# Monoidal categories, representation gap and cryptography

@article{Khovanov2022MonoidalCR, title={Monoidal categories, representation gap and cryptography}, author={Mikhail Khovanov and Maithreya Sitaraman and Daniel Tubbenhauer}, journal={ArXiv}, year={2022}, volume={abs/2201.01805} }

The linear decomposition attack provides a serious obstacle to direct applications of noncommutative groups and monoids 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…

## 2 Citations

### IntroSurvey of Representation Theory

- MathematicsJournal of the Indian Institute of Science
- 2022

There could be thousands of Introductions/Surveys of representation theory, given that it is an enormous field. This is just one of them, quite personal and informal. It has an increasing level of…

### Sandwich cellularity and a version of cell theory

- Mathematics
- 2022

. We explain how the theory of sandwich cellular algebras can be seen as a version of cell theory for algebras. We apply this theory to many examples such as Hecke algebras, and various monoid and…

## References

SHOWING 1-10 OF 109 REFERENCES

### SL2 tilting modules in the mixed case

- Mathematics
- 2021

Using the non-semisimple Temperley–Lieb calculus, we study the additive and monoidal structure of the category of tilting modules for SL2 in the mixed case. This simultaneously generalizes the…

### A Survey of Graphical Languages for Monoidal Categories

- Mathematics
- 2010

This article is intended as a reference guide to various notions of monoidal categories and their associated string diagrams. It is hoped that this will be useful not just to mathematicians, but also…

### On the irreducible representations of a finite semigroup

- Mathematics
- 2007

Work of Clifford, Munn and Ponizovskii parameterized the irreducible representations of a finite semigroup in terms of the irreducible representations of its maximal subgroups. Explicit constructions…

### Combinatorial Group Theory and Public Key Cryptography

- Mathematics, Computer ScienceApplicable Algebra in Engineering, Communication and Computing
- 2006

This paper addresses the following questions: whether choosing a different group, or a class of groups, can remedy the situation, and whether some other “hard” problem from combinatorial group theory can be used, instead of the conjugacy search problem, in a public key exchange protocol.

### CELLULAR STRUCTURES USING Uq-TILTING MODULES

- Mathematics
- 2017

We use the theory of Uq-tilting modules to construct cellular bases for centralizer algebras. Our methods are quite general and work for any quantum group Uq attached to a Cartan matrix and include…

### New Public-Key Cryptosystem Using Braid Groups

- Computer Science, MathematicsCRYPTO
- 2000

The aim of this article is to show that the braid groups can serve as a good source to enrich cryptography and to propose and implement a new key agreement scheme and public key cryptosystem based on these primitives in thebraid groups.

### Finitary birepresentations of finitary bicategories

- MathematicsForum Mathematicum
- 2021

Abstract In this paper, we discuss the generalization of finitary 2-representation theory of finitary 2-categories to finitary birepresentation theory of finitary bicategories. In previous papers on…

### Non-Commutative Cryptography and Complexity of Group-Theoretic Problems

- Mathematics, Computer Science
- 2011

This book explores how non-commutative (infinite) groups, which are typically studied in combinatorial group theory, can be used in public-key cryptography and describes new interesting developments in the algorithmic theory of solvable groups.

### Two-color Soergel Calculus and Simple Transitive 2-representations

- MathematicsCanadian Journal of Mathematics
- 2019

Abstract In this paper, we complete the ADE-like classification of simple transitive 2-representations of Soergel bimodules in finite dihedral type, under the assumption of gradeability. In…