Mathematics Colloquium

Delaram Kahrobaei

(University of York, U.K., New York University, U.S.A.)

"Some applications of arithmetic and graph groups in cryptography"

Date: February 14, 2019
Time: 17:15
Place: Lecture Hall, Research III

Abstract: In this talk we will give various examples of exponentially distorted subgroups in linear groups, including some new example of subgroups of \({\mathrm{SL}}_n( \mathbb{Z}[x])\) for \(n \ge 3\), and show how they can be used to construct symmetric-key cryptographic platforms. This is a joint work K. Mallahi-Karai to appear in the Journal of Groups Complexity, Cryptology, De Gruyter. In the second part of the talk we consider several classical and novel algorithmic problems for right-angled Artin groups (a.k.a. graph groups), some of which are closely related to graph theoretic problems, and study their computational complexity. We study these problems with a view towards applications to cryptography. This is joint work with Ramon Flores and Thomas Koberda, just published in Journal of Algebra, Elsevier.