International Association
for Cryptologic Research

At Eurocrypt 2022, Tang et al proposed a practical digital signature scheme in the context of post-quantum cryptography. The construction of that scheme is based on the assumed hardness of the alternating trilinear form equivalence problem (ATFE), the Goldreich-Micali-Widgerson (GMW) zero-knowledge protocol for graph isomorphism, and the Fiat-Shamir (FS) transformation. We refer to that scheme as the ATFE-GMW-FS scheme. The security of the ATFE-GMW-FS scheme was only proved in the random oracle model (ROM), and its security in the quantum random oracle model (QROM) was left as an open problem.

In this paper, we study the ATFE-GMW-FS scheme from two perspectives, namely the QROM security and (linkable) ring signature schemes. First, we provide two approaches of proving its QROM security, based on the perfect unique response property and lossy identification schemes, respectively. Second, we design (linkable) ring signatures based on the ATFE-GMW-FS scheme, inspired by a recent result of Beullens, Katsumata and Pintore (Asiacrypt 20) on isogeny-based cryptography.