Damien Robert

Damien Robert

@damienrobert.bsky.social

Researcher in algorithmic number theory, notably on abelian varieties and their moduli spaces, and their applications to elliptic and isogeny based cryptography

310 followers181 following252 posts

Damien Robert reposted

Gro-Tsen
@gro-tsen.bsky.social

English translation of an email I sent to a student worried about the future of mathematics: ⬇️ (French original is in the quoted post)

Gro-Tsen@gro-tsen.bsky.social

Réponse que je viens de faire à un étudiant qui s'inquiète de ce que deviennent les maths: ⬇️

Damien Robert
@damienrobert.bsky.social

See also this mail: groups.google.com/a/list.nist.... And this older bluesky thread: bsky.app/profile/dami...

groups.google.comMIKE (Module Isogeny Key Exchange): a fast and compact post-quantum NIKE
Damien Robert@damienrobert.bsky.social

It's been a while since I last posted about MIKE, but a lot of exciting stuff happened meanwhile. MIKE is described in more details in this 4 part thread: - CSIDH bsky.app/profile/dami... - SIDH bsky.app/profile/dami... - MIKE bsky.app/profile/dami... - Speculations: bsky.app/profile/dami...

Damien Robert reposted

Gro-Tsen
@gro-tsen.bsky.social

“Dear mathematician, can you explain to me what mass is?” “Very simple, dear: the mass of a dynamical system is the cohomology class of the Galilean group representing lack of equivariance of the moment map on the symplectic manifold that is the phase space of the system.”

Damien Robert reposted

pianocktailiste
@pianocktailiste.bsky.social

Les scientifiques et ingénieurs, en particulier les mathématiciens : font un effort énorme, mondial, sur plusieurs générations, visant à automatiser la pensée. La pensée : commence à être automatisée. Les scientifiques et ingénieurs, en particulier les mathématiciens :

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Damien Robert
@damienrobert.bsky.social

We won the prize for best song at Eurocrypt's 2026 Rump Session! (Well my colleagues won it, I was not there...). Unfortunately the rump session videos do not seem to be available yet.

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Damien Robert
@damienrobert.bsky.social

We have modular invariants! The MIKE key exchange gives a dimension four abelian fourfold. Alice and Bob ends up with isomorphic abelian varieties. But for key agreement, they need to extract a common shared information.

Damien Robert
@damienrobert.bsky.social

In dimension 1, this is typically done via the $j$-invariant. But we don't really have good modular invariants in dimension 4 (this is a hard problem). Thankfully for MIKE, we land in a special subvariety of the moduli space, on which we managed to build specific modular invariants.

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Damien Robert
@damienrobert.bsky.social

We have a security proof! MIKE's security relies on the (module version of the) CDH problem. We have a proof that, in the (HD version of) the Algebraic Isogeny Model (introduced here: eprint.iacr.org/2026/032), the CDH problem is equivalent to the supersingular endomorphism ring problem.

eprint.iacr.orgThe Algebraic Isogeny Model: A General Model with Applications to SQIsign and Key ExchangesWe introduce the Algebraic Isogeny Model (AIM): an algebraic model, akin to the Algebraic Group Model in the group setting, for isogenies and supersingular elliptic curves. This model is significantly...
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Damien Robert
@damienrobert.bsky.social

*Provable security:* We prove MIKE's security (in the algebraic isogeny model) as a passively-secure NIKE or a KEM assuming only the supersingular endomorphism ring problem (the core assumption in isogeny-based cryptography).

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Damien Robert
@damienrobert.bsky.social

*Fast key exchange:* For NIST Level 1, our Rust implementation requires <1 ms for key generation and <5 ms for the full key exchange (benchmarked on an AMD Ryzen 7 PRO 7840U @ 3.3GHz).

