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

了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遗忘传输，理解实现它的本质对密码学有重要的影响，比如使安全的多方计算更接近现实。本研究发展了一种新的理论来探索这个广泛的概念，即计算相关性理论。本项目定义了计算相关性的适当概念，利用安全保证对计算硬度结果进行论证，并在实际明显传输协议的设计和分析中引入了计算通道的概念。在各种其他应用中，计算相关性理论有助于展示遗忘传输的必要性，以实现某些安全概念，并在计算设置中设计速率最优的遗忘传输协议。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。这包括为本科和研究生课程设计和开发新的课程和课程材料，为传播知识编写积极的学习材料，以及让少数民族和妇女学生参与研究。

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.