# Monoidal categories, representation gap and cryptography

arXiv: https://arxiv.org/abs/2201.01805 · HTML: https://mlsanity.com/paper/2201.01805/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Jan 2022.

## Built on by (most cited first, 2 of 2)

- [Big data comparison of quantum invariants](https://mlsanity.com/paper/2503.15810/) (2025)
- [On knot detection via picture recognition](https://mlsanity.com/paper/2510.06284/) (2025)

## Abstract (arXiv)

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.