Discrete logarithm problem (DLP) and Conjugacy search problem (CSP) are two important tools for designing public key protocols. However DLP is used over commutative as well as non-commutative platforms but CSP is used only over non-commutative platforms. To harden the security of cryptosystems using DLP and CSP as base problems, various authors have combined these two problems to form a new problem called Discrete logarithm with conjugacy search problem (DLCSP). It has been used to design key exchange protocols and signature schemes over the general linear group with entries from group ring, that is, \(GL_n(\mathbb {F}_q[S_r])\). In this paper, we show that, if someone can solve DLP in polynomial time over some finite extension of \(\mathbb {F}_q\), then DLCSP over \(GL_n(\mathbb {F}_q[S_r])\) can also be solved in polynomial time with non-negligible probability.

离散对数问题（DLP）和共轭搜索问题（CSP）是设计公钥协议的两个重要工具。然而，DLP 用于交换和非交换平台，而 CSP 仅用于非交换平台。为了加强使用 DLP 和 CSP 作为基本问题的密码系统的安全性，许多作者将这两个问题结合起来形成一个新问题，称为离散对数与共轭搜索问题 (DLCSP)。它已被用于在具有来自群环的条目的一般线性群上设计密钥交换协议和签名方案，即\(GL_n(\mathbb {F}_q[S_r])\)。在本文中，我们表明，如果有人可以在多项式时间内在\(\mathbb {F}_q\) 的某个有限扩展上解决 DLP ，那么 DLCSP 在\(GL_n(\mathbb {F}_q[S_r])\)也可以在多项式时间内以不可忽略的概率求解。