Jonathan Komada Eriksen
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jonathan.isogeny.club
Jonathan Komada Eriksen
@jonathan.isogeny.club
70 followers 30 following 8 posts
Post-doc at COSIC, probably more known for dubious limericks than research.
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jonathan.isogeny.club
TL;DR: See title 🥳
eprint.ing.bot ePrint Updates @eprint.ing.bot · Oct 8
qt-Pegasis: Simpler and Faster Effective Class Group Actions (Pierrick Dartois, Jonathan Komada Eriksen, Riccardo Invernizzi, Frederik Vercauteren) ia.cr/2025/1859
Abstract. In this paper, we revisit the recent PEGASIS algorithm that computes an effective group action of the class group of any imaginary quadratic order R on a set of supersingular elliptic curves primitively oriented by R. Although PEGASIS was the first algorithm showing the practicality of computing unrestricted class group actions at higher security levels, it is complicated and prone to failures, which leads to many rerandomizations. In this work, we present a new algorithm, qt-Pegasis, which is much simpler, but at the same time faster and removes the need for rerandomization of the ideal we want to act with, since it never fails. It leverages the main technique of the recent qlapoti approach. However, qlapoti solves a norm equation in a quaternion algebra, which corresponds to the full endomorphism ring of a supersingular elliptic curve. We show that the algorithm still applies in the quadratic setting, by embedding the quadratic ideal into a quaternion ideal using a technique similar to the one applied in KLaPoTi. This way, we can reinterpret the output of qlapoti as four equivalent quadratic ideals, instead of two equivalent quaternion ideals. We then show how to construct a Clapoti-like diagram in dimension 2, which embeds the action of the ideal in a 4-dimensional isogeny. We implemented our qt-Pegasis algorithm in SageMath for the CSURF group action, and we achieve a speedup over PEGASIS of 1.8× for the 500-bit parameters and 2.6× for the 4000-bit parameters. Image showing part 2 of abstract.
October 8, 2025 at 8:17 AM
Reposted by Jonathan Komada Eriksen
eprint.ing.bot
Olingo: Threshold Lattice Signatures with DKG and Identifiable Abort (Kamil Doruk Gur, Patrick Hough, Jonathan Katz, Caroline Sandsbråten, Tjerand Silde) ia.cr/2025/1789
Abstract. We present Olingo, a framework for threshold lattice signatures that is the first to offer all desired properties for real-world implementations of quantum-secure threshold signatures: small keys and signatures, low communication and round complexity, non-interactive online signing, distributed key generation (DKG), and identifiable abort. Our starting point is the framework of Gur, Katz, and Silde (PQCrypto 2024). We change the underlying signature scheme to Raccoon (Katsumata et al., Crypto 2024), remove the trapdoor commitments, and apply numerous improvements and optimizations to achieve all the above properties. We provide detailed proofs of security for our new framework and present concrete parameters and benchmarks. At the 128-bit security level, for up to 1024 parties and supporting 2⁶⁰ signatures, our scheme has 2.6 KB public keys and 9.7 KB signatures; while signing requires communication of 953 KB per party. Using the LaBRADOR proof system (Beullens and Seiler, Crypto 2023), this can be further reduced to 596 KB. An optimistic non-interactive version of our scheme requires only 83 KB communication per party. Image showing part 2 of abstract.
October 3, 2025 at 7:25 AM
Reposted by Jonathan Komada Eriksen
maria.isogeny.club
For those who missed it, the recording is live! www.youtube.com/watch?v=lvhh...
The Isogeny Club #7.1 Large smooth twins from short lattice vectors
YouTube video by The Isogeny Club
www.youtube.com
September 25, 2025 at 12:06 PM
Reposted by Jonathan Komada Eriksen
damienrobert.bsky.social
And you solve the failure rate problem, which was a big source of trouble in the previous implementation. And the new algorithm is simpler to implement!

So very exciting result! (Although I had been spoiled already by @jonathan.isogeny.club talk at Bordeaux in May :))
September 15, 2025 at 7:48 AM
Reposted by Jonathan Komada Eriksen
krijn.isogeni.es
Announcing The Isogeny Problems!

