CAREER: Foundations of Cryptographic Proof Systems

现代密码学始于保护公共网络上的通信。今天，我们不仅可以远程相互通信，还可以将计算委托给基于云的服务。我们能相信云吗？正如上半个世纪发展起来的密码技术为互联网上的安全通信提供了基础一样，新技术也提供了类似的机制来确保计算的隐私和完整性。随着这些技术的成熟和部署，仔细研究它们的设计和安全性非常重要。该项目的重点是加密证明系统的理论基础，这是一种用于确保计算隐私和完整性的关键原语。该项目对提供隐私和最小化证明大小的加密证明系统的理论基础进行了系统的研究。重点是从一般和非结构化的假设的建设。这新使密码证明系统从更简单和更弱的密码概念。此外，通过对加密证明系统基础的仔细研究，该项目扩展了我们对证明系统与其他核心加密概念（如公钥加密和证人加密）之间更广泛联系的理解。通过加密证明系统的透镜观察这些概念，该项目为从更简单的加密假设实现这些原语铺平了新的道路。该项目还为各个级别（从K-12学生到研究生）开发新的教育材料，重点关注应用密码学及其在保护数字系统和计算中的作用。该奖项反映了NSF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。

Modern cryptography began with the goal of protecting communications over public networks. Today, not only do we communicate with each other remotely, we also delegate our computations to cloud-based services. But can we trust the cloud? Just as cryptographic techniques developed in the last half century provided the foundation for secure communication on the Internet, new techniques provide similar mechanisms for ensuring privacy and integrity of computations. As these technologies mature and see deployment, it is important to carefully study their design and security. The focus of this project is on the theoretical foundations of cryptographic proof systems, a key primitive used to ensure privacy and integrity of computations. This project conducts a systematic study of the theoretical foundations of cryptographic proof systems that provide privacy and minimize proof size. The focus is on constructions from general and unstructured assumptions. This newly enables cryptographic proof systems from simpler and weaker cryptographic notions. In addition, through the careful study of the foundations of cryptographic proof systems, the project expands our understanding of the broader connections between proof systems and other core cryptographic notions like public-key encryption and witness encryption. By viewing these notions through the lens of cryptographic proof systems, this project paves new paths towards realizing these primitives from simpler cryptographic assumptions. This project also develops new educational material at all levels (from K-12 students to graduate students) focused on applied cryptography and the role it plays in securing digital systems and computations.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.