Isogeny-based Toolbox for Post-quantum Cryptography

Project Information

ISOCRYPT

Grant agreement ID: 101020788

DOI

10.3030/101020788

EC signature date 18 July 2021

Start date 1 January 2022

End date 31 December 2027

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost

€ 2 495 575,00

EU contribution

€ 2 495 575,00

Coordinated by

KATHOLIEKE UNIVERSITEIT LEUVEN
Belgium

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Links to deliverables and publications from FP7 projects, as well as links to some specific result types such as dataset and software, are dynamically retrieved from OpenAIRE .

Deliverables

Open Research Data Pilot (1)

Data Management Plan (DMP)

Data Management Plan DMP

Publications

Conference proceedings (9)

Genus formulas for families of modular curves

Author(s): Hamakiotes, Asimina; Lau, Jun Bo
Published in: Contemporary Mathematics, Issue 2025, 2025
Publisher: American Mathematical Society

Two Remarks on the Vectorization Problem

Author(s): Wouter Castryck, Natan Vander Meeren
Published in: Progress in Cryptology – INDOCRYPT 2022, Issue Lecture Notes in Computer Science book series (LNCS,volume 13774), 2023, Page(s) 658–678, ISBN 978-3-031-22912-1
Publisher: Springer, Cham
DOI: 10.1007/978-3-031-22912-1_29

Efficient Computation of (3n,3n) -Isogenies

Author(s): Thomas Decru, Sabrina Kunzweiler
Published in: Progress in Cryptology - AFRICACRYPT 2023, Issue Lecture Notes in Computer Science book series (LNCS,volume 14064), 2023, Page(s) 53–78, ISBN 978-3-031-37679-5
Publisher: Springer, Cham
DOI: 10.1007/978-3-031-37679-5_3

Weak Instances of Class Group Action Based Cryptography via Self-pairings

Author(s): Wouter Castryck, Marc Houben, Simon-Philipp Merz, Marzio Mula, Sam van Buuren, Frederik Vercauteren
Published in: Advances in Cryptology – CRYPTO 2023, Issue Lecture Notes in Computer Science book series (LNCS,volume 14083), 2023, Page(s) 762–792, ISBN 978-3-031-38548-3
Publisher: Springer, Cham
DOI: 10.1007/978-3-031-38548-3_25

Horizontal Racewalking Using Radical Isogenies

Author(s): Wouter Castryck, Thomas Decru, Marc Houben, Frederik Vercauteren
Published in: Advances in Cryptology – ASIACRYPT 2022, Issue Lecture Notes in Computer Science book series (LNCS,volume 13792), 2023, Page(s) 67–96, ISBN 978-3-031-22966-4
Publisher: Springer, Cham
DOI: 10.1007/978-3-031-22966-4_3

Practical Robust DKG Protocols for CSIDH

Author(s): Shahla Atapoor, Karim Baghery, Daniele Cozzo, Robi Pedersen
Published in: ACNS 2023: Applied Cryptography and Network Security, Issue LNCS,volume 13906, 2023, Page(s) 219–247, ISBN 978-3-031-33490-0
Publisher: Springer, Cham
DOI: 10.1007/978-3-031-33491-7_9

The Permutation Group of Reed-Solomon Codes Over Arbitrary Points

Author(s): Eduardo Camps-Moreno, Jun Bo Lau, Hiram H. López, Welington Santos
Published in: 2025 IEEE International Symposium on Information Theory (ISIT), 2026, Page(s) 1-6
Publisher: IEEE
DOI: 10.1109/isit63088.2025.11195458

An Efficient Key Recovery Attack on SIDH

Author(s): Wouter Castryck, Thomas Decru
Published in: Advances in Cryptology – EUROCRYPT 2023, Issue Lecture Notes in Computer Science book series (LNCS,volume 14008), 2023, Page(s) 423–447, ISBN 978-3-031-30589-4
Publisher: Springer, Cham
DOI: 10.1007/978-3-031-30589-4_15

CSI-SharK: CSI-FiSh with Sharing-friendly Keys

Author(s): Shahla Atapoor, Karim Baghery, Daniele Cozzo, Robi Pedersen
Published in: ACISP 2023: Information Security and Privacy, Issue LNCS,volume 13915, 2023, Page(s) 471–502, ISBN 978-3-031-35485-4
Publisher: Springer, Cham
DOI: 10.1007/978-3-031-35486-1_21

