Dissertations, Theses, and Capstone Projects
Date of Degree
6-2014
Document Type
Dissertation
Degree Name
Ph.D.
Program
Mathematics
Advisor
Delaram Kahrobaei
Subject Categories
Mathematics
Keywords
cryptography, group theory
Abstract
In this work, my advisor Delaram Kahrobaei, our collaborator David Garber, and I explore polycyclic groups generated from number fields as platform for the AAG key-exchange protocol. This is done by implementing four different variations of the length-based attack, one of the major attacks for AAG, and submitting polycyclic groups to all four variations with a variety of tests. We note that this is the first time all four variations of the length-based attack are compared side by side. We conclude that high Hirsch length polycyclic groups generated from number fields are suitable for the AAG key-exchange protocol.
Delaram Kahrobaei and I also carry out a similar strategy with the Heisenberg groups, testing them as platform for AAG with the length-based attack. We conclude that the Heisenberg groups, with the right parameters are resistant against the length-based attack.
Another work in collaboration with Delaram Kahrobaei and Vladimir Shpilrain is to propose a new platform semigroup for the HKKS key-exchange protocol, that of matrices over a Galois field. We discuss the security of HKKS under this platform and advantages in computation cost. Our implementation of the HKKS key-exchange protocol with matrices over a Galois field yields fast run time.
Recommended Citation
Lam, Ha, "Exploring platform (semi)groups for non-commutative key-exchange protocols" (2014). CUNY Academic Works.
https://academicworks.cuny.edu/gc_etds/241