MOR Cryptosystem and classical Chevalley groups in odd characteristic

TL;DR

This paper investigates the security of the MOR cryptosystem when implemented with finite classical Chevalley groups over finite fields of odd characteristic, introducing algorithms and analyzing cryptographic hardness.

Contribution

It develops an algorithm for classical Chevalley groups and assesses the cryptosystem's security specifically for orthogonal and symplectic groups.

Findings

Algorithm for Chevalley groups similar to row-column operations

Analysis of cryptosystem hardness for orthogonal groups

Analysis of cryptosystem hardness for symplectic groups

Abstract

In this paper we study the MOR cryptosystem using finite classical Chevalley groups over a finite field of odd characteristic. In the process we develop an algorithm for these Chevalley groups in the same spirit as the row-column operation for special linear group. We focus our study on orthogonal and symplectic groups. We find the hardness of the proposed MOR cryptosystem for these groups.