SaTC: CORE: Small: Expanding the Frontiers of Isogeny-Based Cryptography

根据我们目前对量子力学定律的理解，基于量子现象的计算机提供了比任何经典计算机更快地解决某些问题的可能性。在这些问题中包括大多数数学问题，这些问题构成了几乎所有当前部署的公钥密码系统的基础。众所周知，目前的公钥密码技术非常容易受到大规模量子计算机的攻击。虽然这样的量子计算机还没有建成，但近年来已经取得了实质性的进展。人们普遍认为，提前计划未来的需求是谨慎的，因为采用新的密码系统部署需要数年时间才能使网络、行业和普通公众保持一致。该项目旨在开发量子安全密码系统的前沿，以满足量子时代对前向保密的需求。该项目的新颖性包括基于椭圆曲线和它们之间的同源(映射)的协议和算法的设计和开发。该项目的影响首先是对这类密码系统的标准化，以及对随后的实施和部署的指导和见解。本项目主要致力于高效开发基于同源的密码系统，因为它是美国国家标准与技术研究所(NIST)后量子密码标准化进程的候选之一，与同行相比，它提供了最小的公钥大小。基于同源的密码学的这一特性和其他独特的特性使其适用于某些应用，例如嵌入式设备。研究人员将专注于基于超奇异异源的密钥封装(SIKE)、基于同源的签名、组密钥交换机制的高效开发和实现，以及它们与现实世界应用的集成。这一研究对当前密码界关注的新一代后量子密码系统的设计和安全性分析具有一定的影响和影响。研究人员的最终目标是将基于同源的密码学确立为后量子密码学的主流选择，并通过NIST和其他标准化组织进行标准化。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。

According to our current understanding of the laws of quantum mechanics, computers based on quantum phenomena offer the possibility of solving certain problems much quicker than any classical computer. Included among these problems are the majority of mathematical problems that form a basis for almost all currently deployed public-key cryptosystems. Current public-key cryptographic technologies are all known to be highly vulnerable to attacks by large-scale quantum computers. Although such quantum computers have not yet been built, substantial progress has been made in recent years. It is widely accepted that it is prudent to plan ahead for future needs, as adoption of new cryptosystem deployment takes several years to align networks, industry, and the general public. This project aims to develop frontiers of quantum-safe cryptography systems to address the need of forward secrecy in the quantum age. The project’s novelties include design, and development of protocols and algorithms based on elliptic curve and isogenies (maps) between them. The project’s impact is on the standardization of such cryptosystems in first place as well as directions and insights on the implementations and deployments afterwards. This project focuses mainly on efficient development of isogeny-based cryptography system as it is one of the candidates for National Institute of Standards and Technologies (NIST) post-quantum cryptography standardization process offering smallest public key sizes in comparison to the counterparts. This and other unique characteristic of isogeny-based cryptography make it suitable for certain applications such as embedded devices. The investigator will focus on efficient development and implementations of supersingular isogeny-based key encapsulation (SIKE), isogeny-based signatures, group key exchange mechanisms, and their integration into real-world applications. This research provides impact and influence on the design and security analysis of the next generation post-quantum cryptosystems which is the main focus on cryptography community these days. The investigator’s ultimate objective is to establish isogeny-based cryptography as a mainstream option for post-quantum cryptography and get standardized through NIST and other standardization organizations.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.