Public-key Quantum money with a classical bank

Quantum money is a main primitive in quantum cryptography, that enables a bank to distribute to parties in the network, called wallets, unclonable quantum banknotes that serve as a medium of exchange between wallets. While quantum money suggests a theoretical solution to some of the fundamental problems in currency systems, it still requires a strong model to be implemented; quantum computation and a quantum communication infrastructure. A central open question in this context is whether we can have a quantum money scheme that uses "minimal quantumness", namely, local quantum computation and only classical communication. Public-key semi-quantum money (Radian and Sattath, AFT 2019) is a quantum money scheme where the algorithm of the bank is completely classical, and quantum banknotes are publicly verifiable on any quantum computer. In particular, such scheme relies on local quantum computation and only classical communication. The only known construction of public-key semi-quantum is based on quantum lightning (Zhandry, EUROCRYPT 2019), which is based on a computational assumption that is now known to be broken. In this work, we construct public-key semi-quantum money, based on quantum-secure indistinguishability obfuscation and the sub-exponential hardness of the Learning With Errors problem. The technical centerpiece of our construction is a new 3-message protocol, where a classical computer can delegate to a quantum computer the generation of a quantum state that is both, unclonable and publicly verifiable.