评估用于安全长期安全存储的DV/CV-QKD架构：一种风险模型和基于整数线性规划的成本优化方法
Evaluating DV/CV-QKD Architectures for SAFE Long-Term Secure Storage: A Risk Model and ILP-Based Cost Optimization Approach
AI总结：
研究用于安全长期存储的DV/CV-QKD架构，提出结合定量风险模型与ILP的统一成本建模和优化框架，通过纳入现实因素及SAA管道，在随机和现实网络上评估，揭示链路容量与成本非单调关系及最优架构依赖场景等特性。
AI中文摘要：
本文提出了一个统一的成本建模和优化框架，用于评估在安全高效长期存储（LTSS）协议内运行的混合离散变量/连续变量量子密钥分发（DV/CV-QKD）基础设施。我们的方法通过将定量风险模型与随机整数线性规划（ILP）公式相结合，共同解决了多十年时间范围内密码耐久性的信息理论和计算维度问题。该框架超越了理想化的物理信息限制，纳入了现实的下一代工业实现和复用共存规范，以及样本平均近似（SAA）管道，以确定在传输预算和安全约束下成本最优且结构可行的安全拓扑。在随机合成部署和现实的大都市规模QKD基础设施（包括巴黎地铁规模和大巴黎网络）上对所提出的框架进行了评估，以表征网络拓扑、QKD模式和部署成本之间的相互作用，同时强制执行目标全局妥协容忍度$\epsilon$。数值结果表明，经济上最优的架构高度依赖于场景，并且混合和同质模式分配自然地从优化中出现。更重要的是，分析揭示了所需的最小QKD链路容量与基础设施成本之间的非单调关系：与直觉相反，增加每条链路所需的最小密钥率可能会通过使全局向更经济的基于CV的解决方案过渡来降低总体部署成本，而进一步增加容量不一定会带来额外的节省。
英文摘要：
This paper presents a unified cost-modeling and optimization framework designed to evaluate hybrid discrete-variable/continuous-variable quantum key distribution (DV/CV-QKD) infrastructures operating within the SAFE (Secure and Efficient) long-term storage (LTSS) protocol. Our methodology jointly addresses the information-theoretic and computational dimensions of cryptographic durability over multi-decade horizons by coupling a quantitative risk model with a stochastic integer linear programming (ILP) formulation. Going beyond idealized physics-informed limits, the framework incorporates realistic next-generation industrial implementations and multiplexed coexistence specifications, together with a sample-average approximation (SAA) pipeline, to determine cost-optimal and structurally feasible SAFE topologies under transmission-budget and security constraints. The proposed framework is evaluated on both randomized synthetic deployments and realistic metropolitan-scale QKD infrastructures, including the Paris Metro-Scale and Greater Paris networks, to characterize the interplay between network topology, QKD modality, and deployment cost while enforcing a target global compromise tolerance $ε$. Numerical results show that the economically optimal architecture is highly scenario-dependent and that both hybrid and homogeneous modality allocations naturally emerge from the optimization. More importantly, the analysis reveals a non-monotonic relationship between the minimum required QKD link capacity and the infrastructure cost: contrary to intuition, increasing the minimum required per-link secret-key rate may reduce the overall deployment cost by enabling a global transition toward more economical CV-based solutions, whereas further capacity increases do not necessarily yield additional savings.
