Supersingular Curves You Can Trust

Generating a supersingular elliptic curve such that nobody knows its endomorphism ring is notoriously hard task, despite several isogeny-based protocols relying on an object. A trusted setup often proposed as workaround, but aspects remain unclear. In this work, we develop the tools necessary to practically run distributed trusted-setup ceremony. Our key contribution first statistically zero-knowledge proof of isogeny knowledge compatible with any base field. To prove statistical ZK, introduce graphs Borel level structure and they have Ramanujan property. Then, analyze security protocol based our ZK in simplified universal composability framework. Lastly, optimized implementation proof, propose strategy concretely deploy protocol.