Exploring platform (semi)groups for non-commutative key-exchange protocols

<p>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. </p> <p>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. </p> <p>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. </p>

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

Doctoral

Discipline thesis:degree_discipline

Mathematics

Grantor

The Graduate School and University Center of The City University of New York

Year dc:date.available

2014

Author dc:creator

• Lam, Ha

Advisor dc:contributor.advisor

• Delaram Kahrobaei

• Mathematics
• cryptography
• group theory

Repository record dc:identifier

https://academicworks.cuny.edu/gc_etds/241

OAI identifier oai:identifier

oai:academicworks.cuny.edu:gc_etds-1240