Book chapters (24)

Faster SCALLOP from Non-prime Conductor Suborders in Medium Sized Quadratic Fields

Author(s): Bill Allombert, Jean-François Biasse, Jonathan Komada Eriksen, Péter Kutas, Chris Leonardi, Aurel Page, Renate Scheidler, Márton Tot Bagi
Published in: Lecture Notes in Computer Science, Public-Key Cryptography – PKC 2025, 2025, Page(s) 333-363
Publisher: Springer Nature Switzerland
DOI: 10.1007/978-3-031-91826-1_11

Radical $$\root N \of {\mathrm {\acute{e}lu}}$$ Isogeny Formulae

Author(s): Thomas Decru
Published in: Lecture Notes in Computer Science, Advances in Cryptology – CRYPTO 2024, Issue 14924, 2024, Page(s) 107-128, ISBN 978-3-031-68387-9
Publisher: Springer Nature Switzerland
DOI: 10.1007/978-3-031-68388-6_5

Timed Commitments and Timed Encryption: Generic Constructions and Instantiations from Isogenies

Author(s): Mingjie Chen, Jonas Meers
Published in: Lecture Notes in Computer Science, Advances in Cryptology – CRYPTO 2026, 2026, Page(s) 447-477
Publisher: Springer Nature Switzerland
DOI: 10.1007/978-3-032-35398-6_15

A Polynomial Time Attack on Instances of M-SIDH and FESTA

Author(s): Wouter Castryck, Frederik Vercauteren
Published in: Lecture Notes in Computer Science, Advances in Cryptology – ASIACRYPT 2023, Issue LNCS,volume 14444, 2023, Page(s) 127-156, ISBN 978-981-99-8738-2
Publisher: Springer Nature Singapore
DOI: 10.1007/978-981-99-8739-9_5

Generalized Class Group Actions on Oriented Elliptic Curves with Level Structure

Author(s): Sarah Arpin, Wouter Castryck, Jonathan Komada Eriksen, Gioella Lorenzon, Frederik Vercauteren
Published in: Lecture Notes in Computer Science, Arithmetic of Finite Fields, 2025, Page(s) 171-190
Publisher: Springer Nature Switzerland
DOI: 10.1007/978-3-031-81824-0_12

Orient Express: Using Frobenius to Express Oriented Isogenies

Author(s): Wouter Castryck, Riccardo Invernizzi, Gioella Lorenzon, Jonas Meers, Frederik Vercauteren
Published in: Lecture Notes in Computer Science, Progress in Cryptology – LATINCRYPT 2025, 2025, Page(s) 145-173
Publisher: Springer Nature Switzerland
DOI: 10.1007/978-3-032-06754-8_6

Lie Algebras and the Security of Cryptosystems Based on Classical Varieties in Disguise

Author(s): Wouter Castryck, Mingjie Chen, Péter Kutas, Jun Bo Lau, Alexander Lemmens, Mickaël Montessinos
Published in: Lecture Notes in Computer Science, Advances in Cryptology – EUROCRYPT 2026, 2026, Page(s) 389-419
Publisher: Springer Nature Switzerland
DOI: 10.1007/978-3-032-25327-9_14

On the Active Security of the PEARL-SCALLOP Group Action

Author(s): Tako Boris Fouotsa, Marc Houben, Gioella Lorenzon, Ryan Rueger, Parsa Tasbihgou
Published in: Lecture Notes in Computer Science, Post-Quantum Cryptography, 2026, Page(s) 74-104
Publisher: Springer Nature Switzerland
DOI: 10.1007/978-3-032-22698-3_3

PIKE: Faster Isogeny-Based Public Key Encryption with Pairing-Assisted Decryption

Author(s): Shiping Cai, Mingjie Chen, Yi-Fu Lai, Kaizhan Lin
Published in: Lecture Notes in Computer Science, Public-Key Cryptography – PKC 2026, 2026, Page(s) 58-91
Publisher: Springer Nature Switzerland
DOI: 10.1007/978-3-032-26737-5_3

Fully Homomorphic Encryption for Cyclotomic Prime Moduli

Author(s): Robin Geelen, Frederik Vercauteren
Published in: Lecture Notes in Computer Science, Advances in Cryptology – EUROCRYPT 2025, 2025, Page(s) 366-397
Publisher: Springer Nature Switzerland
DOI: 10.1007/978-3-031-91131-6_13

