Semi-Quantum Money

Private quantum money allows a bank to mint quantum money states that it can later verify, but that no one else can forge. In classically verifiable quantum money - introduced by Gavinsky (CCC 2012) - the verification is done via an interactive protocol between the bank and the user, where the communication is classical, and the computational resources required of the bank are classical. In this work, we consider memoryless interactive protocols in which the minting is likewise classical, and construct a private money scheme that achieves these two notions simultaneously (i.e., classical verification and classical minting). We call such a construction a private semi-quantum money scheme, since all the requirements from the bank in terms of computation and communication are classical. In terms of techniques, our main contribution is a strong parallel repetition theorem for Noisy Trapdoor Claw Free Functions (NTCF), a notion introduced by Brakerski et al. (FOCS 2018).