A curated list of the seven foremost unsolved problems in isogeny-based cryptography. Solving one of these profound questions would mark a monumental advance, and as a resolver you'd get eternal honor and epic rewards!

Full list: isogeni.es/problems
The Isogeny Problems
isogeni.es
September 15, 2025 at 7:43 AM
jonathan.isogeny.club
... The paper might have been out for less than 24 hours, but that is clearly plenty for yx7 to implement a more computer-algebra friendly implementation that works for any "nice" order! 🥳🥳

github.com/yyyyx4/qlapo...
September 12, 2025 at 2:58 PM
Reposted by Jonathan Komada Eriksen
maria.isogeny.club
TL;DR: we solve norm equations in a better way and get around a 2x improvement to IdealToIsogeny routines crucial in both SQIsign and PRISM.
eprint.ing.bot ePrint Updates @eprint.ing.bot · Sep 11
Qlapoti: Simple and Efficient Translation of Quaternion Ideals to Isogenies (Giacomo Borin, Maria Corte-Real Santos, Jonathan Komada Eriksen, Riccardo Invernizzi, Marzio Mula, Sina Schaeffler, Frederik Vercauteren) ia.cr/2025/1604
Abstract. The main building block in isogeny-based cryptography is an algorithmic version of the Deuring correspondence, called IdealToIsogeny. This algorithm takes as input left ideals of the endomorphism ring of a supersingular elliptic curve and computes the associated isogeny. Building on ideas from QFESTA, the Clapoti framework by Page and Robert reduces this problem to solving a certain norm equation. The current state of the art is however unable to efficiently solve this equation, and resorts to a relaxed version of it instead. This impacts not only the efficiency of the IdealToIsogeny procedure, but also its success probability. The latter issue has to be mitigated with complex and memory-heavy rerandomization procedures, but still leaves a gap between the security analysis and the actual implementation of cryptographic schemes employing IdealToIsogeny as a subroutine. For instance, in SQIsign the failure probability is still 2⁻⁶⁰ which is not cryptographically negligible. The main contribution of this paper is a very simple and efficient algorithm called Qlapoti which approaches the norm equation from Clapoti directly, solving all the aforementioned problems at once. First, it makes the IdealToIsogeny subroutine between 2.2 and 2.6 times faster. This signigicantly improves the speed of schemes using this subroutine, including notably SQIsign and . On top of that, Qlapoti has a cryptographically negligible failure probability. This eliminates the need for rerandomization, drastically reducing memory consumption, and allows for cleaner security reductions. Image showing part 2 of abstract.
September 12, 2025 at 2:00 PM
Reposted by Jonathan Komada Eriksen
eprint.ing.bot
Qlapoti: Simple and Efficient Translation of Quaternion Ideals to Isogenies (Giacomo Borin, Maria Corte-Real Santos, Jonathan Komada Eriksen, Riccardo Invernizzi, Marzio Mula, Sina Schaeffler, Frederik Vercauteren) ia.cr/2025/1604
Abstract. The main building block in isogeny-based cryptography is an algorithmic version of the Deuring correspondence, called IdealToIsogeny. This algorithm takes as input left ideals of the endomorphism ring of a supersingular elliptic curve and computes the associated isogeny. Building on ideas from QFESTA, the Clapoti framework by Page and Robert reduces this problem to solving a certain norm equation. The current state of the art is however unable to efficiently solve this equation, and resorts to a relaxed version of it instead. This impacts not only the efficiency of the IdealToIsogeny procedure, but also its success probability. The latter issue has to be mitigated with complex and memory-heavy rerandomization procedures, but still leaves a gap between the security analysis and the actual implementation of cryptographic schemes employing IdealToIsogeny as a subroutine. For instance, in SQIsign the failure probability is still 2⁻⁶⁰ which is not cryptographically negligible. The main contribution of this paper is a very simple and efficient algorithm called Qlapoti which approaches the norm equation from Clapoti directly, solving all the aforementioned problems at once. First, it makes the IdealToIsogeny subroutine between 2.2 and 2.6 times faster. This signigicantly improves the speed of schemes using this subroutine, including notably SQIsign and . On top of that, Qlapoti has a cryptographically negligible failure probability. This eliminates the need for rerandomization, drastically reducing memory consumption, and allows for cleaner security reductions. Image showing part 2 of abstract.
September 11, 2025 at 4:14 PM
Reposted by Jonathan Komada Eriksen
tjesi.bsky.social
The EU Parliament has published a new proposal for Chat Control to mass-surveil all digital communication in Europe. The proposal is ineffective, weakens secure communication, and violates basic human privacy. This must be stopped immediately. #ChatControl
csa-scientist-open-letter.org/Sep2025
csa-scientist-open-letter.org
September 9, 2025 at 11:11 AM
Reposted by Jonathan Komada Eriksen
krijn.isogeni.es
Perhaps @jonathan.isogeny.club really really hates embedded devices?
September 3, 2025 at 5:39 PM
Reposted by Jonathan Komada Eriksen
kennyog.bsky.social
Some impressions of Longyearbyen from the last few days.
July 8, 2025 at 5:27 PM
Reposted by Jonathan Komada Eriksen
krijn.isogeni.es
9 out of 10 dentists recommend solving log(p) KLPT