VSS fromDistributed ZK Proofs andApplications

Author(s): Shahla Atapoor, Karim Baghery, Daniele Cozzo, Robi Pedersen
Published in: Lecture Notes in Computer Science, Advances in Cryptology – ASIACRYPT 2023, 2024, Page(s) 405-440
Publisher: Springer Nature Singapore
DOI: 10.1007/978-981-99-8721-4_13

Towards a Quantum-Resistant Weak Verifiable Delay Function

Author(s): Thomas Decru, Luciano Maino, Antonio Sanso
Published in: Lecture Notes in Computer Science, Progress in Cryptology – LATINCRYPT 2023, 2024, Page(s) 149-168
Publisher: Springer Nature Switzerland
DOI: 10.1007/978-3-031-44469-2_8

$$\textsf{qt}$$-$$\textsf{Pegasis}$$: Simpler and Faster Effective Class Group Actions

Author(s): Pierrick Dartois, Jonathan Komada Eriksen, Riccardo Invernizzi, Frederik Vercauteren
Published in: Lecture Notes in Computer Science, Advances in Cryptology – EUROCRYPT 2026, 2026, Page(s) 636-665
Publisher: Springer Nature Switzerland
DOI: 10.1007/978-3-032-25327-9_22

SQIsign2D-East: A New Signature Scheme Using 2-Dimensional Isogenies

Author(s): Kohei Nakagawa, Hiroshi Onuki, Wouter Castryck, Mingjie Chen, Riccardo Invernizzi, Gioella Lorenzon, Frederik Vercauteren
Published in: Lecture Notes in Computer Science, Advances in Cryptology – ASIACRYPT 2024, 2024, Page(s) 272-303
Publisher: Springer Nature Singapore
DOI: 10.1007/978-981-96-0891-1_9

PEGASIS: Practical Effective Class Group Action using 4-Dimensional Isogenies

Author(s): Pierrick Dartois, Jonathan Komada Eriksen, Tako Boris Fouotsa, Arthur Herlédan Le Merdy, Riccardo Invernizzi, Damien Robert, Ryan Rueger, Frederik Vercauteren, Benjamin Wesolowski
Published in: Lecture Notes in Computer Science, Advances in Cryptology – CRYPTO 2025, 2026, Page(s) 67-99
Publisher: Springer Nature Switzerland
DOI: 10.1007/978-3-032-01855-7_3

Expander Properties of Superspecial Isogeny Digraphs with Level Structure

Author(s): Thomas Decru, Krijn Reijnders
Published in: Lecture Notes in Computer Science, Advances in Cryptology – CRYPTO 2026, 2026, Page(s) 478-505
Publisher: Springer Nature Switzerland
DOI: 10.1007/978-3-032-35398-6_16

PRISM: Simple and Compact Identification and Signatures from Large Prime Degree Isogenies

Author(s): Andrea Basso, Giacomo Borin, Wouter Castryck, Maria Corte-Real Santos, Riccardo Invernizzi, Antonin Leroux, Luciano Maino, Frederik Vercauteren, Benjamin Wesolowski
Published in: Lecture Notes in Computer Science, Public-Key Cryptography – PKC 2025, 2025, Page(s) 300-332
Publisher: Springer Nature Switzerland
DOI: 10.1007/978-3-031-91826-1_10

Error Floor Prediction with Markov Models for QC-MDPC Codes

Author(s): Sarah Arpin, Jun Bo Lau, Antoine Mesnard, Ray Perlner, Angela Robinson, Jean-Pierre Tillich, Valentin Vasseur
Published in: Lecture Notes in Computer Science, Advances in Cryptology – CRYPTO 2025, 2026, Page(s) 221-252
Publisher: Springer Nature Switzerland
DOI: 10.1007/978-3-032-01855-7_8

New Proof Systems andanOPRF fromCSIDH

Author(s): Cyprien Delpech de Saint Guilhem, Robi Pedersen
Published in: Lecture Notes in Computer Science, Public-Key Cryptography – PKC 2024, 2024, Page(s) 217-251
Publisher: Springer Nature Switzerland
DOI: 10.1007/978-3-031-57725-3_8

$$\text {KLPT}^2$$: Algebraic Pathfinding in Dimension Two and Applications

Author(s): Wouter Castryck, Thomas Decru, Péter Kutas, Abel Laval, Christophe Petit, Yan Bo Ti
Published in: Lecture Notes in Computer Science, Advances in Cryptology – CRYPTO 2025, 2026, Page(s) 167-200
Publisher: Springer Nature Switzerland
DOI: 10.1007/978-3-032-01855-7_6

