Public Key Encryption in Non-Abelian Groups

TL;DR

This paper introduces a novel public key encryption scheme based on non-abelian Lie groups, establishing new intractability assumptions and proving security under the random oracle model.

Contribution

It proposes the first CCA-secure encryption scheme in non-abelian Lie groups using FO technique and new intractability assumptions.

Findings

The scheme is proven secure under the non-abelian inserting assumption.

Introduces new intractability assumptions for Lie groups.

Demonstrates feasibility of encryption in non-abelian groups.

Abstract

In this paper, we propose a brand new public key encryption scheme in the Lie group that is a non-abelian group. In particular, we firstly investigate the intractability assumptions in the Lie group, including the non-abelian factoring assumption and non-abelian inserting assumption. After that, by using the FO technique, a CCA secure public key encryption scheme in the Lie group is proposed. At last, we present the security proof in the random oracle based on the non-abelian inserting assumption.