Radical 2-isogenies and cryptographic hash functions in dimensions 1, 2 and 3

Sabrina Kunzweiler; Luciano Maino; Tomoki Moriya; Christophe Petit; Giacomo Pope; Damien Robert; Miha Stopar; Yan Bo Ti

doi:10.1007/978-3-031-91826-1_9

Radical 2-isogenies and cryptographic hash functions in dimensions 1, 2 and 3

Sabrina Kunzweiler^*
, Luciano Maino
, Tomoki Moriya
, Christophe Petit
, Giacomo Pope
, Damien Robert
, Miha Stopar
, Yan Bo Ti

^*Corresponding author for this work

Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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Abstract

We provide explicit descriptions for radical 2-isogenies in dimensions one, two and three using theta coordinates. These formulas allow us to efficiently navigate in the corresponding isogeny graphs.
As an application of this, we implement different versions of the CGL hash function. Notably, the three-dimensional version is fastest, which demonstrates yet another potential of using higher dimensional isogeny graphs in cryptography

Original language	English
Title of host publication	Public-Key Cryptography – PKC 2025
Subtitle of host publication	28th IACR International Conference on Practice and Theory of Public-Key Cryptography, Røros, Norway, May 12–15, 2025, Proceedings, Part III
Editors	Tibor Jager, Jiaxin Pan
Publisher	Springer
Pages	265-299
Number of pages	34
ISBN (Electronic)	9783031918261
ISBN (Print)	9783031918254
DOIs	https://doi.org/10.1007/978-3-031-91826-1_9
Publication status	Published - 5 May 2025
Event	28th IACR International Conference on Practice and Theory of Public-Key Cryptography - Røros, Norway Duration: 12 May 2025 → 15 May 2025 https://pkc.iacr.org/2025/

Publication series

Name	Lecture Notes in Computer Science
Publisher	Springer
Volume	15676
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	28th IACR International Conference on Practice and Theory of Public-Key Cryptography
Abbreviated title	PKC 2025
Country/Territory	Norway
City	Røros
Period	12/05/25 → 15/05/25
Internet address	https://pkc.iacr.org/2025/

Bibliographical note

Publisher Copyright:
© International Association for Cryptologic Research 2025.

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-031-91826-1_9Licence: None: All rights reserved

KunzweilerS2025Radical
This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/10.1007/978-3-031-91826-1_9
Accepted author manuscript, 665 KBLicence: Other (please specify with Rights Statement)

Post-Quantum Cryptography: a Cryptanalysis Approach
Petit, C. (Principal Investigator)
Engineering & Physical Science Research Council
1/10/21 → 31/03/27
Project: Research Councils

Cite this

Kunzweiler, S., Maino, L., Moriya, T., Petit, C., Pope, G., Robert, D., Stopar, M., & Ti, Y. B. (2025). Radical 2-isogenies and cryptographic hash functions in dimensions 1, 2 and 3. In T. Jager, & J. Pan (Eds.), Public-Key Cryptography – PKC 2025: 28th IACR International Conference on Practice and Theory of Public-Key Cryptography, Røros, Norway, May 12–15, 2025, Proceedings, Part III (pp. 265-299). (Lecture Notes in Computer Science; Vol. 15676). Springer. https://doi.org/10.1007/978-3-031-91826-1_9

Kunzweiler, Sabrina ; Maino, Luciano ; Moriya, Tomoki et al. / Radical 2-isogenies and cryptographic hash functions in dimensions 1, 2 and 3. Public-Key Cryptography – PKC 2025: 28th IACR International Conference on Practice and Theory of Public-Key Cryptography, Røros, Norway, May 12–15, 2025, Proceedings, Part III. editor / Tibor Jager ; Jiaxin Pan. Springer, 2025. pp. 265-299 (Lecture Notes in Computer Science).

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abstract = "We provide explicit descriptions for radical 2-isogenies in dimensions one, two and three using theta coordinates. These formulas allow us to efficiently navigate in the corresponding isogeny graphs. As an application of this, we implement different versions of the CGL hash function. Notably, the three-dimensional version is fastest, which demonstrates yet another potential of using higher dimensional isogeny graphs in cryptography",

author = "Sabrina Kunzweiler and Luciano Maino and Tomoki Moriya and Christophe Petit and Giacomo Pope and Damien Robert and Miha Stopar and Ti, \{Yan Bo\}",

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Kunzweiler, S, Maino, L, Moriya, T, Petit, C, Pope, G, Robert, D, Stopar, M & Ti, YB 2025, Radical 2-isogenies and cryptographic hash functions in dimensions 1, 2 and 3. in T Jager & J Pan (eds), Public-Key Cryptography – PKC 2025: 28th IACR International Conference on Practice and Theory of Public-Key Cryptography, Røros, Norway, May 12–15, 2025, Proceedings, Part III. Lecture Notes in Computer Science, vol. 15676, Springer, pp. 265-299, 28th IACR International Conference on Practice and Theory of Public-Key Cryptography, Røros, Norway, 12/05/25. https://doi.org/10.1007/978-3-031-91826-1_9

Radical 2-isogenies and cryptographic hash functions in dimensions 1, 2 and 3. / Kunzweiler, Sabrina; Maino, Luciano; Moriya, Tomoki et al.
Public-Key Cryptography – PKC 2025: 28th IACR International Conference on Practice and Theory of Public-Key Cryptography, Røros, Norway, May 12–15, 2025, Proceedings, Part III. ed. / Tibor Jager; Jiaxin Pan. Springer, 2025. p. 265-299 (Lecture Notes in Computer Science; Vol. 15676).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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AU - Stopar, Miha

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Kunzweiler S, Maino L, Moriya T, Petit C, Pope G, Robert D et al. Radical 2-isogenies and cryptographic hash functions in dimensions 1, 2 and 3. In Jager T, Pan J, editors, Public-Key Cryptography – PKC 2025: 28th IACR International Conference on Practice and Theory of Public-Key Cryptography, Røros, Norway, May 12–15, 2025, Proceedings, Part III. Springer. 2025. p. 265-299. (Lecture Notes in Computer Science). doi: 10.1007/978-3-031-91826-1_9

Radical 2-isogenies and cryptographic hash functions in dimensions 1, 2 and 3

Abstract

Publication series

Conference

Bibliographical note

ASJC Scopus subject areas

Access to Document

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Projects

Post-Quantum Cryptography: a Cryptanalysis Approach

Cite this