(from @jonathan.isogeny.club's talk at ARCTICCRYPT 2025!)
July 7, 2025 at 3:19 PM
Reposted by Jonathan Komada Eriksen
eprint.ing.bot
Evaluation of Modular Polynomials from Supersingular Elliptic Curves (Maria Corte-Real Santos, Jonathan Komada Eriksen, Antonin Leroux, Michael Meyer, Lorenz Panny) ia.cr/2025/1154
Abstract. We present several new algorithms to evaluate modular polynomials of level ℓ modulo a prime p on an input j. More precisely, we introduce two new generic algorithms, sharing the following similarities: they are based on a CRT approach; they make use of supersingular curves and the Deuring correspondence; and, their memory requirements are optimal. The first algorithm combines the ideas behind a hybrid algorithm of Sutherland in 2013 with a recent algorithm to compute modular polynomials using supersingular curves introduced in 2023 by Leroux. The complexity (holding around several plausible heuristic assumptions) of the resulting algorithm matches the O(ℓ³log³ℓ+ℓlogp) time complexity of the best known algorithm by Sutherland, but has an optimal memory requirement. Our second algorithm is based on a sub-algorithm that can evaluate modular polynomials efficiently on supersingular j-invariants defined over 𝔽_(p), and achieves heuristic complexity quadratic in both ℓ and log j, and linear in log p. In particular, it is the first generic algorithm with optimal memory requirement to obtain a quadratic complexity in~ℓ. Additionally, we show how to adapt our method to the computation of other types of modular polynomials such as the one stemming from Weber’s function. Finally, we provide an optimised implementation of the two algorithms detailed in this paper, though we emphasise that various modules in our codebase may find applications outside their use in this paper. Image showing part 2 of abstract.
June 20, 2025 at 8:55 PM
Reposted by Jonathan Komada Eriksen
cosic.bsky.social
Registration for the Leuven Isogeny Days 6 is now open!
📅 10–12 Sept 2025 @ KU Leuven
Morning: research talks
Afternoon: brainstorming sessions
More info: www.esat.kuleuven.be/cosic/projec...
#isogeny #isocrypt #erc #postquantum
June 16, 2025 at 6:17 AM
Reposted by Jonathan Komada Eriksen
andreavbasso.bsky.social
We (finally) published all the material from this course on SQIsign, including lecture slides and exercise sheets for the Sage laboratory. Available here: github.com/andreavico/S...
June 10, 2025 at 3:58 PM
Reposted by Jonathan Komada Eriksen
We are hosting the Information Security Conference (ISC) 2025 at Sungkyunkwan University! ISC is a long-standing security conference with a 28-year history

Prof. Hyungjoon Kevin Koo and Hojoon Lee will jointly serve as General Chairs this year.

