Thèse Signatures à Seuil Post-Quantiques H/F - Doctorat.Gouv.Fr

Établissement : Institut Polytechnique de Paris Télécom Paris École doctorale : Ecole Doctorale de l'Institut Polytechnique de Paris Laboratoire de recherche : Laboratoire de Traitement et Communication de l'Information Direction de la thèse : Matthieu RAMBAUD ORCID 0009000330426504 Début de la thèse : 2026-10-01 Date limite de candidature : 2026-10-01T23:59:59 ``Threshold cryptography'' are algorithms magically enabling a number $n$ of distrustful participants to collectively evaluate some function over all their secret inputs, without disclosing their inputs to each other (see left picture).
They deliver an output as soon as a threshold number $t+1
The most known ones are called \emph{\bfseries threshold signatures} \cite{usenixmldsa}.
They enable $n$ machines to produce a single signature on behalf of a client, such that any colluding $t$ machines are unable to create a signature which was not queried by the client.
Threshold signatures are used by Coinbase (32Bn\$ market cap) to manage the crypto-wallets of more than 5M clients \cite{coinbasewallet}, by Fireblocks (8Bn\$ market cap) \cite{fireblocksrefresh}, and by their French competitor Dfns in collaboration with Matthieu Rambaud.
%Threshold signatures enable to solve the trilemma of a client needing to quickly sign transactions, but at the same time not leaking its secret signing-key to the adversary nor having its key erased by accident (if it was stored only on a single machine).
These deployments are part of the market of digital asset custody, which was worth over 600 Billion dollars in 2024 and is expected to skyrocket in the coming years \cite{digitalasset}.
A more advanced example is \emph{\bfseries threshold fully homomorphic encryption (trFHE)}, of which a flagship application is to enable a group of distrustful nodes to validate confidential transactions on the blockchain without seeing their amounts (e.g. JP Morgan + the French startup Zama \cite{zamafhevm}, and the concurrent system of Circle \cite{circle}).\paragraph{Various possible goals (the details are confidential).}
The default goal is to join an ongoing collaboration with Dfns towards submitting a new or improved threshold signature to the NIST competition \cite{pqtnist}.

An alternative goal would to scale post-quantum threshold signatures, i.e., enable more participants.
Indeed, the only public threshold signature which enjoys a small standard size ('ML-DSA') \cite{usenixmldsa} operates for at most 6 participants.
This would continue an ongoing M2 internship.

A possible alternative contribution which would be interesting in itself, would be to design a post-quantum \emph{distributed key generation (DKG)} \cite{finally,borin}.
DKG is indeed the algorithm which sets-up the participants in their initial state, where each of them holds a share of the secret signing key.
This would continue an ongoing research collaboration. cf sujet

mathématics or cryptography, and a bit programming