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加密中的现有基原料，例如离散对数问题或整数分解问题。实际上，一旦建立了大规模的量子计算机，就必须过渡到量子后加密。令人震惊的是，只有几个量子后加密系统被认为是安全的。这激发了寻找加密原始图的新结构，这些构造将保证长期安全的网络空间，这是该项目的重点。该项目的更广泛影响目标所有年龄段，包括夏季训练营的组织，研究生培训和针对老年人的反扫描研讨会。我们的项目支持在加密术中建造新的原始原始人，这些新原始人使用代数和数字理论引起的新的硬性数学问题，尤其是我们的构建范围，以构建新的框架，以构建新的框架。在等级度量标准中基于代码的密码学的上下文中的原语。在这一研究基础上建立，可以针对使用新离散指标的基于代码的加密方案的构建。此外，该项目还支持探索锤子指标的新变体（用于基于古典代码的密码学），以提供新的代码理论，其目标是构建全新的代数结构，这些结构可以用作基于代码的密码框架中的密码原始人，这些奖励反映了NSF的合法传统和范围的范围。 标准。