基于分解问题的密钥交换协议
A new key exchange protocol based on the decomposition problem
摘要：
本文提出了一种新的基于非交换群分解问题的密钥建立协议：给定平台群$G$的两个元素$w, w_1$和两个子群$A, B \subseteq G$（不一定是不同的），找到元素$a \in A, b \in B$使得$w_1 = a w b$ .在这里，我们介绍了两个新的想法，提高安全性的密钥建立协议的基础上的分解问题。特别是，我们隐藏（即，不显式地公布）的子组之一$A, B$，从而引入了额外的计算困难的问题，对手，即，找到一个给定的中心化生成的子组。
英文摘要：
In this paper we present a new key establishment protocol based on the decomposition problem in non-commutative groups which is: given two elements $w, w_1$ of the platform group $G$ and two subgroups $A, B \subseteq G$ (not necessarily distinct), find elements $a \in A, b \in B$ such that $w_1 = a w b$. Here we introduce two new ideas that improve the security of key establishment protocols based on the decomposition problem. In particular, we conceal (i.e., do not publish explicitly) one of the subgroups $A, B$, thus introducing an additional computationally hard problem for the adversary, namely, finding the centralizer of a given finitely generated subgroup.
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