SaTC: CORE: Small: Expanding the Frontiers of Isogeny-Based Cryptography

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According to our current understanding of the laws of quantum mechanics, computers based on quantum phenomena offer the possibility of solving certain problems much quicker than any classical computer. Included among these problems are the majority of mathematical problems that form a basis for almost all currently deployed public-key cryptosystems. Current public-key cryptographic technologies are all known to be highly vulnerable to attacks by large-scale quantum computers. Although such quantum computers have not yet been built, substantial progress has been made in recent years. It is widely accepted that it is prudent to plan ahead for future needs, as adoption of new cryptosystem deployment takes several years to align networks, industry, and the general public. This project aims to develop frontiers of quantum-safe cryptography systems to address the need of forward secrecy in the quantum age. The project’s novelties include design, and development of protocols and algorithms based on elliptic curve and isogenies (maps) between them. The project’s impact is on the standardization of such cryptosystems in first place as well as directions and insights on the implementations and deployments afterwards. This project focuses mainly on efficient development of isogeny-based cryptography system as it is one of the candidates for National Institute of Standards and Technologies (NIST) post-quantum cryptography standardization process offering smallest public key sizes in comparison to the counterparts. This and other unique characteristic of isogeny-based cryptography make it suitable for certain applications such as embedded devices. The investigator will focus on efficient development and implementations of supersingular isogeny-based key encapsulation (SIKE), isogeny-based signatures, group key exchange mechanisms, and their integration into real-world applications. This research provides impact and influence on the design and security analysis of the next generation post-quantum cryptosystems which is the main focus on cryptography community these days. The investigator’s ultimate objective is to establish isogeny-based cryptography as a mainstream option for post-quantum cryptography and get standardized through NIST and other standardization organizations.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.