Conference Agenda

Overview and details of the sessions of this conference. Please select a date or location to show only sessions at that day or location. Please select a single session for detailed view (with abstracts and downloads if available).

 
Session Overview
Session
MS134, part 5: Coding theory and cryptography
Time:
Thursday, 11/Jul/2019:
3:00pm - 5:00pm

Location: Unitobler, F-122
52 seats, 100m^2

Presentations
3:00pm - 5:00pm

Coding theory and cryptography

Chair(s): Alessio Caminata (University of Neuchâtel, Switzerland), Alberto Ravagnani (University College Dublin, Ireland)

The focus of this proposal is on coding theory and cryptography, with emphasis on the algebraic aspects of these two research fields. Error-correcting codes are mathematical objects that allow reliable communications over noisy/lossy/adversarial channels. Constructing good codes and designing efficient decoding algorithms for them often reduces to solving algebra problems, such as counting rational points on curves, solving equations, and classifying finite rings and modules. Cryptosystems can be roughly defined as functions that are easy to evaluate, but whose inverse is difficult to compute in practice. These functions are in general constructed using algebraic objects and tools, such as polynomials, algebraic varieties, and groups. The security of the resulting cryptosystem heavily relies on the mathematical properties of these. The sessions we propose feature experts of algebraic methods in coding theory and cryptography. All levels of experience are represented, from junior to very experienced researchers.

 

(25 minutes for each presentation, including questions, followed by a 5-minute break; in case of x<4 talks, the first x slots are used unless indicated otherwise)

 

Classifications of some partial MDS codes

Anna-Lena Horlemann-Trautmann
University of St. Gallen

Partial MDS codes are optimal locally recoverable codes, used for distributed storage systems. We will present some classification results of these codes for certain parameter sets. One of these results gives a relation to classical MDS codes, from which we can derive results about the neccessary minimal field size for the existence of these codes. The second classification gives a relation to projective lines in general position and hence a geometric point of view for these codes.

 

Batch properties of Affine Cartesian Codes

Felice Manganiello
Clemson University

Batch codes were introduced by Ishai et al. in 2004 and are useful for information retrieval. In this seminar we examine the properties of affine cartesian codes as batch codes. Starting from their local properties, we deduce a partition of the evaluation points into buckets that allows multiple independent users to simultaneously retrieve information.

 

Improved quantum codes from the Hermitian curve

Olav Geil
Aalborg University

We apply the CSS construction and Steane's enlargement to construct quantum codes from the Hermitian curve. Using improved information on the classical minimum distances of the involved nested codes and employing improved code constructions we obtain quantum codes that are much better than what could be obtained by using only one-point algebraic geometric codes in combination with the Goppa bound. We construct both asymmetric and symmetric codes. Our work includes closed formula estimates on the dimension of order bound improved Hermitian codes. This is joint work with René Bødker Christensen.

 

Concatenated constructions of LCD and LCP of codes

Cem Güneri
Sabancı University

Linear complementary dual (LCD) codes are codes which intersect their dual trivially. These codes, and their generalizations called linear complementary pair (LCP) of codes, have drawn attention lately due to their applications in the context of side channel and fault injection attacks in cryptography. It is known that LCD codes have higher density in the family of all linear codes when the alphabet size is large. So, using such codes over large finite fields (extension field) to obtain similar codes over small finite fields (base field) is a reasonable strategy. In this respect, concatenation is a natural technique to try, although finding concatenations that preserve LCD or LCP properties of codes over an extension, when descending to the base field, is a nontrivial problem. The problem of interest in this talk is to find such suitable concatenations. Results we will present have been obtained in joint works with Carlet, Özbudak, Saçıkara and Solé.