Supersingular Curves You Can Trust
WESOLOWSKI, Benjamin
Centre National de la Recherche Scientifique [CNRS]
Unité de Mathématiques Pures et Appliquées [UMPA-ENSL]
Lithe and fast algorithmic number theory [LFANT]
Analyse cryptographique et arithmétique [CANARI]
< Reduce
Centre National de la Recherche Scientifique [CNRS]
Unité de Mathématiques Pures et Appliquées [UMPA-ENSL]
Lithe and fast algorithmic number theory [LFANT]
Analyse cryptographique et arithmétique [CANARI]
Language
en
Communication dans un congrès
This item was published in
Eurocrypt 2023, 2023-04-23, Lyon.
English Abstract
Generating a supersingular elliptic curve such that nobody knows its endomorphism ring is a notoriously hard task, despite several isogeny-based protocols relying on such an object. A trusted setup is often proposed as a ...Read more >
Generating a supersingular elliptic curve such that nobody knows its endomorphism ring is a notoriously hard task, despite several isogeny-based protocols relying on such an object. A trusted setup is often proposed as a workaround, but several aspects remain unclear. In this work, we develop the tools necessary to practically run such a distributed trusted-setup ceremony. Our key contribution is the first statistically zero-knowledge proof of isogeny knowledge that is compatible with any base field. To prove statistical ZK, we introduce isogeny graphs with Borel level structure and prove they have the Ramanujan property. Then, we analyze the security of a distributed trusted-setup protocol based on our ZK proof in the simplified universal composability framework. Lastly, we develop an optimized implementation of the ZK proof, and we propose a strategy to concretely deploy the trusted-setup protocol.Read less <
English Keywords
Isogenies
Ramanujan Graphs
Zero-knowledge Proofs
Trusted Setup
ANR Project
Méthodes pour les variétés abéliennes de petite dimension - ANR-20-CE40-0013
Post-quantum padlock for web browser - ANR-22-PETQ-0008
Post-quantum padlock for web browser - ANR-22-PETQ-0008
Origin
Hal imported