A polynomial algorithm for the braid double shielded public key cryptosystems

Abstract

We propose new provable practical deterministic polynomial time algorithm of cryptographic analysis for the braid Wang, Xu, Li, Lin and Wang «Double shielded public key cryptosystems», where the authors recommended the Artin braid groups B_n as platforms for proposed protocols. We show that a linear decomposition attack based on the decomposition method introduced by the author works for the image of braids under the Lawrence-Krammer representation by finding the exchanging keys in the both two main protocols by Wang et. al. These keys can be effectively computed in their original form too. Thus the protocols propоsed by Wang et. al. are vulnerable.