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

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

Discrete logarithm for nilpotent groups and cryptanalysis of polylinear cryptographic system

We present an efficient algorithm to compute a discrete logarithm in a finite nilpotent group, or more generally, in a finitely generated nilpotent group. Special cases of a finite p-group (p is a prime) and a finitely generated torsion free nilpotent group are considered. Then we show how the derived algorithm can be generalized to an arbitrary finite or finitely generated nilpotent group respectively. We suppose that group is presented by generating elements and defining relators or as a subgroup of a triangular matrix group over a prime finite field (in finite case) or over the ring of integers (in torsion-free case). On the base of the derived algorithm we give a cryptanalysis of some schemes of polylinear cryptography known in the literature

Cryptanalysis of protocols using (Simultaneous) Conjugacy Search Problem in certain Metabelian Platform Groups

There are many group-based cryptosystems in which the security relies on the difficulty of solving Conjugacy Search Problem (CSP) and Simultaneous Conjugacy Search Problem (SCSP) in their underlying platform groups. In this paper we give a cryptanalysis of these systems which use certain semidirect product of abelian groups