On the Security of the Cha-Ko-Lee-Han-Cheon Braid Group Public Key Cryptosystem

TL;DR

This paper analyzes the security of the Cha-Ko-Lee-Han-Cheon braid group public key cryptosystem, revealing its reliance on the MSCSP and implications for related cryptosystems.

Contribution

It demonstrates that several non-commutative semigroup-based cryptosystems, including the braid group cryptosystem, are fundamentally based on the MSCSP, highlighting potential vulnerabilities.

Findings

Cryptosystems are based on the MSCSP

Braid group cryptosystem's security depends on MSCSP difficulty

Related cryptosystems share similar security assumptions

Abstract

We show that a number of cryptographic protocols using non-commutative semigroups including the Cha-Ko-Lee-Han-Cheon braid group public-key cryptosystem and related public-key cryptosystems such as the Shpilrain-Ushakov public-key cryptosystems are based on the MSCSP.