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

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.