"Preview Talk" (by Team PQarrots) @ MPTS 2026, in reply to the NIST Threshold Call
Abstract: Cryptographic group actions offer a flexible framework for instantiating plausibly post-quantum schemes, effectively generalizing core ideas behind classical discrete logarithm cryptography. In particular, the group structure allows for an (almost) immediate application of well-known threshold secret sharing techniques, to obtain distributed post-quantum cryptographic protocols such as digital signatures and public key encryption. These schemes can also be augmented with a distributed key generation procedure. In this presentation we give an overview of our package submission based on isogeny group actions. We explain advantages and limitations of group actions in general and of isogenies in particular. We also discuss the security of the underlying assumptions, with a focus on quantum attacks against group actions, and on the appropriate security models for group actions.
Joint work: PQarrots: Isogenies-TGA, Marius A. Årdal, Shahla Atapoor, Karim Baghery, Andrea Basso, Xavier Bonnetain, Giacomo Borin, Daniele Cozzo, Pierrick Dartois, Luca De Feo, Max Duparc, Jonathan K. Eriksen, Tako Boris Fouotsa, Arthur Herlédan Le Merdy, Riccardo Invernizzi, Samuel Jaques, Yi-Fu Lai, Dania Lazzarini, Jason T. LeGrow, Chloe Martindale, Luciano Maino, Jonas Meers, Michael Meyer, Sikhar Patranabis, Robi Pedersen, Giacomo Pope, Doreen Riepel, Damien Robert, Ryan Rueger, Sina Schaeffler, André Schrottenloher, Frederik Vercauteren.
[Slides] Suggested readings:
- Preview Writeup: PQarrots: Macaw, Kea and Kakapo: Threshold primitives from (isogeny-based) group actions
- Threshold Schemes from Isogeny Assumptions (ia.cr/2019/1288)