Damien Robert reposted

Gro-Tsen
@gro-tsen.bsky.social

A long thread about variants of Kőnig's lemma in relation to computability theory, because this caused me a lot of headaches yesterday and today, so maybe this will clarify things for other people. 🧵⤵️ •1/32

Damien Robert reposted

Gro-Tsen
@gro-tsen.bsky.social

I posted a question of MathOverflow asking whether the line of research that sought to relate higher-order computability with computability on large countable ordinals died out post 1980, and if so, why. (I give several examples of such results.) mathoverflow.net/q/512688/17064

mathoverflow.netRelating higher-order computability and computably large countable ordinalsIn the period going roughly from the late 1960's to early 1980's, a number of results appeared in computability that have roughly the following flavor, relating higher-order computability with

Damien Robert reposted

Gro-Tsen
@gro-tsen.bsky.social

Replying to @johncarlosbaez.bsky.social

“How can we construct a non-Borel set explicitly?” is a fascinating question by @arula-ratnakar.bsky.social, and in fact we can do this by a diagonal argument that is deeply analogous to how we construct a noncomputable subset of ℕ, but sadly nowhere written clearly AFAICT.🧵⤵️ •1/17

Damien Robert reposted

Andrea Basso
@andreavbasso.bsky.social

New paper out 🎉 We introduce a new UPKE based on FESTA that supports unbounded updates and whose security is equivalent to FESTA! Our main result: a (four-dimensional) variant of FESTA has uniformly random public keys, which means that any random walk is a valid pk update.

ePrint Updates@eprint.ing.bot

Updatable Public-Key Encryption from FESTA (Andrea Basso, Tako Boris Fouotsa, Fatna Kouider, Péter Kutas, Luciano Maino, Laurane Marco) ia.cr/2026/1014

Damien Robert reposted

Gro-Tsen
@gro-tsen.bsky.social

Replying to @gro-tsen.bsky.social

Despite this proof, I don't have much intuition about what this (or Scott's formula) really “means”. But it certainly shows that there are important differences between these two models of computability in higher types. See also this previous thread: 🔽

Gro-Tsen@gro-tsen.bsky.social

So there ensued an informal discussion of the intuitive content and differences between the (Hyland) effective topos, the Kleene-Vesley topos, and Mulry's recursive topos, and what each one is good for. The sort of remarks you won't find in books. [See also: mathoverflow.net/q/495788/17064 ]

mathoverflow.netRegarding the realizability topos on the computable part of Kleene's second algebraLet: $\mathcal{K}_1$ be the first Kleene algebra, meaning $\mathbb{N}$ endowed with the partial operation $(p,n) \mapsto p\bullet n := \varphi_p(n)$ where $\varphi$ is the $p$-th partial computable

Damien Robert reposted

Gro-Tsen
@gro-tsen.bsky.social

I'm beginning to feel more and more that the meaning of the ‘∞’ in “∞-categories” is that you can only explain what an ∞-category is to someone who already knows what an ∞-category is.

Damien Robert reposted

Gro-Tsen
@gro-tsen.bsky.social

🔽 So, @jeanas.bsky.social and I are please to announce a new preprint in computability, in which we show that the Turing degrees can be embedded upside down in (what we call) the “Arthur-Nimue-Merlin degrees”. The paper opens with a riddle, which I hope will be of interest!

arXiv math.LO Logic@mathlo-bot.bsky.social

Jean Abou Samra, David Alexander Madore: An order-reversing embedding of Turing degrees into Arthur-Nimue-Merlin degrees https://arxiv.org/abs/2603.19946 https://arxiv.org/pdf/2603.19946 https://arxiv.org/html/2603.19946

Damien Robert reposted

Luca De Feo
@bsky.defeo.lu

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.ioMaGIC 2026 - Marche Workshop on Group Actions in CryptographyA 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...

Damien Robert reposted

Krijn Reijnders
@krijn.isogeni.es

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!

ePrint Updates@eprint.ing.bot

Expander properties of superspecial isogeny digraphs with level structure (Thomas Decru, Krijn Reijnders) ia.cr/2026/500

Damien Robert reposted

Luca De Feo
@bsky.defeo.lu

TL;DR: - SQIsign more general than initially thought. - More space for protocol design! - SQIsign NIST v2 still the best signature, by a small margin. Ilinca already foreshadowed some of this in www.youtube.com/watch?v=5tGb..., though that's a different POV we're still writing up.

ePrint Updates@eprint.ing.bot

The SQInstructor: a guide to SQIsign and the Deuring Correspondence with level structures (Giacomo Borin, Luca De Feo, Guido Maria Lido, Sina Schaeffler) ia.cr/2026/493

Damien Robert reposted

Andrea Basso
@andreavbasso.bsky.social

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.ioMaGIC 2026 - Marche Workshop on Group Actions in CryptographyA 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...