Threshold Ring Signature Scheme from Cryptographic Group Actions

A t-out-of-N threshold ring signature, which is extended from ring signature scheme, allow t users jointly sign a message on the behalf of a ring of N users, selected in an arbitrary way, while keeping their identities anonymous. This thesis presents a threshold ring signature construction using cryptographic group action, based on the OR proof of group action and the idea of creating a threshold ring signature scheme from a ring signature scheme. We also instantiate the proposed protocol in both isogeny and lattice settings, using the GAIP and MLWE problems, respectively. Our isogeny-based construction provides a smaller signature size than the existing threshold ring signature scheme (e.g. 65 KB signatures compared to 187 KB for the same ring size).