Security Boundaries of Quantum Key Reuse: A Quantitative Evaluation Method for QKD Key Rotation Interval and Security Benefits Combined with Block Ciphers

Abstract: With the rapid development of quantum computing, classical cryptography systems are facing increasing security threats, making it urgent to build architectures resilient to quantum attacks. Although Quantum Key Distribution (QKD) technology provides information-theoretic security, its limited bandwidth requires it to be combined with classical cryptography-particularly block ciphers such as AES and SM4-in practical deployments.However, when a single key is used to process multiple multi-block files, the resulting reduction in security strength has not yet been systematically quantified.In this work, we focus on the use of both QKD keys and block ciphers, and construct a precise calculation model for the key rotation interval. We further propose a quantitative method to evaluate the security benefit of using QKD keys for block cipher. Building on concrete security models and the security properties of various block cipher modes (CTR, CBC, and ECBC-MAC), we derive the maximum number of files that can be safely encrypted under a single key, denoted Q*, and quantify the benefits of key rotation interval in enhancing security levels. Using SM4 as a case study, our results show that, under an 80-bit security target, uniformly performing k key rotations can increase the security strength by log2(k) to 2log2(k) bits. This study provides theoretical support and a basis for parameter optimization for the integrated application of QKD keys with classical cryptographic algorithms and the engineering deployment of cryptographic systems.