CAREER: Fundamental Limits of Cryptographic Primitives Through Network Information Theory

现代信息时代的到来是由无处不在的网络通信和计算设备推动的，这些设备以前所未有的速度加快了数据的生成、交换和访问，并将安全和隐私问题置于首位。加密原语是规范的和代表性的问题公式，捕捉了理解安全保护技术基本原理的关键挑战，并且是更复杂的保密系统和协议的基本构建块。这个项目通过网络信息理论和编码工具来研究各种密码原语阵列的基本限制。该项目还将为本科生和高中生提供这一国家重点学科的培训，培养他们在STEM领域的兴趣。该项目从信息论的角度研究密码原语的基本限制。这种香农理论的观点关注信息理论容量度量和数据大小的缩放，与大多数现有的密码学和理论计算机科学研究相反，后者关注复杂性理论度量和系统大小的缩放。该项目由三个主要部分组成：第一部分重点研究广播加密和安全组播的消息速率、密钥存储大小和广播带宽；第二部分重点研究有条件泄露秘密的能力特征；第三部分重点是将这一观点扩展到更多的重新制定和新的原语，从而扩展了信息论在安全领域的应用。该项目预计将揭示对密码原语的理论和实践见解，并加强对其基本限制的理解。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

The advent of the modern information age is enabled by pervasive networked communication and computation devices, which accelerate data generation, exchange, and access at an unprecedented pace and bring security and privacy concerns to the forefront. Cryptographic primitives are canonical and representative problem formulations that capture key challenges in understanding the fundamentals of security preserving techniques, and are essential building blocks for more sophisticated secrecy systems and protocols. This project studies the fundamental limits of a diverse array of cryptographic primitives through network information theory and coding tools. The project will also provide training in this national priority discipline for undergraduate and high school students and cultivate their interests in the STEM fields.The project takes an information theoretic view of the investigation of the fundamental limits of cryptographic primitives. This Shannon-theoretic view, which focuses on the information-theoretic capacity metric and the scaling of data size, is in contrast to most existing cryptography and theoretical computer science studies, which focus on complexity theoretic metrics and the scaling of system size. This project is comprised of three main thrusts: the first thrust focuses on the investigation of the message rate, key storage size, and broadcast bandwidth of broadcast encryption and secure groupcast; the second thrust focuses on the capacity characterization of conditional disclosure of secrets; the third thrust focuses on extending this viewpoint to additional reformulated and new primitives that expand the application of information theory to security. The project is expected to unveil theoretical and practical insights into cryptographic primitives, and enhance the understanding on their fundamental limits.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.