CAREER: Rank Metric Codes from Drinfeld Modules and New Primitives in Code Based Cryptography

职业：对来自 Drinfeld 模块的度量代码和基于代码的密码学中的新原语进行排名

• 批准号: 2338424
• 负责人: Giacomo Micheli
• 金额: $ 50万
• 依托单位: University of South Florida
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2024
• 资助国家: 美国
• 起止时间: 2024-07-01 至 2029-06-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2338424&HistoricalAwards=false
• 关键词: CAREER; Rank; Metric; Codes; Drinfeld

The rapid development of quantum computing is currently threatening the existing primitives in classical cryptography, such as the discrete logarithm problem or the problem of integer factorization. In fact, once a large scale quantum computer will be built, a transition to post-quantum cryptography will be necessary. Alarmingly, only a few post-quantum cryptographic systems are deemed secure. This motivates the search for new constructions of cryptographic primitives that would guarantee a long-term secure cyberspace, which is the focus of this project. The broader impacts of this project target all age groups, including the organization of summer camps, graduate students training, and anti-scam seminars for elderly people.Our project supports the construction of new primitives in cryptography that make use of new hard mathematical problems arising from algebra and number theory.In particular, we focus on the development of a framework that allows to use the theory of Drinfeld modules to construct rank metric codes, and in turn to build new primitives in the context of code based cryptography in the rank metric. Building up on this line of research allows to target the construction of code-based cryptographic schemes that use new discrete metrics. Also, this project supports the exploration of new variants of the Hamming metric (used in classical code based cryptography) to provide a new theory of codes, with the goal to construct completely new algebraic structures that can be used as cryptographic primitives in the framework of code-based 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.

量子计算的快速发展目前正在威胁经典密码学中现有的原语，例如离散对数问题或整数分解问题。事实上，一旦建造出大规模量子计算机，就必须向后量子密码学过渡。令人担忧的是，只有少数后量子密码系统被认为是安全的。这促使人们寻找新的密码基元结构，以保证网络空间的长期安全，这也是该项目的重点。该项目的更广泛影响针对所有年龄段，包括组织夏令营、研究生培训和针对老年人的反诈骗研讨会。我们的项目支持利用出现的新数学难题构建密码学新原语特别是，我们专注于开发一个框架，该框架允许使用 Drinfeld 模块的理论来构造等级度量代码，然后在基于代码的密码学背景下在等级度量中构建新的原语。在此研究基础上，可以针对使用新的离散指标构建基于代码的加密方案。此外，该项目支持探索汉明度量的新变体（用于基于经典代码的密码学），以提供新的代码理论，其目标是构建全新的代数结构，可在以下框架中用作密码原语：基于代码的密码学。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。