EAGER: Quantum-Safe Cryptosystems Based on Isogenies

该奖项支持对基于称为椭圆曲线同源的数学结构的一族新密码系统的安全性的研究。这项研究还将包括开发新的基于同源的协议。在用替代方案取代当前的公钥原语的过程中，这些协议是领跑者之一，这些替代方案将确保免受量子计算机的攻击。向量子安全的网络空间过渡是密码界的当务之急。事实上，在建造大规模量子计算机之前很久，量子安全原语就需要准备好并部署好，以说明加密数据的保质期。这项研究对行业有更广泛的影响，行业需要遵循安全使用同源密码系统的建议。它还通过在大学和高中一级开发新的网络安全课程来影响教育。这个项目将包括分析在有限域上寻找两条给定椭圆曲线之间的同源的任务的难度。特别是，将开发新的量子算法来计算同源。对这些算法性能的仔细分析是基于同源的方案安全性的指标。它将允许为使用户远离量子攻击的密钥识别合适的大小。该项目还将探索基于同源的密码原语的新应用。将研究静态-静态密钥交换协议的有效解决方案。这些原语还具有环签名的潜力，可以有许多实际应用，包括区块链上的匿名交易和量子安全的匿名加密货币。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

This award supports research into the security of a new family of cryptosystems based on a mathematical structure called isogenies of elliptic curves. The research will also include the development of new isogeny-based protocols. These protocols are among the front runners in the process of replacement of the current public key primitives by alternatives that will be secure against attacks by quantum computers. The transition towards a quantum-safe cyberspace is an immediate priority for the cryptography community. Indeed, quantum-safe primitives will need to be ready and deployed long before the construction of large scale quantum computers to account for the shelf life of encrypted data. This research has broader impacts to industry which will need to follow recommendations for a secure use of isogeny cryptosystems. It also impacts education through the development of new cybersecurity curriculum at the university and high school level. This project will involve the analysis of the hardness of the task of finding an isogeny between two given elliptic curves over a finite field. In particular, new quantum algorithms will be developed for computing isogenies. The careful analysis of the performances of these algorithms is the indicator of the security of isogeny-based schemes. It will permit the identification of an appropriate size for keys that keep users out of the reach of quantum attacks. The project will also explore new applications of cryptographic primitives based on isogenies. Efficient solutions for static-static key exchange protocols will be investigated. These primitives also have potential for ring signatures that can have many practical applications including anonymous transactions on the blockchain, and quantum-safe anonymous cryptocurrencies.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.