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SaTC: CORE: Small: Multivariate Public Key Cryptosystems - Candidates for the Next Generation Post-Quantum Standards

SaTC：核心：小型：多元公钥密码系统 - 下一代后量子标准的候选者

基本信息

批准号：
1814221
负责人：
Seungki Kim
金额：
$ 30万
依托单位：
University of Cincinnati Main Campus
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2018
资助国家：
美国
起止时间：
2018-08-01 至 2023-07-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1814221&HistoricalAwards=false
关键词：
SaTC CORE Small Multivariate Public

项目摘要

Public-key cryptosystems, a revolutionary breakthrough in cryptography, are indispensable for our modern communication network. The Internet, as well as other communication systems, rely principally on public-key cryptosystems that depend for security on the difficulty of certain number-theoretic problems such as integer factorization or the "discrete log problem." However, it is now known that a quantum computer could efficiently solve these problems, thus rendering all public-key cryptosystems based on such assumptions impotent if a large-scale quantum computer can be built. To address this issue, technologies resistant to such quantum attack are becoming a central topic in information security; this new science bears the moniker "post-quantum cryptography." One of the four main families of post-quantum cryptosystems under development is known as multivariate public-key cryptosystems (MPKCs). This research project is devoted to an in-depth study of multivariate public-key cryptosystems, with the goal of facilitating the analysis of several multivariate candidates that have great potential for cyber security. Results of the project are expected to produce secure and efficient alternatives for the post-quantum computer world, with application both to addressing the threat that quantum computers pose to existing cryptosystems and to the growing security needs for small devices with limited computing resources. The project includes a diverse group of undergraduate and graduate students who will receive training through involvement in the research.The focus of the project is on developing more efficient and more secure MPKCs and their fast implementations, as well as exploring provable security for MPKCs and analyzing the security of specific MPKCs. The approach is a combination of new mathematical ideas and computer experiments, relying primarily on mathematical tools from algebraic geometry and the theory of symmetry. Since the systems under study cannot be analyzed by hand, the investigator will use computer experiments to build intuitive understanding and will use theoretical methods to study the mathematical structures hidden within the MPKC constructions. The results are expected to lead to a better understanding of the fundamentals of the MPKCs and of how to design secure and efficient MPKCs. Furthermore, the project should make a significant contribution in developing the next generation of standards for post-quantum cryptography.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.

公钥密码体制是密码学的一个革命性突破，是现代通信网络不可缺少的组成部分。互联网以及其他通信系统主要依赖于公钥密码系统，该公钥密码系统的安全性取决于某些数论问题的难度，例如整数因子分解或“离散对数问题”。“然而，现在已知量子计算机可以有效地解决这些问题，因此如果可以建造大规模量子计算机，那么基于这些假设的所有公钥密码系统都将变得无效。为了解决这个问题，抵抗这种量子攻击的技术正在成为信息安全的中心话题;这门新科学被称为“后量子密码学”。正在开发的四个主要的后量子密码系统家族之一被称为多变量公钥密码系统（MPKC）。该研究项目致力于深入研究多变量公钥密码系统，其目标是促进对网络安全具有巨大潜力的多变量候选者的分析。该项目的结果预计将为后量子计算机世界产生安全和有效的替代方案，应用于解决量子计算机对现有密码系统构成的威胁，以及对计算资源有限的小型设备日益增长的安全需求。该项目包括一组不同的本科生和研究生，他们将通过参与研究接受培训。该项目的重点是开发更高效，更安全的MPKC及其快速实现，以及探索MPKC的可证明安全性和分析特定MPKC的安全性。该方法是新的数学思想和计算机实验的结合，主要依赖于代数几何和对称理论的数学工具。由于所研究的系统不能用手工分析，研究人员将使用计算机实验来建立直观的理解，并将使用理论方法来研究隐藏在MPKC结构中的数学结构。预计结果将导致更好地了解MPKC的基本原理以及如何设计安全有效的MPKC。此外，该项目还将为开发下一代后量子密码学标准做出重大贡献。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。