CIF: Small: Key Dissemination over Networks

共享的随机性资源，即共享密钥，在网络通信系统的理论和实践中起着基础性的作用。统一分布的密钥在某些网络用户之间共享，有时对其他用户隐藏，在各种通信任务（如安全通信、私有通信、分布式计算、统计推断、分布式学习等）中作为中心资源出现。鉴于共享随机性在对现代技术至关重要的应用程序中的核心作用，设计支持网络上密钥分发的高效高速通信方案具有重要意义。传统的密钥分发方案将密钥视为源生成的消息，因此不一定受益于密钥分发任务所固有的某些灵活性。该项目承担了开发适合密钥传播任务的通信方案的挑战，因此该项目提出了有望影响资源受限网络系统中共享随机性分布的新技术。传统的通信研究解决了消息从其产生源到其预期目的地的传输问题，可用于（安全地）建立共享密钥。然而，这种方法在共享随机密钥的上下文中是次优的，因为分发密钥只需要共享随机性的分布；分发密钥不需要重建源信息。消除源重构的要求为通信过程提供了灵活性，与需要源重构的传统通信形式相比，这可能会增加密钥率。本项目通过网络编码的方法，启动了复杂多源多终端网络背景下的密钥传播研究，并寻求无噪声和有噪声网络拓扑的综合理论。通过放弃传统的通信要求重构源，而只关注重构共同随机性，该研究有望产生优于传统方案的高效、高速率通信策略，从而推进密钥传播领域的发展。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

The resource of shared randomness, i.e., shared keys, plays a fundamental role in the theory and practice of network communication systems. A uniformly distributed key, shared among some network users and, at times, hidden from others, appears as a central resource in a variety of communication tasks such as secure communication, private communication, distributed computing, statistical inference, distributed learning, and more. Given the central role of shared randomness in applications critical to modern technology, there is significant importance in the design of efficient high-rate communication schemes that support key dissemination over networks. Traditional schemes for key distribution treat keys as source-generated messages and as such do not necessarily benefit from certain flexibilities that are inherent to the task of key dissemination. This project takes up the challenge of developing communication schemes tailor-made to fit the task of key dissemination, and as such the project suggests novel technology expected to impact the distribution of shared randomness in resource-constrained network systems. Traditional studies of communication, which address the transfer of messages from their source of generation to their intended destination, may be used to (securely) establish shared keys. However, such a methodology is suboptimal in the context of shared random keys, since distributing keys requires only the distribution of shared randomness; distributing keys does not require the reconstruction of source information. Removing the requirement of source reconstruction grants a flexibility to the communication process which gives rise to the potential of increased key-rates when compared to traditional forms of communication that require source reconstruction. This project initiates the study of key dissemination in the context of complex multi-source multi-terminal networks through the methodology of network coding, and seeks a comprehensive theory for both noiseless and noisy network topologies. By foregoing the traditional communication requirement to reconstruct sources and focusing instead only on reconstructing common randomness, the research is expected to yield efficient, high-rate communication strategies, that outperform traditional schemes, thereby advancing the area of key dissemination.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.