Project

Finite Geometry, Coding Theory and Cryptography

Code
W003224N
Duration
01 January 2024 → 31 December 2028
Funding
Research Foundation - Flanders (FWO)
Promotor-spokesperson
Research disciplines
  • Natural sciences
    • Number theory
    • Convex and discrete geometry
    • Combinatorics
    • Computer system security
    • Cryptography, privacy and security
    • Applied discrete mathematics
    • Coding and information theory
Keywords
Finite geometry coding theory cryptography
 
Project description

Coding theory and cryptography are two interacting research areas, of great relevance for our modern society. More and more information is transmitted via computers, often via wireless networks. The increase in transmitted data continuously asks for better codes and for better cryptographical techniques to ensure a correct and secure transmission of the information. Coding theory constructs codes for the transmission of information through a communication channel in which errors can occur during transmission, and develops techniques to detect and correct transmission errors. All of us use codes in mobile phones, in wireless networks, but at the same time, we all use cryptographical systems. Cryptography develops encryption and decryption techniques to transmit confidential information in a secure way. Thus both research areas concern the transmission of information, but the connection between them goes much further than this high-level connection. Indeed, there is a long-standing history of mutual influence and stimulation. Examples include: (1) the use of a linear MDS code within AES (which is the world-wide standard for encryption), (2) Code-based cryptography which uses error-correcting codes to build cryptographic systems that can withstand attacks by large-scale quantum computers, and (3) the use of error-correcting codes to realize certain access structures within multi-party computation. This Scientific Research Network will investigate research problems in new research domains of coding theory and cryptography which are of relevance for our current society. This includes the new research domain Random Network Coding which investigates problems regarding the transmission of information via wireless networks. In the transmission protocol of Random Network Coding, network nodes transmit linear combinations of incoming packages. Simulations have proven that this speeds up the transmission of the information. To describe this mathematically, codewords are identified with subspaces of vector spaces over finite fields. That is why the corresponding codes are called subspace codes, and this is also why so many problems on subspace codes are equivalent to geometrical problems of Finite Geometry. This is why Finite Geometry is the third main aspect of this Scientific Research Network.