Public-key cryptosystem based on invariants of diagonalizable groups

TL;DR

This paper introduces a new public-key cryptosystem leveraging invariants of diagonalizable groups, analyzing its security across different algebraic structures and highlighting parameter restrictions to prevent attacks.

Contribution

It presents a novel cryptosystem based on group invariants and thoroughly examines its security properties over various mathematical settings.

Findings

Security depends on parameter restrictions

System is analyzed over finite fields, number fields, and rings

Prevents linear algebra and Euclidean algorithm attacks

Abstract

We develop a public key cryptosystem based on invariants of diagonalizable groups and investigate properties of such cryptosystem first over finite fields, then over number fields and finally over finite rings. We consider the security of these cryptosystem and show that it is necessary to restrict the set of parameters of the system to prevent various attacks (including linear algebra attacks and attacks based on Euclidean algorithm).