Research Output per year

# Organization profile

### Introduction / mission

The three chairs within DM maintain the three main research areas: the more applied coding theory and cryptology; the combinatorial optimization which goes into problems in operational management; and the more fundamental discrete algebra and geometry.

### Highlighted phrase

The section DM is interested in all mathematical problems of a discrete nature.

### Organisational profile

**The section DM has three chairs:**

The chair for **Coding Theory and Cryptology (CC)** performs research in theoretical and applied areas of both topics:

**Coding Theory** is the mathematical theory of encoding information in such a way that it becomes resistant to transmission errors. The main topics are the study of the properties of various codes (cyclic codes, BCH-codes, MDS-codes, algebraic-geometric codes) and the construction of efficient decoding algorithms for these codes.

**Cryptology** is the mathematical theory of protecting information against unauthorized access (privacy), determining if a message has been altered by a third party (integrity), adding a signature to an electronic document and verifying the identity.

The **Combinatorial Optimization (CO)** group focuses on the analysis and solution of discrete algorithmic problems that are computationally difficult (NP-hard). A generic formulation of such problems is: given a number of boundary conditions and constraints, find a solution that minimizes the cost or maximizes the profit.

Phenomena throughout mathematics and the natural sciences have discrete algebraic aspects, often along with analytical counterparts. While the latter are typically modelled using real numbers, differential equations, and numerical computations, describing the discrete-algebraic aspects involves objects like nite elds, graphs, polynomials, groups, algebras, and symbolic computations. The **Discrete Algebra and Geometry (DAG)** group at the TU/e develops the mathematics needed for such a description.

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## Profiles

## Jacob R. Appelbaum

- Department of Mathematics and Computer Science, Discrete Mathematics - Doctoral Candidate
- Department of Mathematics and Computer Science, Discrete Mathematics W&I - Doctoral Candidate

Person: Prom. : doctoral candidate (PhD)

## Tomer Ashur

- Department of Mathematics and Computer Science, Discrete Mathematics - Assistant Professor

Person: UD : Assistant Professor

## Nikhil Bansal

- Department of Mathematics and Computer Science, Combinatorial Optimization
- Department of Mathematics and Computer Science, Discrete Mathematics W&I - Full Professor
- Department of Mathematics and Computer Science, Discrete Mathematics - Full Professor

Person: HGL : Professor

## Research Output 1973 2019

## An algorithm for komlós conjecture matching Banaszczyk's bound

Bansal, N., Dadush, D. & Garg, S., 30 Apr 2019, In : SIAM Journal on Computing. 48, 2, p. 534-553 20 p.Research output: Contribution to journal › Article › Academic › peer-review

## Application of complementary dual AG codes to entanglement-assisted quantum codes

Fernandes Pereira, F., Pellikaan, R., Gadioli La Guardia, G. & de Assis, F. M., 2019, (Accepted/In press)*Proceedings of the IEEE International Symposium on Information Theory.*Piscataway: Institute of Electrical and Electronics Engineers

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

## A reaction attack against cryptosystems based on LRPC codes

Samardjiska, S., Santini, P., Persichetti, E. & Banegas, G., 2019,*Progress in Cryptology -- LATINCRYPT 2019.*Schwabe, P. & Thériault, N. (eds.). Cham: Springer International Publishing Switzerland, p. 197-216 20 p. (Lecture Notes in Computer Science; vol. 11774)

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

## Prizes

## Algorithms for coping with uncertainty and intractability

Nikhil Bansal (Recipient), 2013

Recognition: ERC › Consolidator › Scientific

## Best investigative reporting

Jacob Appelbaum (Recipient), 2014

Recognition: Other › Career, activity or publication related prizes (lifetime, best paper, poster etc.) › Scientific

## Best Paper Award at IH&MMSec 2015

Thijs Laarhoven (Recipient), 19 Jun 2015

Recognition: Other › Career, activity or publication related prizes (lifetime, best paper, poster etc.) › Scientific

## Activities 2014 2019

## Strong IP Formulations Need Large Coefficients

Christopher Hojny (Speaker)Activity: Talk or presentation types › Contributed talk › Scientific

## Symmetry Handling in Binary Programs: Combining Symretopes and Orbital Fixing

Christopher Hojny (Speaker)Activity: Talk or presentation types › Invited talk › Scientific

## Strong IP Formulations Need Large Coefficients

Christopher Hojny (Speaker)Activity: Talk or presentation types › Invited talk › Scientific

## Press / Media

## Fast, Furious and Insecure: Passive Keyless Entry and Start in Modern Supercars

10/09/18 → 27/08/19

2 items of media coverage

Press/Media: Research

## Post-Quanten-Kryptographie — Wenn Ihre Daten auch in Zukunft Geheimnisse bleiben sollen

7/09/18

1 media contribution

Press/Media: Expert Comment

## Dutch report finds cybersecurity not keeping up with growing number of attacks

24/04/18

1 item of media coverage

Press/Media: Expert Comment

## Student theses

## A characterization of the special linear and unitary Lie algebra via its extremal geometry

Author: Oostendorp, M., 31 Aug 2018Supervisor: Cuypers, F. (Supervisor 1)

Student thesis: Master

## Achieving differential privacy in secure multiparty computation

Author: Thissen, K., 15 May 2019Supervisor: Schoenmakers, B. (Supervisor 1), Koster, R. (. (External person) (External coach) & van Liesdonk, P. (External coach)

Student thesis: Master

## An adaption of the crossbred algorithm for solving multivariate quadratic systems over F2 on GPUs

Author: Ning, K., 27 Nov 2017Supervisor: Lange, T. (Supervisor 1), Bernstein, D. (External coach) & Niederhagen, R. (External coach)

Student thesis: Master