
ISBN (Electronic)9783030812935
ISBN (Print)9783030812928
Publication statusPublished - 15 Jul 2021
Event12th International Conference on post-quantum cryptography, PQCrypto 2021 - Daejeon, Korea, Republic of
Duration: 20 Jul 202122 Jul 2021

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12841 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference12th International Conference on post-quantum cryptography, PQCrypto 2021
Country/TerritoryKorea, Republic of

Bibliographical note

Publisher Copyright:
© 2021, Springer Nature Switzerland AG.


  • PKE
  • Post-quantum cryptography
  • SiGamal
  • SimS
  • Supersingular isogenies

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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