Number Theoretic Foundations

Number theory offers a framework for many cryptographic systems and provides most of the hard computational problems used to provide security for these schemes. Finite fields, algebraic curves, and number fields serve as the basis for much of public key cryptography. For example, the security of the well-known RSA system is based on the difficulty of factoring a large integer. Most key agreement protocols rely on the difficulty of a class of number theoretic problems generally combined under the term discrete logarithm problem (DLP).

Researchers at CISaC explore number theoretic structures that can serve as the basis for cryptographic schemes. Our investigations focus on class groups and infrastructures of global fields (algebraic number field and function fields) as well as Jacobians of algebraic curves. Our research not only contributes to a better understanding to the DLP in these mathematical settings, but is also of mathematical interest in its own right.