Algebra and Discrete Mathematics
Welcome to the home page of the research area of
Algebra and Discrete Mathematics at Aalto University. Our members conduct research in areas that include algebraic geometry, algebraic statistics, combinatorics, coding theory, cryptography, Lie theory, matrix theory, number theory, and representation theory.
Members
Faculty
Algebra and algebraic geometry
Coding theory and cryptography
Combinatorics
Lie theory and representation theory
Number theory
News
- Rahinatou Yuh Njah Nchiwo won the 3 Minute Thesis competition at the Finnish Quantum Days in September 2024.
- Oscar Kivinen started as an Assistant Professor in September 2023.
Prospective students
Research
We provide
bachelor's,
master's and
doctoral theses topics related to the above areas. The links contain lists of current topics and past theses. Contact the faculty and check their personal webpages for more info.
You are also welcome to take part in any of our
lecture courses related to algebra and discrete mathematics.
Recent publications
Here is the
research output for the Algebra and Discrete Mathematics area. On this site you can also find the research output of individuals and links to full texts of articles when available. For preprints check the
math arxiv and individual homepages.
Scientific events
Seminars
Upcoming seminars
- 9.10. 15:15 Prof. Iván Blanco Chacón (U. Alcalá): The LAC cryptosystem. A realistic alternative to Kyber? – M3 (M234)
We discuss the LAC cryptosystem, which was presented to the NIST contest and although discarded in the outcome of the third round, was seriously considered as a rival for Kyber and is recently regaining attention from other different public committees.
One of the main features of LAC is the small modulus size, which is taken of the order of bytes, in comparison with Kyber, where q is at least 3329. This fact renders LAC one of the most compact cryptosystems, suitable to be used for small devices and with the same reduction security warranties as other RLWE-based schemes. However, the smallness of q brings an extra difficulty: the absence of NTT, which implies an obvious decrease in efficiency. This is overcome by the use of error correction in the cyphertext.
As proved by the authors, LAC outperforms Kyber at 128 and 256 bits security levels in terms of key size and cyphertext size while remaining more geneours in the security margin. It is true that these security levels are not recommended nowadays by NIST anymore, but the authors also suggested that LAC-192-v3b may be considered to achieve NIST Security Level 5 since it outperforms Kyber 1024 at this level. The goal of this talk is to report about this claim after the introduction of the foundations of the cryptosystem.
- 10.10. 12:00 Okko Makkonen: PhD Defence: Algebraic methods for secure coded computing (further info) – M1 (M232)
- 14.10. 15:15 Prof. Gretchen Matthews (Virginia Tech): Colloquium talk (TBA) – M1 (M232)
Algebra and Discrete Mathematics at Aalto is supported by
Page content by: webmaster-math [at] list [dot] aalto [dot] fi
