Cloud-based Semi-Quantum Money

TL;DR

The paper tackles the practicality of quantum money by introducing Cloud-based Semi-Quantum Money (CSQM), which replaces fully quantum minting and verification with classical banks and users that outsource quantum tasks to an untrusted cloud via quantum fully homomorphic encryption. The approach leverages a two-phase QFHE framework and indistinguishability obfuscation to enable secure minting, verification, signing, and transactions entirely with classical entities while preserving quantum-state security. A formal CSQM protocol is presented, including a 4-qubit demonstration, an information-theoretic security analysis, and a concrete assessment of quantum-resource requirements. The work indicates that CSQM can significantly reduce the quantum hardware burden, offering a feasible near-term path for quantum-money-like capabilities through cloud-based quantum computation and strong cryptographic protections. These contributions could enable practical quantum-finance applications that maintain strong unforgeability while leveraging centralized classical infrastructure and outsourced quantum services.

Abstract

In the 1970s, Wiesner introduced the concept of quantum money, where quantum states generated according to specific rules function as currency. These states circulate among users with quantum resources through quantum channels or face-to-face interactions. Quantum mechanics grants quantum money physical-level unforgeability but also makes minting, storing, and circulating it significantly challenging. Currently, quantum computers capable of minting and preserving quantum money have not yet emerged, and existing quantum channels are not stable enough to support the efficient transmission of quantum states for quantum money, limiting its practicality. Semi-quantum money schemes support fully classical transactions and complete classical banks, reducing dependence on quantum resources and enhancing feasibility. To further minimize the system's reliance on quantum resources, we propose a cloud-based semi-quantum money (CSQM) scheme. This scheme relies only on semi-honest third-party quantum clouds, while the rest of the system remains entirely classical. We also discuss estimating the computational power required by the quantum cloud for the scheme and conduct a security analysis.

Figures (6)

• Figure 1: Top: the quantum circuit of encrypted CNOT gate defined in mahadev2020classical. Lower left: the abstract form of the encrypted CNOT operation. Lower right: the simplest form of the encrypted CNOT operation, which will be used in other diagrams.
• Figure 2: Left: the quantum circuit of the QFHE Tofolli operation. Right: the abstract form of QFHE Tofolli operation.
• Figure 3: Quantum Token Process.
• Figure 4: Mint Circuit of a Quantum Token Unit
• Figure 5: Demonstration of a 4-Qubit Quantum Token Unit