Threshold Ring Signature Scheme from Cryptographic Group Action

A threshold ring signature (t-out-of-N) is an extension of ring signatures that allow t users jointly sign a message on the behalf of N users, selected in an arbitrary manner, while keeping their identities anonymous. This paper presents a construction of threshold ring signature from 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 instantiate the proposed protocols in both isogeny and lattice settings. The signature size of our isogeny-based construction is smaller than the existing threshold ring signature scheme (e.g. 65 KB signatures compared to 187 KB for the same ring size).