An improved quantum payment protocol based on group signature without entanglement

Abstract

With the popularization of E-payment, more and more electronic payment protocols have been proposed. In 2021, Lin et al. proposed a trusted third-party E-Payment protocol based on a set of three-particle local indistinguishable orthogonal product (X-LIOP) states. In this paper, we first point out that there is a security flaw where the merchant can forge the purchase goods information to sell something that the customer does not want to buy in Lin et al. protocol. Besides, the X-LIOP states used by Lin are not orthogonal and can be discriminated by Local Operation and Classical Communication (LOCC). Second, we propose a new electronic payment protocol that combines group signature and the three-particle X-LIOP states. Compared with Lin et al. protocol, customers can purchase goods anonymously in our protocol and the unforgeability of messages and signatures is guaranteed.