Gaussian elimination in unitary groups with an application to cryptography

TL;DR

This paper extends Gaussian elimination techniques to unitary groups and demonstrates their application in constructing a new public-key cryptosystem, advancing algebraic methods in cryptography.

Contribution

The paper introduces a novel Gaussian elimination algorithm for unitary groups and applies it to develop a cryptographic scheme.

Findings

Extended Gaussian elimination to unitary groups

Developed a new cryptographic scheme based on these algorithms

Demonstrated the cryptosystem's potential in secure communications

Abstract

Gaussian elimination is used in special linear groups to solve the word problem. In this paper, we extend Gaussian elimination to unitary groups. These algorithms have an application in building a public-key cryptosystem, we demonstrate that.