CRII: SaTC: Computational Correlations: A New Tool for Cryptography

理解安全实现密码原语的计算难度是密码学中的一个基本问题。其中一个重要的密码学原语是不经意传输，理解实现它的本质对密码学有着重要的影响，比如使安全的多方计算更接近现实。这项研究发展了一个新的理论来探索这个广泛的概念，即计算相关性理论。该项目定义了一个适当的概念的计算相关性，利用安全保证来论证计算硬度的结果，并引入了计算通道的概念，在设计和分析的实际明显的传输协议。 计算相关性的理论是，在各种其他应用中，有用的展示不经意传输的必要性，以实现某些概念的安全性和设计速率最优的不经意传输协议的计算设置。培训下一代密码学研究和安全专业人员是该项目的中心目标。这包括为本科生和研究生课程设计和开发新课程和教材，为传播知识开发积极的学习材料，以及让少数民族学生和女学生参与研究。

Understanding the computational hardness of securely realizing cryptographic primitives is a fundamental problem in cryptography. One such vital cryptographic primitive is oblivious transfer and understanding the essence of implementing it has significant consequences to cryptography, like bringing secure multi-party computation closer to reality. This research develops a new theory to explore this broad concept, namely the theory of computational correlations. This project defines an appropriate notion of computational correlations, leverages security guarantees to argue computational hardness results, and introduces the concept of computational channels in design and analysis of practical obvious transfer protocols. The theory of computational correlations is, among various other applications, useful to exhibit necessity of oblivious transfer to achieve certain notions of security and design rate optimal oblivious transfer protocols in the computational setting. Training the next generation of cryptography research and security professionals is a central goal of this project. This includes the design and development of new courses and course materials for undergraduate and graduate courses, development of active learning materials for the dissemination of knowledge, and engagement of minority and women students in research.