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 3: Coding theory and cryptography
Time:
Wednesday, 10/Jul/2019:
10:00am - 12:00pm

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

Presentations
10:00am - 12:00pm

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)

 

Linear Complementary Pair of Codes and Some Results on Boolean Functions

Ferruh Özbudak
Middle East Technical University, Ankara

This talk consists of two parts. In the first part we explain some constructions on linear complementary pair of codes and some applications to cryptography. In the second part we present some recent results on constructions and on counting certain functions related to Boolean functions. This talk presents some joint works including a number of colleagues, who will be cited in the talk.

 

Optimal Locally Recoverable Codes via Chebotarev Density Theorem

Giacomo Micheli
EPFL

We provide a Galois theoretical framework which allows to produce good polynomials for the Tamo and Barg construction of optimal locally recoverable codes (LRC). Our approach allows to prove existence results and to construct new good polynomials, which in turn allows to build new LRCs. The existing theory of good polynomials fits in our new framework.

 

Explicit optimal-length locally repairable codes of small distances

Hiram H. Lopez Valdez
Cleveland State University

Locally repairable codes (LRCs) have received significant recent attention as a method of designing data storage systems robust to server failure. Optimal LRCs offer the ideal trade-off between minimum distance and locality, a measure of the cost of repairing a single codeword symbol. For optimal LRCs with minimum distance greater than or equal to 5, block length is bounded by a polynomial function of alphabet size. In this talk, we give explicit constructions of optimal length (in terms of alphabet size), optimal LRCs with small minimum distances.

 

Fast Computation of the Roots of Polynomials Over the Ring of Power Series

Eric Schost
University of Waterloo

We give an algorithm for computing all roots of polynomials over a univariate power series ring over a field K. Given a precision d and a polynomial Q whose coefficients are power series in x, the algorithm computes a representation of all power series f(x) such that Q(f(x)) = 0 mod x^d. The algorithm works unconditionally, in particular also with multiple roots, where Newton iteration fails.

The cost bound for our algorithm matches the worst-case input and output size d deg(Q), up to logarithmic factors. This improves upon previous algorithms which were quadratic in at least one of d and deg(Q). Our algorithm is a refinement of a divide-and-conquer algorithm by Alekhnovich (2005), where the cost of recursive steps is better controlled via the computation of a factor of Q which has a smaller degree while preserving the roots.