This paper considers two challenges faced by practical quantum networks: the bootstrapping of seedless Quantum Random Number Generators (QRNGs) and the resilient combination of Post-Quantum Cryptography (PQC) and Quantum Key Distribution (QKD) keys. These issues are addressed using universal hash functions as strong seeded extractors, with security foundations provided by the Quantum Leftover Hash Lemma (QLHL). First, the 'randomness loop' in QRNGs -- the requirement of an initial random seed to generate further randomness -- is resolved by proposing a bootstrapping method using raw data from two independent sources of entropy, given by seedless QRNG sources. Second, it is argued that strong seeded extractors are an alternative to XOR-based key combining that presents different characteristics. Unlike XORing, our method ensures that if the combined output and one initial key are compromised, the remaining key material retains quantifiable min-entropy and remains secure in exchange of longer keys. Furthermore, the proposed method allows to bind transcript information with key material in a natural way, providing a tool to replace computationally based combiners to extend ITS security of the initial key material to the final combined output. By modeling PQC keys as having HILL (Hastad, Impagliazzo, Levin and Luby) entropy, the framework is extended to hybrid PQC-QKD systems. This unified approach provides a mathematically rigorous and future-proof mechanism for both randomness generation and secure key management against quantum adversaries.

翻译：本文探讨了实用量子网络面临的两大挑战：无种子量子随机数生成器（QRNG）的引导启动问题，以及后量子密码（PQC）与量子密钥分发（QKD）密钥的弹性组合问题。针对上述问题，本文采用通用哈希函数作为强种子提取器进行解决，其安全性基础由量子剩余哈希引理（QLHL）提供。首先，针对QRNG中的"随机性循环"——即生成更多随机性需要初始随机种子的问题——我们提出了一种引导方法，该方法利用两个独立熵源（由无种子QRNG源提供）的原始数据。其次，本文论证了强种子提取器可作为基于异或（XOR）的密钥组合方案的替代方案，且具有不同特性。与异或操作不同，我们的方法确保：若组合输出和初始密钥之一被攻破，剩余密钥材料仍保有可量化的最小熵，并在增加密钥长度的前提下保持安全性。此外，所提方法能以自然方式将会话信息与密钥材料绑定，从而提供一种替代基于计算的组合器的工具，将初始密钥材料的信息论安全性（ITS）扩展至最终组合输出。通过将PQC密钥建模为具有HILL（Hastad、Impagliazzo、Levin与Luby）熵，该方法框架进一步扩展至混合PQC-QKD系统。这一统一方案为随机数生成及针对量子敌手的密钥安全管理提供了数学上严谨且面向未来的机制。