Workshop on Coding Theory: Engineers meet Mathematicians

Workshop on Coding Theory: Engineers meet Mathematicians
1 - 2 December 2011, Sabancı University Karaköy Communication Center

Program:

Thursday, December 1: 

14:00-14:50: Erdal Arıkan (Bilkent University)--Polar coding 

15:00-15:50: Patrick Solé (Telecom ParisTech)--A new class of codes for Boolean masking of cryptographic computations 

16:00-17:30: Discussion 


Friday, December 2: 

9:30-10:20: Ferruh Özbudak (Middle East Technical University)--Some planar maps, related function fields and semifields 

10:20-10:50: Coffee break 

10:50-11:40: Wolfgang Willems (University of Magdeburg)--Extremal codes: Existence and performance 

This workshop is supported by TUBITAK ISBAP project 107T897 and Sabancı University.


Abstracts:
Erdal Arıkan: Polar coding

Abstract: Polar coding is a provably capacity-achieving coding method with low-complexity encoding and decoding algorithms.This talk will give a tutorial introduction to polar coding and also consider its potential for applications.

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Ferruh Özbudak: "Some Planar maps, related function fields and semifields"

Abstract: Let $\F_q$ be a finite field with $q$ elements, where $q$ is odd.
In this talk we classify {\it $q$-quadratic planar binomials} over $\F_{q3}$ completely. We also give
connections to certain semifields and obtain some results on the related algebraic function fields.

This a report on a joint work with Gohar M. Kyureghyan and Alexander Pott.

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Patrick Solé: A new class of codes for Boolean masking of cryptographic computations (joint work with Claude Carlet, Philippe Gaborit, Jon Lark Kim)

Abstract: We introduce a new class of rate one half binary codes: complementary information set codes.
A binary linear code of length 2n and dimension n is called a complementary information set code
(CIS code for short) if it has two disjoint information sets. This class of codes contains self-dual
codes as a subclass. It is connected to graph correlation immune Boolean functions of use in the
security of hardware implementations of cryptographic primitives. Such codes permit to improve the
cost of masking cryptographic algorithms against side channel attacks. In this paper we investigate this
new class of codes: we give optimal or best known CIS codes of length <132. We derive general
constructions based on cyclic codes and on double circulant codes. We derive a Varshamov-Gilbert
bound for long CIS codes, and show that they can all be classified in small lengths ≤ 12 by the
building up construction. Some nonlinear S-boxes are constructed by using Z4-codes, based on the
notion of dual distance of an unrestricted code.

Keywords: cyclic codes, self-dual codes, S-boxes, dual distance, double circulant codes, Z4-codes
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Wolfgang Willems: Extremal Codes: Existence and Performance

Abstract: In the class of binary self-dual codes the extremal ones are best
since they have the largest possible minimum distance. Thus we are interested
in existence and construction. For mathematicians, doubly-even codes
are of particular interest and have been studied well since they provide a
rich mathematical structure. However, from the point of view of applications
singly-even codes should deserve more attention since they have applications
in cryptography (secret sharing schemes) and perform often better (i.e. the
decoding error probability is smaller) than doubly-even codes if the symbol
error probability of the channel is small enough.

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