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 2: Coding theory and cryptography
Time:
Tuesday, 09/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)

 

Privacy and lifted codes

Ragnar Freij-Hollanti
Aalto University

For any linear code and abstract simplicial complex on the same ground set, we define the lift of the linear code to be the smallest code whose projection to any simplex agrees with that of the original code. The motivation for this construction comes from private information retrieval (PIR), and in particular from the so-called star-product schemes for PIR from coded storage systems with colluing servers. We study the basic combinatorial and algebraic properties of the lifted code, and relate the PIR rate of a star product scheme to the quotient of a lifted code modulo its underlying code.

 

Decoding of 2D convolutional codes

Raquel Pinto
University of Aveiro

In this talk, we present a decoding algorithm for 2D convolutional codes over the erasure channel. This algorithm breaks down the decoding of the 2D convolutional code to several decoding steps with 1D convolutional codes. Moreover, we present constructions of codes, which are especially suitable for this algorithm.

 

On the computation of the duals of certain Algebraic Geometric codes with an application to quantum codes

Fernando Hernando
Universidad Jaume I

We consider a family of smooth projective and absolutely irreducible plane curves over $mathbb{F}_q$. We compute the number of rational points and a canonical divisor for it. Thanks to it we can deduce when the associated algebraic geometric code is self-orthogonal and construct stabilizer quantum codes. This work was inspired by the work titled " Quantum error-correcting codes from Algebraic Geometry codes of Castle type."

 

Generalization of the ball-collision algorithm

Violetta Weger
University of Zurich

Since 1978 it is known that decoding a random linear code is an NP-complete problem, this was shown by Berlekamp, McEliece and van Tilburg. One of the methods to decode a random linear code is called Information Set Decoding (ISD). Many improvements for the ISD algorithm over the binary field have been suggested, amongst them is the ball-collision algorithm by Bernstein, Lange and Peters. The problem of decoding a random linear code has recently received prominence with the McEliece cryptosystem, since ISD attacks on this cryptosystem determine the choices of secure parameters and hence the key size. Since some of the new variants of the McEliece cryptosystem involve codes over general finite fields, we present in this talk the generalization of the ball-collision algorithm to an arbitrary finite field.