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Krijn Reijnders

@krijn.isogeni.es
165 followers 100 following 66 posts

Post-doc in post-quantum cryptography. Mostly isogenies nowadays. See krijnreijnders.com

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Krijn Reijnders @krijn.isogeni.es · 30/09/2026
New paper! Given a Jacobian over Fp, can you easily check supersingularity? If you've worked with these objects in magma, you know how annoying this question can be. Turns out it's very easy: we give efficient probabilistic tests, and conclusive if you need to be absolutely sure. ia.cr/2026/2259
eprint.iacr.org
Supersingularity and Superspeciality Verification of Abelian Surfaces
Supersingular abelian surfaces are essential in isogeny-based cryptography. Despite this, we have no efficient algorithm to verify if a given abelian surface is supersingular. In this work, we initiat...
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Maria Corte-Real Santos @maria.isogeny.club · 23/09/2026
On 29 September, Benjamin Wesolowski will give a talk at The Isogeny Club on his recent p^{1/3+o(1)} attack on the isogeny problem! See you all there 🥳 isogeny.club
isogeny.club
The Isogeny Club
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spooky Deirdre Connolly¹ ² at a distance @durumcrustulum.com · 27/08/2026
About that Classic McEliece distinguisher, we may have a new key recovery attack: eprint.iacr.org/2026/1630 (updated)
eprint.iacr.org
Quasipolynomial Cryptanalysis of the McEliece Cryptosystem (or: PIR Meets McEliece)
The McEliece code-based cryptosystem, utilizing binary Goppa codes, is the earliest public-key encryption scheme that is still considered post-quantum secure. We present a simple, classical quasipolyn...
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Krijn Reijnders @krijn.isogeni.es · 06/08/2026
Update to isogeni.es Now includes isogeny papers from arXiv! You'll never have to visit either ePrint or arXiv anymore 😊
isogeni.es
isogeny-based cryptography
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ePrint Updates @eprint.ing.bot · 23/07/2026
The supersingular isogeny problem in time and memory p^(1/3 + o(1)) (Benjamin Wesolowski) ia.cr/2026/1486
Abstract. We prove that under a plausible heuristic assumption (on the smoothness of certain random integers), the supersingular isogeny problem can be solved in time and memory p^(1/3 + o(1)). This improves upon the previous best complexity of p^(1/2) ⋅ (log p)^(O(1)). This problem is arguably the central hard problem underlying isogeny-based cryptography, and the cost of its resolution is a major (and often the only) factor in the choice of secure parameters. The impact on concrete parameter sets remains to be clarified, as the asymptotic advantage of the new algorithm is mitigated by a superpolynomial overhead hiding in the o(1) exponent, and by its high memory requirement.
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COSIC @cosic.bsky.social · 22/07/2026
We’re excited to announce the 7th edition of the Leuven Isogeny Days (Sept 16–18, 2026)! Registration is now open, join us! More info & signup: esat.kuleuven.be/cosic/projec... #LID #Isogeny #IsogenyDays
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ePrint Updates @eprint.ing.bot · 16/07/2026
The Isogeny Problems (Wouter Castryck, Luca De Feo, Steven D. Galbraith, Péter Kutas, Krijn Reijnders, Benjamin Wesolowski) ia.cr/2026/1431
Abstract. This work contains an exposition of the seven foremost unsolved problems in the domain of isogeny-based cryptography, obtained by asking eleven experts in isogeny-based cryptography what they considered to be the most important unsolved problems in isogeny-based cryptography, and curated down to the seven problems in this document. For each problem, an expert wrote a short write-up giving the precise statements and descriptions per problem.
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Krijn Reijnders @krijn.isogeni.es · 16/07/2026
Excited about isogenies? Wanna claim some rewards? Solve one of the seven Isogeny Problems, the hardest open problems in isogeny-based cryptography! Full write-up now on ePrint: ia.cr/2026/1431 Webpage: isogeni.es/problems Now with EVEN MORE REWARDS!!
isogeni.es
The Isogeny Problems
A list of foremost unsolved problems in isogeny-based cryptography, with expositions by leading experts.
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Krijn Reijnders @krijn.isogeni.es · 16/07/2026
Excited to share that I've been awarded a Veni grant from the NWO! This grant allows me the freedom to explore research of my own choosing, and to achieve faster, better, and simpler post-quantum cryptography using deep mathematical insight. More info: www.ru.nl/en/about-us/...
ru.nl
Veni grants for eight Radboud researchers | Radboud University
The Dutch Research Council (NWO) has awarded a Veni grant to eight young researchers of the Radboud University and Radboudumc.
