The goal of this research is to solve some important problems in nnnntorus-based, pairing-based, multilinear, and elliptic curve and abelian variety cryptography. Elliptic curve cryptography helps to secure the Internet and is used by the U.S. and other governments and institutions to provide secure communication. Abelian variety cryptography includes elliptic and hyperelliptic curve cryptography, scales well to high security levels, and is especially advantageous in constrained environments. Pairing-based cryptography is a recent cutting-edge use of elliptic curves, with numerous useful security applications. Torus-based cryptography and compression-based abelian variety cryptography improve the efficiency of discrete log and pairing-based cryptography. Multilinear cryptography, which generalizes pairing-based cryptography, is an open question; an efficient and secure solution would give efficient and secure multi- party communication. The security of these systems and the difficulty of the number theoretic problems on which they are based are crucial for the health of the economy and for national and international security.
The project focuses on the security of the elliptic curve discrete log problem and other number theoretic problems on which cryptographic security is based, and on the construction of efficient, secure, and scalable public key cryptosystems. The techniques will involve some deep and interesting mathematics.
This project will educate and train a diverse workforce in cybersecurity by supporting graduate students, promoting the participation of underrepresented groups, furthering the development of new courses in cutting-edge cybersecurity, and promoting outreach that educates the public.
