CAREER: Unifying Provable Security Techniques for

该项目侧重于开发用于设计和证明先进密码系统安全性的新工具。对敏感数据的细粒度访问控制的需求从未像现在这样大，而像功能加密这样的新范式有可能提供可针对各种数据使用和隐私需求进行定制的加密系统。然而，随着系统变得越来越复杂，它们自然变得越来越难以推理。通过构建新的安全降低框架和增强可用于实例化这些框架的数学基础，该项目在灵活和更统一的密码学理论方面取得了快速进展，可以应对这些日益严峻的挑战。特别是，该项目将格密码学的最新结果与设计安全性降低的新进展相结合，以便为高度灵活和可定制的密码系统的安全性提供强有力的论据。该项目的成果被纳入高级研究生课程，以提供更完整的加密系统设计原理视图。在本科和研究生阶段的学生研究人员积极参与并获得宝贵的研究经验。此外，还包括面向低年级学生的推广活动，即制作一本通过童话故事向中学学生介绍数学推理的书。从长远来看，该项目为分析和设计灵活的密码系统提供了新的工具，同时也为新兴的年轻科学家提供了切入点和培训基地。

This project focuses on the development of new tools for designing and proving the security of advancing cryptographic systems. The need for fine-grained access control to sensitive data has never been greater, and new paradigms like functional encryption have the potential to deliver cryptographic systems that can be tailored to a variety of data uses and privacy needs. However, as systems have grown more complex, they have naturally grown more difficult to reason about. By building new frameworks for security reductions and enhancing the mathematical foundations available to instantiate these frameworks, this project makes fast progress towards a flexible and more unified theory of cryptography that can meet these mounting challenges. In particular, the project integrates recent results in lattice cryptography with new advances in designing security reductions in order to provide strong arguments for the security of highly flexible and customizable cryptographic systems. The project results are incorporated into the curriculum of advanced graduate classes to provide a more integrated view of cryptographic system design principles. Student researchers at the undergraduate and graduate levels are heavily involved and gaining valuable research experience. Outreach activities to younger student populations are also included, namely the production of a book that introduces middle-grade students to mathematical reasoning through a fairy-tale setting. In the long term, this project provides new tools for analyzing and designing flexible cryptographic systems, while also serving as an entry point and training ground for emerging young scientists.