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Paolo Santini @palli-santini.bsky.social · 15/07/2026
📢 Upcoming online seminar organized by the "UMI Crittografia e Codici" Group 🗣️ Giuseppe D'Alconzo (Telsy S.p.A.) 📅 July 22, 3:00 PM (CEST) Title: Invariants and Group Actions: An Algebraic Attack Framework for Isomorphism Problems More information on 👉 sites.google.com/view/crittog...
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Jonathan Komada Eriksen @jonathan.isogeny.club · 29/06/2026
TL;DR: The main idea is that given an p.p.a.v. A and an endomorphism 𝛼 of polarized degree d > 1, the points of A that are "eventually fixed by 𝛼" share similarities to an ab. var. over a finite field (both are naturally Zhat-modules), and thus Bruin's formula for the Tate-pairing generalizes 🥳
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ePrint Updates @eprint.ing.bot · 08/06/2026
A computational framework for principally polarized abelian varieties and applications (Maria Corte-Real Santos, Etienne Piasecki, Benjamin Wesolowski) ia.cr/2026/1142
Abstract. We construct a new framework for cryptographers to work with principally polarized abelian varieties (PPAVs). This framework offers a computational approach to abelian varieties agnostic to the choice of a coordinate system, culminating in the definition of an efficient model for principally polarised abelian varieties. We exhibit an instantiation of our framework by means of the theta model, thereby streamlining the documented capacities of the model, and extending them with new fundamental algorithms, like the computation of automorphism groups. Our framework focuses on what can be done with these objects, computationally, while relegating low-level considerations to the background, like the specific choice of a coordinate system (and thus the necessity to rely on Mumford’s theory of theta coordinates). We illustrate the utility of our framework by proving that we can interpolate polarised isogenies in any dimension, generalizing to higher dimensions the most disruptive algorithm for elliptic curves in recent years. We prove that this interpolation offers a universal, canonical, and compact way to represent isogenies.
Image showing part 2 of abstract.
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Andrea Basso @andreavbasso.bsky.social · 14/05/2026
Round 3 of the NIST additional signatures process announced! 🎉 And SQIsign is part of it!! ⛷️⛷️
Screenshot of email announcement saying:

Nine Candidates Advance to the Third Round of the Additional Digital Signatures for the PQC Standardization Process

 After 18 months of evaluation, NIST has selected nine candidates for the third round of the Additional Digital Signatures for the Post-Quantum Cryptography (PQC) Standardization Process. The advancing digital signature algorithms are:

FAEST
HAWK
MAYO
MQOM
QR-UOV
SDitH
SNOVA
SQIsign
UOV
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Krijn Reijnders @krijn.isogeni.es · 22/04/2026
Even though its not actually post-quantum crypto, I would never pass on a cool application of the Tate pairing: Much faster subgroup membership testing! (the credits go to the rest of the team, though, who write amazingly fast code!!)
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Luca De Feo @bsky.defeo.lu · 12/04/2026
Looking forward to AM-PQC 2026, the Workshop on Algebraic Methods in Post-Quantum Cryptography this August in Macedonia! pqcrypto.cs.ru.nl/ampqc/ Stipends for students are available. Apply before May 4th!
pqcrypto.cs.ru.nl
Workshop on Algebraic Methods in Post-Quantum Cryptography 2026
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COSIC @cosic.bsky.social · 07/04/2026
Pierre Pébereau just joined COSIC as a postdoc in Fre Vercauteren's team: "I chose COSIC to work with excellent researchers on the analysis of post-quantum signature algorithms." #choosecosic
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spooky Deirdre Connolly¹ ² at a distance @durumcrustulum.com · 02/04/2026
from @bwesterb.bsky.social: bas.westerbaan.name/notes/2026/0...
bas.westerbaan.name
Factoring is not a good benchmark to track Q-day
Homepage of dr. Bas Westerbaan, principal research engineer at Cloudflare, working on making the Internet post-quantum secure
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Krijn Reijnders @krijn.isogeni.es · 02/04/2026
I should add to this: winner of best paper award at Eurocrypt 2026!! As a single author. During his PhD. Incredible achievement!(protip: he will graduate soon-ish 👀)
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mccurley.bsky.social @mccurley.bsky.social · 31/03/2026
In honor of April Fool's Day (which has already started in Australia), I offer you debrisprint.iacr.org for AI-generated cryptology content.
debrisprint.iacr.org
Craptology debrisPrint Snarkive
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Jonathan Komada Eriksen @jonathan.isogeny.club · 30/03/2026
Writeup of the crypto-challenge MonoDOOM ETERNAL from #KalmarCTF - A follow up from last-years MonoDOOM challenge, this time with botched side-channel protection! jonathke.github.io/monoDOOM-ETE...
