Threshold ring signature: generic construction and logarithmic size instantiation

A ring signature is a variant of normal digital signature and protects the privacy of a specific signer in the sense that a ring signature can be verified, but the signer’s identity can only be traced to a limited set. The concept was further enhanced to threshold setting to distribute signing ability among several signers. Since threshold ring signature was introduced, it was a hard problem whether one can have efficient constructions for it. In this paper, we introduce a new generic construction of threshold ring signature, named GTRS, based on canonical identification of a specific form. Our signature consists of a polynomial (represented by \(n - t + 1\) coefficients) and a single response, resulting in significantly shorter threshold ring signatures. Instantiating the generic construction with specific DL-based components, e.g. Schnorr identification and a novel vector argument of knowledge developed in this paper, we obtain GTRS-EC, which is shorter than all existing threshold ring signatures without any trusted setup.