Projects per year
Organisation profile
Introduction / mission
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 ecommerce.
Highlighted phrase
The cluster Discrete Mathematics is interested in all mathematical problems of a discrete nature
Organisational profile
Applied and Provable Security
Coding Theory and Cryptology
Discrete Algebra and Geometry
Mathematical Communication Theory
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 multiparty 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 codebased cryptography, an area of postquantum 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 discretealgebraic 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
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Collaborations and top research areas from the last five years
Profiles

Gianira Alfarano
 Mathematics and Computer Science, Mathematical Communication Theory  University Researcher
Person: OWP : University Teacher / Researcher

Jacob R. Appelbaum
Person: PD : Postdoc

Elena Berardini
 Mathematics and Computer Science, Mathematical Communication Theory  University Researcher
Person: OWP : University Teacher / Researcher
Projects
 1 Active

Batch Signatures, Revisited.
Melchor, C. A., Albrecht, M. R., Bailleux, T., Bindel, N., Howe, J., Hülsing, A., Joseph, D. & Manzano, M., 2023, In: IACR Cryptology ePrint Archive. 2023, p. 492 1 p.Research output: Contribution to journal › Article › Academic

Cryptanalysis of Strong Physically Unclonable Functions
Kraleva, L., Mahzoun, M., Posteuca, R., Toprakhisar, D., Ashur, T. & Verbauwhede, I., 2023, In: IEEE Open Journal of the SolidState Circuits Society. 3, p. 3240 9 p., 9971721.Research output: Contribution to journal › Article › Academic › peerreview
Open AccessFile9 Downloads (Pure) 
Densities of Codes of Various Linearity Degrees in TranslationInvariant Metric Spaces
Gruica, A., Horlemann, AL., Ravagnani, A. & Willenborg, N., 23 May 2023, (Epub ahead of print) In: Designs, Codes and Cryptography. XX, XResearch output: Contribution to journal › Article › Academic › peerreview
Open AccessFile1 Downloads (Pure)
Prizes

Algorithms for coping with uncertainty and intractability
Bansal, N. (Recipient), 2013
Prize: ERC › Consolidator › Scientific


A solid theory for postquantum cryptography
Hülsing, Andreas T. (Recipient), 2019
Prize: NWO › Vidi › Scientific
Activities

MixedInteger Programming Techniques for the Connected MaxkCut Problem
Christopher Hojny (Speaker)
4 Jun 2020Activity: Talk or presentation types › Invited talk › Scientific

Multileague scheduling; how to schedule thousands of matches
Roel Lambers (Speaker)
13 Jan 2020Activity: Talk or presentation types › Contributed talk › Scientific

Symretopes and Symresacks: A Framework for Deriving Generic and Problem Specific Symmetry Handling Inequalities
Christopher Hojny (Speaker)
9 Dec 2019Activity: Talk or presentation types › Invited talk › Scientific
Press/Media

Asymptotics of degrees and ED degrees of Segre products
25/08/21
1 item of Media coverage
Press/Media: Expert Comment

Data anonymization in the context of the IsraelPfizer Agreement
Tomer Ashur
24/01/21 → 25/01/21
2 Media contributions
Press/Media: Expert Comment

Fast, Furious and Insecure: Passive Keyless Entry and Start in Modern Supercars
Tomer Ashur
10/09/18 → 27/08/19
2 items of Media coverage
Press/Media: Research
Student theses

Accountability and Access Control using Anonymous Credentials
Author: Godtschalk, L. J. D., 14 Dec 2022Supervisor: Schoenmakers, L. A. M. (Supervisor 1)
Student thesis: Master
File 
A characterization of the special linear and unitary Lie algebra via its extremal geometry
Author: Oostendorp, M. G. C., 31 Aug 2018Supervisor: Cuypers, F. G. M. T. (Supervisor 1)
Student thesis: Master
File 
Achieving differential privacy in secure multiparty computation
Author: Thissen, K. K. A., 15 May 2019Supervisor: Schoenmakers, B. (Supervisor 1), Koster, R. P. (External person) (External coach) & van Liesdonk, P. P. (External coach)
Student thesis: Master
File