论文标题
基于编织组的密码学中的根提取问题
The root extraction problem in braid group-based cryptography
论文作者
论文摘要
编织组中的根提取问题如下：给定一个编织$β\ in \ mathcal {b} _n $和一个数字$ k \ in \ mathbb {n} $，找到$α\ in \ mathcal {b} _n $，这样$α^k =β$。在过去的几十年中，已经提出了许多基于根提取问题的认证方案和数字签名等密码系统。在本文中，我们首先描述了这些密码系统围绕辫子组建立的。然后，我们证明，通常，这些身份验证方案和数字签名无法通过为每个攻击呈现可能的攻击来确保安全。
The root extraction problem in braid groups is the following: given a braid $β\in \mathcal{B}_n$ and a number $k\in \mathbb{N}$, find $α\in \mathcal{B}_n$ such that $α^k=β$. 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.