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Luca De Feo @bsky.defeo.lu · 16/03/2026
We still have a few spots left at MaGIC! Registration closes this week... Hurry up if you want to be on top of all the latest news on Cryptographic Group Actions! magic-workshop.github.io
magic-workshop.github.io
MaGIC 2026 - Marche Workshop on Group Actions in Cryptography
A workshop dedicated to the study of cryptographic group actions, a rapidly evolving area at the intersection of algebraic geometry, number theory, and post-quantum cryptography. The workshop will bri...
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Krijn Reijnders @krijn.isogeni.es · 13/03/2026
Thomas and I looked at directed isogeny graphs! In dim 1, we often ignore directedness, as there are only 2 "problematic" curves. Not so in dim 2: we analyze the action of automorphisms on level structures and the resulting directed graphs. Crucial: Directed (2,2)-graphs looks Ramanujan after all!
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Maria Corte-Real Santos @maria.isogeny.club · 06/03/2026
The second variant (salt-PRISM) is implemented in C. We find that signing is between 1.4 and 1.6 times faster than SQIsign, whereas verification is between 1.2 times slower to 1.01 times faster. Notably, for Level V, salt-PRISM is faster than SQIsign in both. github.com/mariascrs/PR...
github.com
GitHub - mariascrs/PRISM_v2: A C implementation of PRISM v2 (the salted variant).
A C implementation of PRISM v2 (the salted variant). - mariascrs/PRISM_v2
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ePrint Updates @eprint.ing.bot · 07/03/2026
The principal ideal problem for endomorphism rings of superspecial abelian varieties (Wouter Castryck, Jonathan Komada Eriksen, Riccardo Invernizzi, Frederik Vercauteren) ia.cr/2026/454
Abstract. We describe a Las Vegas algorithm for the principal ideal problem in matrix rings M_(g)(O) for g ≥ 2, over maximal orders O in the rational quaternion algebra B_(p, ∞) ramified at ∞ and a prime number p. Under plausible heuristic assumptions, the method has expected polynomial runtime. An implementation in SageMath shows that it runs very efficiently in practice, with compact output. Our main auxiliary result is a method for finding endomorphisms of superspecial abelian varieties (i.e., powers of supersingular elliptic curves) with a prescribed kernel.
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ePrint Updates @eprint.ing.bot · 05/03/2026
PRISM with a pinch of salt: Simple, Efficient and Strongly Unforgeable Signatures from Isogenies (Andrea Basso, Giacomo Borin, Wouter Castryck, Maria Corte-Real Santos, Riccardo Invernizzi, Antonin Leroux, Luciano Maino, Frederik Vercauteren, Benjamin Wesolowski) ia.cr/2026/443
Abstract. The problem of computing an isogeny of large prime degree from a supersingular elliptic curve of unknown endomorphism ring is assumed to be hard both for classical as well as quantum computers. In this work, we first build a two-round identification protocol whose security reduces to this problem. The challenge consists of a random large prime q and the prover simply replies with an efficient representation of an isogeny of degree q from its public key. Using the hash-and-sign paradigm, we then derive a signature scheme with a very simple and flexible signing procedure and prove its security in the standard model. The most efficient variant of our signature schemes features a signing which is 1.4× to 1.6× faster than the most recent implementaion of SQIsign, whereas verification ranges from 1.2× slower to 1.01× faster depending on the security level. The sizes of public key and signature are comparable to existing schemes.
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Andrea Basso @andreavbasso.bsky.social · 02/03/2026
We're organizing a workshop on cryptographic group actions bringing together the isogeny and code communities. The workshop is just before Eurocrypt, a quick train away from Rome in the beautiful Marche. Early registration ends this week, so grab your spot soon! magic-workshop.github.io
magic-workshop.github.io
MaGIC 2026 - Marche Workshop on Group Actions in Cryptography
A workshop dedicated to the study of cryptographic group actions, a rapidly evolving area at the intersection of algebraic geometry, number theory, and post-quantum cryptography. The workshop will bri...
