EAGER: Implementing Practical Provably Secure Authenticated Key Exchange for the Post-Quantum World

网络安全被认为是我们以信息技术为基础的社会最重要的方面之一。密钥交换(KE)是一种基本的密码原语，而认证KE(AKE)是互联网上安全通信协议(如SSL/TLS、IPSec、SSH)中最常用的密码工具之一。鉴于量子计算机对RSA和ECC等密码系统构成的威胁，该项目致力于为后量子计算机世界开发安全高效的AKE替代品，这现在被美国政府视为高度优先事项。该项目将有助于开发在网络安全方面具有巨大潜力的新ACES，为我们的社会。该项目的成功不仅将具有非常重大的实用价值，而且将对理论数学和计算产生广泛的影响。这个项目将对我们与美国国家标准技术研究所后量子密码学小组开展的合作产生重大影响，在该小组中，大量工作致力于量子抗性AKS的研究。这个项目旨在开发AKE方案，但基于抗量子计算机攻击的问题，我们希望基于错误学习问题(LWE)和环-LWE问题(RLWE)开发高效和安全的AKE实现，以及为应用程序选择具体参数，目标是为后量子世界开发安全和高效的系统。这样的系统应该享受基于格子的构造的潜在好处，如渐近效率、概念简单性、最坏情况下的难度假设和可证明的安全性，这使其成为后量子世界的完美。该项目的这一关键组成部分是基于从初步实验和我们建立的理论结果中产生的几个有希望的创新想法，该项目还包括在解决ACES设计中的各种挑战方面的基本新想法。这些结果将有助于更好地理解基于LWE的ACES的基本原理，以及如何为实际应用设计更安全和更高效的ACES的方法。我们的研究方法是新的数学思想和系统的计算机实验的协同结合。

Cyber security is considered one of the most important aspects of our information technology based society. Key Exchange(KE) is a fundamental cryptographic primitive, and authenticated KE (AKE) is one of the most used cryptographic tools in secure communication protocols (e.g. SSL/TLS, IPSec, SSH) over the Internet. In light of the threat that quantum computers pose to cryptosystems such as RSA and ECC, this project is devoted to the development of secure and efficient AKE alternatives for the post-quantum computer world, which is now considered of a high priority by the US government. This project will help develop new AKEs that have the great potential in cyber security for our society. The success of the project will not only have very significant practical values, but also will have a broad impact on theoretical mathematics and computation. This project will have a significant impact on the collaboration we are developing with the Post-Quantum cryptography group at the National Institute of Standard of Technology, where a significant amount of efforts is devoted to the study of quantum resistant AKEs. The PI will teach and work with undergraduate and graduate students, and recruit students from under represented groups in science.This project intends to develop AKE schemes but based on problems resistant to quantum computer attacks, in particular, we would like to develop efficient and secure implementations of AKE based on the learning with errors problems (LWE) and ring-LWE (RLWE) problems, as well as the selection of concrete parameters for applications with the goal developing secure and efficient systems for the post-quantum world. Such a system should enjoy the potential benefits of lattice-based constructions such as asymptotic efficiency, conceptual simplicity, worst-case hardness assumptions, and provable security, which makes it perfect for the post-quantum world. This key component of the project is based on several promising innovative ideas coming from preliminary experiments and theoretical results we have established, and this project also includes fundamental new ideas in addressing a diverse set of challenges in the design of AKEs. The results will lead to a better understanding of the fundamentals of the AKEs based on LWE and to methods on how to design more secure and efficient AKEs for practical applications. Our research approach is a synergistic combination of new mathematical ideas and systematic computer experiments.