CFP: isc25.skku.edu/call-for-pap...
ISC 2025: Information Security Conference
The 28th edition of ISC will be organized by Sungkyunkwan University. The conference will be held in-person at the 600 Years Anniversary Hall, Sungkyunkwan University (Humanities & Social Sciences Campus). The proceedings of ISC 2025 will be published as a separate LNCS volume by Springer.
isc25.skku.edu
May 12, 2025 at 8:41 AM
Reposted by Jonathan Komada Eriksen
krijn.isogeni.es
tl;dr: dr. ✅

Very happy to share that I successfully defended my thesis "Isogenies & Isometries" yesterday! A thrilling experience, would recommend, 10/10
May 13, 2025 at 5:36 PM
Reposted by Jonathan Komada Eriksen
cosic.bsky.social
🥇The paper "PRISM: Simple And Compact Identification and Signatures From Large Prime Degree Isogenies", co-authored by COSIC, has won the best paper award at @IACR_News #PKC 2025 in Røros, Norway. #pkc2025
Link: link.springer.com/chapter/10.1...
May 12, 2025 at 9:14 AM
jonathan.isogeny.club
April 25, 2025 at 10:29 PM
jonathan.isogeny.club
As a surprise for everyone attending, we will even have a mystery guest joining us as well, who you don't want to miss! In fact, we have already started the train journey from Leuven!

Curious about the mystery guest? Well, what are you waiting for, sign up and find out next weekend!
April 24, 2025 at 5:04 PM
Reposted by Jonathan Komada Eriksen
maria.isogeny.club
Good news is that we're still accepting brainstorm topics!! If you have a brainstorm idea, send us a short description by email !
April 23, 2025 at 11:00 AM
Reposted by Jonathan Komada Eriksen
krijn.isogeni.es
New work: we explain cubical arithmetic in simple terms to show you how easy it is to compute pairings. Essentially, you only need to know the Montgomery ladder!

As a bonus, pairings from cubical arithmetic are faster than those from Miller's loop for applications in isogeny-based cryptography.
eprint.ing.bot ePrint Updates @eprint.ing.bot · Apr 15
Simpler and Faster Pairings from the Montgomery Ladder (Giacomo Pope, Krijn Reijnders, Damien Robert, Alessandro Sferlazza, Benjamin Smith) ia.cr/2025/672
Abstract. We show that Montgomery ladders compute pairings as a by-product, and explain how a small adjustment to the ladder results in simple and efficient algorithms for the Weil and Tate pairing on elliptic curves using cubical arithmetic. We demonstrate the efficiency of the resulting cubical pairings in several applications from isogeny-based cryptography. Cubical pairings are simpler and more performant than pairings computed using Miller’s algorithm: we get a speed-up of over 40% for use-cases in SQIsign, and a speed-up of about 7% for use-cases in CSIDH. While these results arise from a deep connection to biextensions and cubical arithmetic, in this article we keep things as concrete (and digestible) as possible. We provide a concise and complete introduction to cubical arithmetic as an appendix.
April 15, 2025 at 12:34 PM
Reposted by Jonathan Komada Eriksen
tjesi.bsky.social
IACR Public Key Cryptography 2025 registration is open! Please check out pkc.iacr.org/2025/registr... to attend the conference in Røros, Norway from May 12 to 15 🤩 @bordekock.bsky.social , @tiborj.bsky.social
PKC 2025 registration
The International Conference on Practice and Theory in Public Key Cryptography
pkc.iacr.org
March 25, 2025 at 12:33 PM
Reposted by Jonathan Komada Eriksen
bsky.defeo.lu
Fancy some isogeny crypto?

Join us for a 3-day workshop on isogeny-based cryptography in Lleida, Catalonia, April 28-30

www.cig.udl.cat/icrypto2025_...

Brought to you by ULleida's Cryptography+Graphs group, the SQIsign team and friends!

Registration and program coming soon
Registration is free!
Cathedral of La Seu Vella in Lleida
March 13, 2025 at 5:30 PM
jonathan.isogeny.club
GG everyone who played #KalmarCTF 2025!

Writeups for my two challs:

MonoDOOM: jonathke.github.io/monoDOOM
A chal based on a sick sidechannel attack by @damienrobert.bsky.social !

Not-so-complex multiplication: jonathke.github.io/not-so-complex
An easy chal based on complex multiplication.
Jonathan Komada Eriksen - Notes
jonathke.github.io
March 9, 2025 at 5:24 PM