POKÉ: A Compact and Efficient PKE from Higher-dimensional Isogenies

Andrea Basso; Luciano Maino

doi:10.1007/978-3-031-91124-8_4

POKÉ: A Compact and Efficient PKE from Higher-dimensional Isogenies

Andrea Basso
, Luciano Maino

Research output: Chapter in Book/Report/Conference proceeding › Conference Contribution (Conference Proceeding)

10 Citations (Scopus)

97 Downloads (Pure)

Abstract

We introduce a new PKE protocol, POKÉ, based on isogenies of unknown degree. The protocol relies on two new techniques: the first constructs an SIDH square while also working with higher-dimensional representations, whereas the second allows us to obtain a shared secret even when all curves in the commutative diagram are known.

The resulting protocol is compact and extremely efficient. We provide a proof-of-concept implementation in SageMath of POKÉ that shows encryption and decryption taking about a hundred milliseconds at security level I: POKÉ is thus the most efficient encryption protocol from isogenies, and it outperforms existing protocols by more than an order of magnitude.

Original language	English
Title of host publication	Advances in Cryptology – EUROCRYPT 2025
Subtitle of host publication	44th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Madrid, Spain, May 4–8, 2025, Proceedings
Editors	Serge Fehr, Pierre-Alain Fouque
Publisher	Springer, Cham
Pages	94-123
Number of pages	30
Volume	2
ISBN (Electronic)	9783031911248
ISBN (Print)	9783031911231
DOIs	https://doi.org/10.1007/978-3-031-91124-8_4
Publication status	Published - 28 Apr 2025
Event	Eurocrypt 2025 - Madrid, Spain Duration: 4 May 2025 → 8 May 2025 https://eurocrypt.iacr.org/2025/

Publication series

Name	Lecture Notes in Computer Science
Volume	15602 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	Eurocrypt 2025
Country/Territory	Spain
City	Madrid
Period	4/05/25 → 8/05/25
Internet address	https://eurocrypt.iacr.org/2025/

Bibliographical note

Publisher Copyright:
© International Association for Cryptologic Research 2025.

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10.1007/978-3-031-91124-8_4

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Accepted author manuscript, 641 KBLicence: CC BY

https://eprint.iacr.org/2024/624Licence: CC BY-NC-SA

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Basso, A., & Maino, L. (2025). POKÉ: A Compact and Efficient PKE from Higher-dimensional Isogenies. In S. Fehr, & P.-A. Fouque (Eds.), Advances in Cryptology – EUROCRYPT 2025: 44th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Madrid, Spain, May 4–8, 2025, Proceedings (Vol. 2, pp. 94-123). (Lecture Notes in Computer Science; Vol. 15602 LNCS). Springer, Cham. https://doi.org/10.1007/978-3-031-91124-8_4

Basso, Andrea ; Maino, Luciano. / POKÉ : A Compact and Efficient PKE from Higher-dimensional Isogenies. Advances in Cryptology – EUROCRYPT 2025: 44th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Madrid, Spain, May 4–8, 2025, Proceedings. editor / Serge Fehr ; Pierre-Alain Fouque. Vol. 2 Springer, Cham, 2025. pp. 94-123 (Lecture Notes in Computer Science).

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title = "POK{\'E}: A Compact and Efficient PKE from Higher-dimensional Isogenies",

abstract = "We introduce a new PKE protocol, POK{\'E}, based on isogenies of unknown degree. The protocol relies on two new techniques: the first constructs an SIDH square while also working with higher-dimensional representations, whereas the second allows us to obtain a shared secret even when all curves in the commutative diagram are known. The resulting protocol is compact and extremely efficient. We provide a proof-of-concept implementation in SageMath of POK{\'E} that shows encryption and decryption taking about a hundred milliseconds at security level I: POK{\'E} is thus the most efficient encryption protocol from isogenies, and it outperforms existing protocols by more than an order of magnitude.",

author = "Andrea Basso and Luciano Maino",

note = "Publisher Copyright: {\textcopyright} International Association for Cryptologic Research 2025.; Eurocrypt 2025 ; Conference date: 04-05-2025 Through 08-05-2025",

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Basso, A & Maino, L 2025, POKÉ: A Compact and Efficient PKE from Higher-dimensional Isogenies. in S Fehr & P-A Fouque (eds), Advances in Cryptology – EUROCRYPT 2025: 44th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Madrid, Spain, May 4–8, 2025, Proceedings. vol. 2, Lecture Notes in Computer Science, vol. 15602 LNCS, Springer, Cham, pp. 94-123, Eurocrypt 2025, Madrid, Spain, 4/05/25. https://doi.org/10.1007/978-3-031-91124-8_4

POKÉ: A Compact and Efficient PKE from Higher-dimensional Isogenies. / Basso, Andrea; Maino, Luciano.
Advances in Cryptology – EUROCRYPT 2025: 44th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Madrid, Spain, May 4–8, 2025, Proceedings. ed. / Serge Fehr; Pierre-Alain Fouque. Vol. 2 Springer, Cham, 2025. p. 94-123 (Lecture Notes in Computer Science; Vol. 15602 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference Contribution (Conference Proceeding)

TY - GEN

T1 - POKÉ

T2 - Eurocrypt 2025

AU - Basso, Andrea

AU - Maino, Luciano

PY - 2025/4/28

Y1 - 2025/4/28

N2 - We introduce a new PKE protocol, POKÉ, based on isogenies of unknown degree. The protocol relies on two new techniques: the first constructs an SIDH square while also working with higher-dimensional representations, whereas the second allows us to obtain a shared secret even when all curves in the commutative diagram are known. The resulting protocol is compact and extremely efficient. We provide a proof-of-concept implementation in SageMath of POKÉ that shows encryption and decryption taking about a hundred milliseconds at security level I: POKÉ is thus the most efficient encryption protocol from isogenies, and it outperforms existing protocols by more than an order of magnitude.

AB - We introduce a new PKE protocol, POKÉ, based on isogenies of unknown degree. The protocol relies on two new techniques: the first constructs an SIDH square while also working with higher-dimensional representations, whereas the second allows us to obtain a shared secret even when all curves in the commutative diagram are known. The resulting protocol is compact and extremely efficient. We provide a proof-of-concept implementation in SageMath of POKÉ that shows encryption and decryption taking about a hundred milliseconds at security level I: POKÉ is thus the most efficient encryption protocol from isogenies, and it outperforms existing protocols by more than an order of magnitude.

UR - https://eurocrypt.iacr.org/2025/

U2 - 10.1007/978-3-031-91124-8_4

DO - 10.1007/978-3-031-91124-8_4

M3 - Conference Contribution (Conference Proceeding)

SN - 9783031911231

VL - 2

T3 - Lecture Notes in Computer Science

SP - 94

EP - 123

BT - Advances in Cryptology – EUROCRYPT 2025

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ER -

Basso A, Maino L. POKÉ: A Compact and Efficient PKE from Higher-dimensional Isogenies. In Fehr S, Fouque PA, editors, Advances in Cryptology – EUROCRYPT 2025: 44th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Madrid, Spain, May 4–8, 2025, Proceedings. Vol. 2. Springer, Cham. 2025. p. 94-123. (Lecture Notes in Computer Science). Epub 2025 Apr 27. doi: 10.1007/978-3-031-91124-8_4

POKÉ: A Compact and Efficient PKE from Higher-dimensional Isogenies

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