Group Signatures and Accountable Ring Signatures from Isogeny-based Assumptions

Group signatures are an important cryptographic primitive providing both anonymity and accountability to signatures. Accountable ring signatures (ARS) combine features from ring signatures (RS) and group signatures (GS), and can be directly transformed into either of both. While there exist extensive works on constructing GS from various post-quantum assumptions, there has not been any research using isogeny-based assumptions. In this work, we propose the first isogeny-based GS, which is a direct result of our isogeny-based ARS. Our schemes are based on the decisional CSIDH assumption (D-CSIDH) and are proven secure under the quantum random oracle model (QROM). This work is also the first post-quantum ARS and GS that are proven QROM-secure.