Isogeny-based Group Signatures and Accountable Ring Signatures in QROM

Abstract

We provide the first isogeny-based group signature (GS) and accountable ring signature (ARS) that are provably secure in the quantum random oracle model (QROM). We do so by building an intermediate primitive called openable sigma protocol and show that every such protocol gives rise to a secure ARS and GS. Additionally, the QROM security is guaranteed if the perfect unique-response property is satisfied. Our design, with the underlying protocol satisfying this essential unique-response property, is sophisticatedly crafted for QROM security. From there, with clever twists to available proving techniques, we obtain the first isogeny-based ARS and GS that are proven QROM-secure. Concurrently, an efficient construction was proposed by Beullens et al. (Eurocrypt 2022), but is only proven secure in the classical random oracle model (ROM). Our proposal seeks stronger QROM security, although it is less efficient due to the signature size quadratically scaling with the ring/group size