论文标题
关于类外的共和性搜索问题，$ p $ - 群
On the Conjugacy Search Problem in Extraspecial $p$-Groups
论文作者
论文摘要
在最近新兴的基于组的密码学领域中，共轭搜索问题（CSP）已成为离散日志问题（DLP）的非交换性替代品的吸引力。找到一个安全的非亚伯群体作为平台的问题是开放的，并且是一个积极研究的主题。本文展示了CSP在一类重要的非亚伯群体中的多项式时间解决方案，即外部$ p $群体。为此，为了进一步的结果，我们在某些类型的中央产品中提供了CSP的减少。我们的结果的后果实际上与将几个群体排除为平台有关，因为几个非亚伯群是通过使用直接和中央产品组合较小的组来构建的。
In the recently emerging field of group-based cryptography, the Conjugacy Search Problem (CSP) has gained traction as a non-commutative replacement of the Discrete Log Problem (DLP). The problem of finding a secure class of nonabelian groups for use as platforms is open and a subject of active research. This paper demonstrates a polynomial time solution of the CSP in an important class of nonabelian groups, the extraspecial $p$-groups. For this purpose, and as a further result, we provide a reduction of the CSP in certain types of central products. The consequences of our results are practically relevant for ruling out several groups as platforms, since several nonabelian groups are constructed by combining smaller groups by taking direct and central products.
