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) the security of the MOR cryptosystem is similar to the hardness of the discrete logarithm problem in Fq2d . 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.