Security improvement for a novel semiquantum key distribution protocol with Bell states

Abstract

Abstract Semiquantum key distribution (SQKD) facilitates the establishment of secure keys even when one user (designated as the classical user) is constrained to performing quantum state preparation and measurement only within a fixed computational basis. From a resource-theoretic perspective, this approach presents both novelty and theoretical significance. Recently, a novel SQKD protocol based on Bell states, where the classical user’s REFLECT operations directly contribute to the generation of the final shared key was proposed [ Laser Physics Letters , 21 (9):095201, 2024]. However, our analysis reveals that this protocol is vulnerable to double CNOT attacks, posing security risks. To address this, we propose an improved SQKD protocol that maintains resistance to double CNOT attacks while preserving the classical user’s REFLECT operations as a functional component for key generation. Notably, we rigorously prove the unconditional security of the improved protocol and derive a maximum allowable error rate of 8.92% in depolarizing channels. This work serves two purposes: (1) it alerts SQKD protocol designers to the identified security vulnerability, and (2) it provides a foundational reference for establishing unconditional security proofs in SQKD protocols where REFLECT operations contribute to key generation.