Secure Multiparty Logical AND Based on Quantum Homomorphic Encryption and Its Applications

Secure multiparty computation is crucial in ensuring effective protection of participant’s privacy. Quantum homomorphic encryption technology is an effective method to facilitate the realization of quantum secure multiparty computation. The logical AND operation is a basic primitive of logical computation, often combined with the NOT operation to perform more complex logical operations. In the field of quantum computing, the Toffoli gate (composed of Clifford gate and T gate) required to implement the logical AND operation has relatively high requirements for the number and computational depth of T gates. This paper proposes a secure multiparty logical AND protocol that effectively reduces the usage and depth of T gates. Compared with previous quantum homomorphic encryption schemes, this protocol improves security based on quantum one time pad encryption and quantum teleportation, and can effectively resist various external and internal security threats including tampering attacks. The introduced quantum state commitment and auxiliary bit mechanism provides support for verifying the correctness of the calculation results. Subsequently, two important applications are derived: quantum multiparty private set intersection and quantum secure multiparty sum algorithm. Tests performed on the IBM Qiskit quantum simulator show the expected effectiveness of our method. The secure multiparty logical AND algorithm proposed in this paper is expected to be widely used in other secure multiparty computation scenarios.