# Discrete Mathematics

## Organisatieprofiel

### Introductie / missie

Discrete Mathematics is concerned with finite structures and their properties. It is an exciting growth area in the modern information age. Just as continuous mathematics led to major scientific developments in the 19th and 20th century, Discrete Mathematics with its various subfields such as algebra, combinatorics, computational algebra, coding theory, cryptography, discrete optimization, information theory, geometry, graph theory, machine learning, number theory, etc., underlies much of the developments in modern fields such as computer technology, communication networks and e-commerce.

### Highlighted phrase

The cluster Discrete Mathematics is interested in all mathematical problems of a discrete nature

### Organisatieprofiel

form the DM cluster

Cryptology is the mathematical theory of protecting information against unauthorized access (confidentiality), ensuring that a message has not been altered by a third party (integrity) and really originated from the person who is claimed to be the sender (authenticity). Work in the groups in DM covers the design of systerms as well as building larger constructions and protocols, including multi-party computation. Moreover, different groups work on analyzing the security of cryptographic schemes using cryptanalysis techniques (analyzing the underlying mathematical problems) and security proofs (relating the security of schemes and protocols to the security of used building blocks). To ensure correctness of security proofs, groups also work on applying tools from formal verification to verify proofs.

Mathematical communication theory enables reliably communicating data over a possibly noisy channel, efficiently storing and retrieving them, and guaranteeing their integrity. Work in the groups in DM covers coding theory, optimization for data storage and recovery, network coding, quantum error correction, and links with cryptography in code-based cryptography, an area of post-quantum cryptography.

The third main area in DM covers discrete algebra and geometry including ,enumerative and algebraic combinatorics. 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.

Publications of the DM cluster can be accessed by clicking on All publications

## Vingerafdruk

Verdiep u in de onderzoeksgebieden waarop Discrete Mathematics actief is. Deze onderwerplabels komen uit het werk van de leden van deze organisatie. Samen vormen ze een unieke vingerafdruk.

## Samenwerkingen en hoofdonderzoeksgebieden uit de afgelopen vijf jaar

Recente externe samenwerking op landen-/regioniveau. Duik in de details door op de stippen te klikken of
• ### KNAW Early Career Award

Ravagnani, A.

14/02/2213/02/26

Project: Third tier

• ### Batch Signatures, Revisited.

Melchor, C. A., Albrecht, M. R., Bailleux, T., Bindel, N., Howe, J., Hülsing, A., Joseph, D. & Manzano, M., 2024, Topics in Cryptology – CT-RSA 2024 - Cryptographers’ Track at the RSA Conference 2024, Proceedings. Oswald, E. (redactie). blz. 163-186 24 blz. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); vol. 14643 LNCS).

• ### Densities of Codes of Various Linearity Degrees in Translation-Invariant Metric Spaces

Gruica, A., Horlemann, A-L., Ravagnani, A. & Willenborg, N., mrt. 2024, 92, 3, blz. 609-637 29 blz.

Open Access
Bestand
1 Citaat (Scopus)
• ### Density and Combinatorial Structure of Error-Correcting Codes

Gruica, A., 4 apr. 2024, Eindhoven: Eindhoven University of Technology. 209 blz.

Onderzoeksoutput: ScriptieDissertatie 1 (Onderzoek TU/e / Promotie TU/e)

Open Access
Bestand
• ### Algorithms for coping with uncertainty and intractability

Bansal, N. (Ontvanger), 2013

Prijs: ERCConsolidatorWetenschappelijk

• ### Ambizione Research Grant

Ravagnani, Alberto (Ontvanger), 2019

Prijs: AndersOverigWetenschappelijk

• ### A solid theory for post-quantum cryptography

Hülsing, Andreas T. (Ontvanger), 2019

Prijs: NWOVidiWetenschappelijk

• ### Editor in Chief for IACR Communications in Cryptology

Andreas T. Hülsing (Ontvanger)

2023 → …

Activiteit: Types andere activiteitenOverigeWetenschappelijk

• ### Mixed-Integer Programming Techniques for the Connected Max-k-Cut Problem

Christopher Hojny (Spreker)

4 jun. 2020

Activiteit: Types gesprekken of presentatiesGenodigd sprekerWetenschappelijk

• ### Multi-league scheduling; how to schedule thousands of matches

Roel Lambers (Spreker)

13 jan. 2020

Activiteit: Types gesprekken of presentatiesAangemelde presentatieWetenschappelijk

• ### TU/e Researchers Awarded NWO Veni Grants for Innovative Studies in Diverse Fields

4/08/23

1 item van Media-aandacht

Pers / media: Vakinhoudelijk commentaar

• ### Asymptotics of degrees and ED degrees of Segre products

Jan Draisma

25/08/21

1 item van Media-aandacht

Pers / media: Vakinhoudelijk commentaar

• ### Data anonymization in the context of the Israel-Pfizer Agreement

Tomer Ashur

24/01/2125/01/21

2 Mediabijdrages

Pers / media: Vakinhoudelijk commentaar

• ### Accountability and Access Control using Anonymous Credentials

Auteur: Godtschalk, L. J. D., 14 dec. 2022

Begeleider: Schoenmakers, L. A. M. (Afstudeerdocent 1)

Scriptie/Masterproef: Master

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

Auteur: Oostendorp, M. G. C., 31 aug. 2018

Begeleider: Cuypers, F. G. M. T. (Afstudeerdocent 1)

Scriptie/Masterproef: Master

Bestand
• ### Achieving differential privacy in secure multiparty computation

Auteur: Thissen, K. K. A., 15 mei 2019

Begeleider: Schoenmakers, B. (Afstudeerdocent 1), Koster, R. P. (Externe persoon) (Externe coach) & van Liesdonk, P. P. (Externe coach)

Scriptie/Masterproef: Master

Bestand