A New Cryptosystem Based on Positive Braids

TL;DR

This paper introduces a new cryptosystem based on positive braids in the braid group, leveraging a hard problem in the semi-group to enhance security against certain attacks.

Contribution

It proposes a novel cryptosystem using positive braid semi-groups and demonstrates its security advantages over existing approaches.

Findings

Cryptosystem based on positive braids is secure against cluster analysis attacks.

The difficulty of the problem is at least as hard as the conjugate search problem.

Includes a key exchange protocol and a public key encryption algorithm.

Abstract

The braid group is an important non commutative group, at the same time, it is an important tool in quantum field theory with better topological structure, and often used as a research carrier for anti-quantum cryptographic algorithms. This paper proposed a difficult problem on a positive braid semi-group, and proved that the difficulty is not lower than the conjugate search problem. Based on this new difficult problem, we propose a new cryptosystem, which include a key exchange protocol and a public key encryption algorithm. Since our cryptosystem is implemented on a semi-group, it effectively avoids the analysis of attack algorithms on the cluster and makes our algorithm more secure.