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ePrint Updates @eprint.ing.bot · 21/02/2026
Breaking digital signatures from tropical matrix semirings (Alessandro Sferlazza) ia.cr/2026/327
Abstract. In a recent preprint, Grigoriev, Monico, and Shpilrain proposed a digital signature protocol based on the use of matrices over the tropical integer semiring. We show some design flaws of the proposed scheme, together with an efficient attack to forge signatures for an arbitrary message, and a key-recovery attack when given access to a list of honest signatures.
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ePrint Updates @eprint.ing.bot · 23/02/2026
Tripling on Hessian curves via isogeny decomposition (Thomas Decru, Sabrina Kunzweiler) ia.cr/2026/334
Abstract. We provide a new interpretation of the arithmetic on Hessian Kummer lines using level-3 theta structures. This allows us to break the record for tripling on elliptic curves and their Kummer lines, requiring only 4 multiplications and 4 squarings per tripling for well-chosen curve parameters.
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Paolo Santini @palli-santini.bsky.social · 16/02/2026
📢📢📢 𝐌𝐚𝐆𝐈𝐂 𝟐𝟎𝟐𝟔 𝐌𝐚𝐫𝐜𝐡𝐞 𝐖𝐨𝐫𝐤𝐬𝐡𝐨𝐩 𝐨𝐧 𝐆𝐫𝐨𝐮𝐩 𝐀𝐜𝐭𝐢𝐨𝐧𝐬 𝐢𝐧 𝐂𝐫𝐲𝐩𝐭𝐨𝐠𝐫𝐚𝐩𝐡𝐲 In May 5-8, let's all gather together to speak about Group Actions! Early registration until March 8! Organized with Marco Baldi, @bsky.defeo.lu, @giacomoborin.bsky.social, @andreavbasso.bsky.social magic-workshop.github.io
magic-workshop.github.io
MaGIC 2026 - Marche Workshop on Group Actions in Cryptography
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Paris Marx @parismarx.com · 18/07/2025
Silicon Valley’s alliance with Donald Trump was a mask off moment and showed the world we can’t depend on US tech companies. For the past few months, I’ve been trying to get off US tech and I put together a guide so you find alternatives too. I hope you find it helpful!
disconnect.blog
Getting off US tech: a guide
I’m in the process of dropping US tech services. Here’s how I did it, and options you should consider.
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Krijn Reijnders @krijn.isogeni.es · 03/01/2026
New year, new pairing
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COSIC @cosic.bsky.social · 22/12/2025
🎄 Happy holidays from all of us in the COSIC research group! Proof that science is better with friends.
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Krijn Reijnders @krijn.isogeni.es · 19/12/2025
Dear publishers, this may come as a shock to you, but in general, I do not want to download a tiny .bib file for every reference. I simply want to copy-paste.
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Maria Corte-Real Santos @maria.isogeny.club · 13/11/2025
Catch up on last weeks Isogeny Club talk! We welcomed Eli Orvis who taught us about abstract isogeny graphs: www.youtube.com/watch?v=Gzcc...
youtube.com
The Isogeny Club #7.4 Ihara zeta functions of abstract isogeny graphs and modular curves
YouTube video by The Isogeny Club
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COSIC @cosic.bsky.social · 03/11/2025
Great news: the paper "Integral cryptanalysis in characteristic $p$" by our researchers Tim Beyne & Michiel Verbauwhede will receive the Best Theory and Early Career Award at #Asiacrypt 2025! asiacrypt.iacr.org/2025/program...
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Maria Corte-Real Santos @maria.isogeny.club · 14/10/2025
Last week at The Isogeny Club we had a great talk by Sebastian Spindler about modular curves! Check it out here: www.youtube.com/watch?v=EDU7... Be sure to join us again next Tuesday at the usual time :) isogeny.club
youtube.com
The Isogeny Club #7.2 Counting l-isogenies with different modular polynomials
YouTube video by The Isogeny Club
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Maria Corte-Real Santos @maria.isogeny.club · 23/09/2025
The Isogeny Club Season 7 starts today! At 5pm CEST, Bruno Sterner will talk about finding large smooth twins from short lattice vectors. More details at isogeny.club
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Diego F. Aranha @dfaranha.bsky.social · 18/09/2025
The impact of Alfred Menezes in cryptography is profound. Francisco RH and I are organizing an afternoon session in Latincrypt to celebrate Alfred's career: menezesfest.info If you're coming to Medellín, consider attending!
menezesfest.info
MenezesFest 2025
MenezesFest brings together researchers, colleagues, and friends to celebrate the career and impact of Alfred Menezes.
