A polynomial time algorithm for the braid double shielded public key cryptosystems

TL;DR

This paper presents a deterministic polynomial time algorithm that can break certain braid-based public key cryptosystems by exploiting their algebraic structure, challenging their security assumptions.

Contribution

The paper introduces a practical polynomial time attack on braid double shielded cryptosystems using a linear decomposition method based on Lawrence-Krammer representation.

Findings

The attack successfully finds exchanging keys in the protocols.

The cryptosystems are vulnerable to the proposed decomposition attack.

The method demonstrates the insecurity of these braid-based schemes.

Abstract

We propose new provable practical deterministic polynomial time algorithm for the braid Wang, Xu, Li, Lin and Wang Double shielded public key cryptosystems. We show that a linear decomposition attack based on the decomposition method introduced by the author in monography "Algebraic Cryptography" (2013) and some papers works for the image of braids under the Lawrence-Krammer representation by finding the exchanging keys in both two main protocols by the authors listed above.