论文标题
单体类别，表示差距和密码学
Monoidal categories, representation gap and cryptography
论文作者
论文摘要
线性分解攻击为直接在密码学中直接应用非交通性群体和单体（或半群）的应用提供了严重的障碍。为了克服这个问题，我们建议在论文中精确地看着只有很大表示的单型，并对此类单型物进行了系统的研究。我们的主要工具之一是格林的细胞理论（格林的关系）。 大量的单体供应由单体类别传递。我们考虑了图解起源的单体类别的简单示例，包括Temperley-Lieb，Brauer和分区类别，并讨论其表示的下限。
The linear decomposition attack provides a serious obstacle to direct applications of noncommutative groups and monoids (or semigroups) in cryptography. To overcome this issue we propose to look at monoids with only big representations, in the sense made precise in the paper, and undertake a systematic study of such monoids. One of our main tools is Green's theory of cells (Green's relations). A large supply of monoids is delivered by monoidal categories. We consider simple examples of monoidal categories of diagrammatic origin, including the Temperley-Lieb, the Brauer and partition categories, and discuss lower bounds for their representations.
