The MOR Cryptosystem and Unitary group in odd characteristic

This paper is a continuation of the work done to understand the security of a MOR cryptosystem over matrix groups defined over a finite field. In this paper we show that in the case of unitary group U$(d,q^2)$ the security of the MOR cryptosystem is similar to the hardness of the discrete logarithm problem in $\mathbb{F}_{q^{2d}}$. In our way of developing the MOR cryptosystem, we developed row-column operations for unitary matrices that solves the word problem in the group of unitary matrices. This is similar to row-column operations in special linear groups that write a matrix as a product of elementary transvections.