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.

翻译：线性分解攻击对非交换群和幺半群（或半群）在密码学中的直接应用构成了严重障碍。为克服这一问题，我们提出关注仅具有大表示的幺半群（其确切含义在本文中阐明），并对这类幺半群开展系统性研究。我们的主要工具之一是格林胞腔理论（格林关系）。幺半范畴为研究者提供了丰富的幺半群实例。我们考察了图式起源的简单幺半范畴实例，包括Temperley-Lieb范畴、Brauer范畴和分拆范畴，并讨论了其表示的下界。