Public-key encryption from a trapdoor one-way embedding of $SL_2(\mathbb{N}$)

TL;DR

This paper introduces a novel public-key encryption scheme based on obfuscating words in a free monoid using the $SL_2( N)$ group, with a simple factorization algorithm, but lacks thorough security analysis.

Contribution

It proposes a new encryption method leveraging group obfuscation in $SL_2( N)$ and provides a reference implementation, opening avenues for further security evaluation.

Findings

Implementation of the encryption scheme in Python

Suggested parameters for practical use

Security analysis remains incomplete and requires future work

Abstract

We obfuscate words of a given length in a free monoid on two generators with a simple factorization algorithm (namely $SL_2(\mathbb{N})$) to create a public-key encryption scheme. We provide a reference implementation in Python and suggested parameters. The security analysis is between weak and non-existent, left to future work.