Collaborative Research: EAGER-QIA: High-Genus Code-Based Cryptography

合作研究：EAGER-QIA：基于高级代码的密码学

• 批准号: 2037833
• 负责人: Gretchen Matthews
• 金额: $ 20.25万
• 依托单位: Virginia Polytechnic Institute and State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2020
• 资助国家: 美国
• 起止时间: 2020-09-01 至 2023-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2037833&HistoricalAwards=false
• 关键词: Collaborative; Research; EAGER; QIA; Genus

Cryptography protects confidential communications: electronic commerce, voter information, diplomatic communication, human-rights interviews, medical records, and much more. However, attackers recording messages today will be able to decrypt those messages with future quantum computers. The most confidence-inspiring response is the McEliece cryptosystem, which has a strong security track record and is a leading contender for standardization of post-quantum cryptography, but this cryptosystem has a key size around a megabyte. Applications that cannot afford megabyte keys are currently forced to use cryptosystems whose security is much less stable. This project aims to build new post-quantum systems that bring McEliece's security stability and confidence to a wider range of applications.The public key in McEliece's cryptosystem is a generator matrix for a subfield subcode of an error-correcting code, specifically a genus-0 Goppa code. Subfield subcodes of higher-genus Goppa codes can correct more errors for the same code length and code dimension, improving the tradeoffs between efficiency and security. Showing that cryptosystems built from these codes can run at reasonable speed will require vertically integrated optimization of cryptosystem design, curve selection, decoding algorithms, algorithms for computer algebra, and vectorized software, with the further challenges of ensuring security against both mathematical and microarchitectural attacks.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.

密码学保护机密通信：电子商务，选民信息，外交沟通，人权访谈，医疗记录等等。但是，今天记录消息的攻击者将能够用未来的量子计算机解密这些消息。最具信心的响应是McEliece Cryptosystem，该系统具有强大的安全记录，并且是标准化后量子加密术的领先竞争者，但是该加密系统在兆字节周围具有关键大小。目前，无法负担得起的巨型键的应用程序被迫使用安全系统的安全系统的稳定性要稳定得多。该项目旨在构建新的量子后系统，以将McEriece的安全稳定性和信心带入更广泛的应用程序。Mceliece的加密系统中的公钥是用于错误校正代码子场子代码的生成器矩阵，特别是属-0 GOPPA代码。高级GOPPA代码的子场子代码可以纠正相同代码长度和代码维度的更多错误，从而改善了效率和安全性之间的权衡。表明，通过这些代码构建的密码系统可以以合理的速度运行将需要对密码系统设计，曲线选择，曲线选择，解码算法，用于计算机代数的算法以及矢量化软件的优化，以及通过对数学和微观攻击的确保进行的确保范围的进一步的挑战，这些挑战是在数学和微观攻击方面的支持。基金会的智力优点和更广泛的影响评论标准。

项目成果

HerA Scheme: Secure Distributed Matrix Multiplication via Hermitian Codes

• DOI: 10.1109/isit54713.2023.10206764
• 发表时间: 2023-03
• 期刊: 2023 IEEE International Symposium on Information Theory (ISIT)
• 作者: R. A. Machado;Welington Santos;Gretchen L. Matthews

Twisted Hermitian Codes

• DOI: 10.3390/math9010040
• 发表时间: 2020-12
• 期刊: Mathematics
• 影响因子: 2.4
• 作者: Austin Allen;Keller Blackwell;Olivia Fiol;Rutuja Kshirsagar;Bethany Matsick;Gretchen L. Matthews;Zoe Nelson