The root extraction problem in braid groups is the following: given a braid
$beta in mathcal{B}_n$ and a number $kin mathbb{N}$, find $alphain
mathcal{B}_n$ such that $alpha^k=beta$. In the last decades, many
cryptosystems such as authentication schemes and digital signatures based on
the root extraction problem have been proposed. In this paper, we first
describe these cryptosystems built around braid groups. Then we prove that, in
general, these authentication schemes and digital signature are not secure by
presenting for each of them a possible attack.
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Author Of this post: <a href="http://arxiv.org/find/cs/1/au:+Cumplido_M/0/1/0/all/0/1">María Cumplido</a>, <a href="http://arxiv.org/find/cs/1/au:+Kahrobaei_D/0/1/0/all/0/1">Delaram Kahrobaei</a>, <a href="http://arxiv.org/find/cs/1/au:+Noce_M/0/1/0/all/0/1">Marialaura Noce</a>