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Krijn Reijnders @krijn.isogeni.es · 15/09/2025
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
isogeni.es
The Isogeny Problems
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ePrint Updates @eprint.ing.bot · 11/09/2025
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.
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COSIC @cosic.bsky.social · 12/09/2025
"Industry perspectives on implementation and deployment" by Bas Westerbaan (Cloudfare) today at the PQCSA Workshop on Tackling the Quantum Threat in Athens. #PQCSA #PQC #postquantum #eudigital
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COSIC @cosic.bsky.social · 26/08/2025
🔐 You're invited! Join us on 18 Nov 2025 in Leuven (Belgium) for the #IEEE Milestone Award Ceremony, honoring #Rijndael, the Belgian cipher selected as #AES, protecting billions worldwide. Register (free) by 25 Oct: rijndael-ieeemilestone.cs.ru.nl/index #CyberSecurity #Cryptography
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COSIC @cosic.bsky.social · 21/08/2025
Proud moment at #CRYPTO 2025! “KLPT²: Algebraic Pathfinding in Dimension Two and Applications” received the Best Paper Award. 🏆 Co-authored by COSIC’s Wouter Castryck & Thomas Decru (presenter). Read it here: eprint.iacr.org/2025/372
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COSIC @cosic.bsky.social · 08/07/2025
"Simpler and Faster Pairings from the Montgomery Ladder" by Giacomo Pope, Krijn Reijnders (COSIC), Damien Robert, Alessandro Sferlazza & Benjamin Smith published in IACR Communications in Cryptology and online now: cic.iacr.org/p/2/2/29 #ISOCRYPT #ISOCRYPTproject
cic.iacr.org
Simpler and Faster Pairings from the Montgomery Ladder
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Krijn Reijnders @krijn.isogeni.es · 07/07/2025
9 out of 10 dentists recommend solving log(p) KLPT (from @jonathan.isogeny.club's talk at ARCTICCRYPT 2025!)
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Krijn Reijnders @krijn.isogeni.es · 03/07/2025
Should let people know that this exists and was exactly what I was missing in the last 5 years: github.com/martisak/vsc... Simply directly searches dblp from VS Code and copy-pastes the bib-entry into the bib file
github.com
GitHub - martisak/vscode-getref: Visual Code Studio interface to dblp.
Visual Code Studio interface to dblp. Contribute to martisak/vscode-getref development by creating an account on GitHub.
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Sam Jaques @sejaques.bsky.social · 19/06/2025
An out-of-schedule update to my quantum landscape chart: sam-jaques.appspot.com/quantum_land..., prompted by @craiggidney.bsky.social 's new paper: arxiv.org/abs/2505.15917. A startling jump (20x) in how easy quantum factoring can be! Also: much improved web design!
A chart for quantum computers, of number of qubits versus error rate, on a logarithmic scale. Broadly it shows a large gap between current quantum computers in the bottom left, and a curve in the top right of the resources they need to break RSA.
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Krijn Reijnders @krijn.isogeni.es · 19/06/2025
Single author, fifteen pages, reduces the bit complexity of millenia-old UOV instances!!
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ePrint Updates @eprint.ing.bot · 19/06/2025
Wedges, oil, and vinegar – An analysis of UOV in characteristic 2 (Lars Ran) ia.cr/2025/1143
Abstract. The Unbalanced Oil and Vinegar construction (UOV) has been the backbone of multivariate cryptography since the fall of HFE-based schemes. In fact, 7 UOV-based schemes have been submitted to the NIST additional call for signatures, and 4 of these made it to the second round. For efficiency considerations, most of these schemes are defined over a field of characteristic 2. This has as a side effect that the polar forms of the UOV public maps are not only symmetric, but also alternating.

In this work, we propose a new key-recovery attack on UOV in characteristic 2 that makes use of this property. We consider the polar forms of the UOV public maps as elements of the exterior algebra. We show that these are contained in a certain subspace of the second exterior power that is dependent on the oil space. This allows us to define relations between the polar forms and the image of the dual of the oil space under the Plücker embedding. With this, we can recover the secret oil space using sparse linear algebra.

This new attack has an improved complexity over previous methods and reduces the security by 4, 11, and 20 bits for uov-Ip, uov-III, and uov-V, respectively. Furthermore, the attack is applicable to MAYO₂ and improves on the best attack by 28 bits.
Image showing part 2 of abstract.
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Krijn Reijnders @krijn.isogeni.es · 16/06/2025
Yessss!!!
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