Leveled Isogeny Problems with Hints

Author(s): Subham Das, Riccardo Invernizzi, Péter Kutas, Jonas Meers
Published in: Lecture Notes in Computer Science, Public-Key Cryptography – PKC 2026, 2026, Page(s) 31-57
Publisher: Springer Nature Switzerland
DOI: 10.1007/978-3-032-26737-5_2

$$\textsf{Qlapoti}$$: Simple and Efficient Translation of Quaternion Ideals to Isogenies

Author(s): Giacomo Borin, Maria Corte-Real Santos, Jonathan Komada Eriksen, Riccardo Invernizzi, Marzio Mula, Sina Schaeffler, Frederik Vercauteren
Published in: Lecture Notes in Computer Science, Advances in Cryptology – ASIACRYPT 2025, 2025, Page(s) 174-205
Publisher: Springer Nature Singapore
DOI: 10.1007/978-981-95-5113-2_6

Computing the Endomorphism Ring of a Supersingular Elliptic Curve from a Full Rank Suborder

Author(s): Mingjie Chen, Christophe Petit
Published in: Lecture Notes in Computer Science, Advances in Cryptology – EUROCRYPT 2025, 2025, Page(s) 446-474
Publisher: Springer Nature Switzerland
DOI: 10.1007/978-3-031-91095-1_16

The Tate Profile

Author(s): Krijn Reijnders
Published in: Lecture Notes in Computer Science, Progress in Cryptology – LATINCRYPT 2025, 2025, Page(s) 209-233
Publisher: Springer Nature Switzerland
DOI: 10.1007/978-3-032-06754-8_8

Peer reviewed articles (6)

Optimal s-boxes against alternative operations and linear propagation

Author(s): Marco Calderini, Roberto Civino, Riccardo Invernizzi
Published in: Discrete Mathematics, Issue 349, 2026, Page(s) 114870, ISSN 0012-365X
Publisher: Elsevier BV
DOI: 10.1016/j.disc.2025.114870

Breaking the Decisional Diffie–Hellman Problem for Class Group Actions Using Genus Theory: Extended Version

Author(s): Wouter Castryck, Jana Sotáková, Frederik Vercauteren
Published in: Journal of Cryptology, Issue 35, Article number: 24 (2022), 2022, Page(s) 1-30, ISSN 0933-2790
Publisher: Springer Verlag
DOI: 10.1007/s00145-022-09435-1

On the decisional Diffie–Hellman problem for class group actions on oriented elliptic curves

Author(s): Wouter Castryck, Marc Houben, Frederik Vercauteren, Benjamin Wesolowski
Published in: Research in Number Theory, Issue 8, Article number: 99 (2022), 2022, Page(s) 1-17, ISSN 2363-9555
Publisher: Springer
DOI: 10.1007/s40993-022-00399-6

Better GBFV Bootstrapping and Faster Encrypted Edit Distance Computation

Author(s): Robin Geelen, Frederik Vercauteren
Published in: IACR Communications in Cryptology, Issue 2, 2026, ISSN 3006-5496
Publisher: International Association for Cryptologic Research
DOI: 10.62056/a3n56chdj

Simpler and Faster Pairings from the Montgomery Ladder

Author(s): Giacomo Pope, Krijn Reijnders, Damien Robert, Alessandro Sferlazza, Benjamin Smith
Published in: IACR Communications in Cryptology, Issue 2, 2025, ISSN 3006-5496
Publisher: International Association for Cryptologic Research
DOI: 10.62056/ah2i893y6

Scrollar invariants, syzygies and representations of the symmetric group

Author(s): Wouter Castryck, Floris Vermeulen, Yongqiang Zhao
Published in: Journal für die reine und angewandte Mathematik (Crelles Journal), Issue 2023, 2023, Page(s) 117-159, ISSN 0075-4102
Publisher: Walter de Gruyter GmbH & Co. KG
DOI: 10.1515/crelle-2022-0088

Thesis and dissertations (1)

Distributed Protocols from Isogenies; Gedistribueerde Protocollen van Isogenieën

Author(s): Pedersen, Robi; Vercauteren, Fréderik (Supervisor); Orsini, Emmanuela (Co_supervisor)
Published in: 2024
Publisher: KU Leuven