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

量子计算的快速发展正在威胁着经典密码学中现有的原语，如离散对数问题或整数因子分解问题。事实上，一旦大规模量子计算机建成，就有必要过渡到后量子密码学。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原语结构，以保证长期安全的网络空间，这是该项目的重点。该项目的广泛影响针对所有年龄组，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。我们的项目支持构建新的密码学原语，这些原语利用代数和数论中出现的新的硬数学问题。特别是，我们专注于一个框架的发展，该框架允许使用Drinfeld模的理论来构造秩度量码，并进而在秩度量中的基于码的密码学的上下文中构建新的原语。建立在这条研究线上，可以针对使用新的离散度量的基于代码的加密方案的构建。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，可用作代码框架中的密码原语-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进行评估，被认为值得支持和更广泛的影响审查标准。

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.