This paper presents an enhanced post-quantum key agreement protocol based on Rényi entropy, addressing vulnerabilities in the original construction while preserving information-theoretic security properties. We develop a theoretical framework leveraging entropy-preserving operations and secret-shared verification to achieve provable security against quantum adversaries. Through entropy amplification techniques and quantum-resistant commitments, the protocol establishes $2^{128}$ quantum security guarantees under the quantum random oracle model. Key innovations include a confidentiality-preserving verification mechanism using distributed polynomial commitments, tightened min-entropy bounds with guaranteed non-negativity, and composable security proofs in the quantum universal composability framework. Unlike computational approaches, our method provides information-theoretic security without hardness assumptions while maintaining polynomial complexity. Theoretical analysis demonstrates resilience against known quantum attack vectors, including Grover-accelerated brute force and quantum memory attacks. The protocol achieves parameterization for 128-bit quantum security with efficient $\mathcal{O}(n^{2})$ communication complexity. Extensions to secure multiparty computation and quantum network applications are established, providing a foundation for long-term cryptographic security.

翻译：本文提出一种基于Rényi熵的增强型后量子密钥协商协议，在保持信息论安全特性的同时解决了原始构造中的脆弱性问题。我们开发了一个理论框架，利用熵保持操作和秘密共享验证来实现对量子对手的可证明安全性。通过熵放大技术和抗量子承诺方案，该协议在量子随机预言机模型下建立了$2^{128}$量级量子安全保证。关键创新包括：采用分布式多项式承诺的保密验证机制、具有保证非负性的紧缩化最小熵边界，以及量子通用可组合框架下的可组合安全性证明。与计算方法不同，我们的方案在保持多项式复杂度的同时，无需依赖硬度假设即可提供信息论安全性。理论分析表明该协议能抵御已知量子攻击向量，包括Grover加速暴力破解和量子存储攻击。该协议实现了128位量子安全的参数化配置，并具有$\mathcal{O}(n^{2})$的高效通信复杂度。研究进一步建立了向安全多方计算和量子网络应用的扩展，为长期密码安全提供了理论基础。