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Algebraic Constructions and Decoding of Subspace Codes

English title Algebraic Constructions and Decoding of Subspace Codes
Applicant Rosenthal Joachim
Number 149716
Funding scheme Project funding
Research institution Institut für Mathematik Universität Zürich
Institution of higher education University of Zurich - ZH
Main discipline Mathematics
Start/End 01.10.2013 - 30.09.2016
Approved amount 285'780.00
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All Disciplines (3)

Discipline
Mathematics
Information Technology
Electrical Engineering

Keywords (4)

Grassmann variety; Coding Theory; Network Codes; Finite Projective Geometries

Lay Summary (German)

Lead
Heute werden oft Informationen über ganze Netzwerke übermittelt und abgespeichert. Ziel des Projektes ist dieEntwicklung besserer Codierungsmethoden welcheFehler entdeckt und auch korrigieren kann. Fortschrittein dieser Forschung wird Auswirkungen auf die nexten Generationenvon kommunikationssystemen haben.
Lay summary

Codierungstheorie befasst sich mit der Beschreibung von Information in einer Weise welche  das Entdecken und das Korrigieren von Fehlern gewährt so lange die Anzahl der Fehler nicht zu gross ist. Traditionelle Kommunikationssysteme betrachteten den Informationsfluss zwischen zwei Parteien  und traditionelle Codierungstheorie beschäftigte sich mit Codierungsmethoden für solche Systeme.

Moderne Kommunikationssysteme und Speichersysteme machen oft Gebrauch von einem ganzen Netzwerk  von Übertragungsstationen. Es kommen oft auch Szenarien vor wo eine Partei Information über eine Vielzahl von Übertragungsstationen an eine Vielzahl von Empfängern schickt. Zum Beispiel ist die TV Übertragung über das Internet und das Handy-Netz von dieser Natur. Mit der Technik von Netzwerk Codierung versuchen Forscher Methoden zu entwickeln welche garantieren dass Fehler entdeckt und korrigiert werden. Die angewandte Algebragruppe der Universität Zürich entwickelt neue Codierungsmethoden für die Netzwerk Übertragung. Die Forschungsgruppe ist dabei auch in ein grösseres europäisches Projekt eingebunden.

Siehe: http://www.network-coding.eu/

 

Direct link to Lay Summary Last update: 08.10.2013

Responsible applicant and co-applicants

Employees

Publications

Publication
Extension of Overbeck’s attack for Gabidulin-based cryptosystems
Horlemann-Trautmann Anna-Lena, Marshall Kyle, Rosenthal Joachim (2018), Extension of Overbeck’s attack for Gabidulin-based cryptosystems, in Designs, Codes and Cryptography, 86(2), 319-340.
On the genericity of maximum rank distance and Gabidulin codes
Neri Alessandro, Horlemann-Trautmann Anna-Lena, Randrianarisoa Tovohery, Rosenthal Joachim (2018), On the genericity of maximum rank distance and Gabidulin codes, in Designs, Codes and Cryptography, 86(2), 341-363.
An active attack on a multiparty key exchange protocol
Schnyder Reto, Lopez-Ramos Juan Antonio, Rosenthal Joachim, Schipani Davide, Schnyder Reto, Lopez-Ramos Juan Antonio, Rosenthal Joachim, Schipani Davide (2016), An active attack on a multiparty key exchange protocol, in Journal of Algebra Combinatorics Discrete Structures and Applications, 31-36.
Considerations for Rank-based Cryptosystems
Horlemann-Trautmann Anna-Lena, Marshall Kyle, Rosenthal Joachim (2016), Considerations for Rank-based Cryptosystems, in 2016 IEEE International Symposium on Information Theory (ISIT), 2544-2548.
Eisenstein polynomials over function fields
Dotti Edoardo, Giacomo Micheli, Dotti Edoardo, Giacomo Micheli (2016), Eisenstein polynomials over function fields, in Applicable Algebra in Engineering, Communication and Computing, 27(2), 159-168.
Group key management based on semigroup actions
Lopez-Ramos Juan Antonio, Rosenthal Joachim, Schipani Davide, Schnyder Reto, Lopez-Ramos Juan Antonio, Rosenthal Joachim, Schipani Davide, Schnyder Reto (2016), Group key management based on semigroup actions, in Journal of Algebra and Its Applications, 16(8), 1750148-1-1750148-17.
Subspace Fuzzy Vault
Davide Schipani Anna-Lena Joachim Rosenthal, Marshall Kyle, Schipani Davide, Trautmann Anna-Lena, Rosenthal Joachim, Davide Schipani Anna-Lena Joachim Rosenthal, Marshall Kyle, Schipani Davide, Trautmann Anna-Lena, Rosenthal Joachim (2016), Subspace Fuzzy Vault, in Baldi Marco, Baldi Marco (ed.), Springer International Publishing, Switzerland, 163-172.
Linear spanning sets for matrix spaces
Micheli Giacomo, Rosenthal Joachim, Vettori Paolo, Micheli Giacomo, Rosenthal Joachim, Vettori Paolo (2015), Linear spanning sets for matrix spaces, in Linear Algebra and its Applications, 483, 309-322.

Scientific events

Active participation

Title Type of contribution Title of article or contribution Date Place Persons involved
Design and Application of Random Network Codes (DARNEC 15) Talk given at a conference Cryptanalyis of McEliece type Public Key Systems based on Gabidulin Codes 04.11.2015 Istanbul, Turkey Rosenthal Joachim;
SIAM Conference on Applied Algebraic Geometry Talk given at a conference How Grassmannians are relevant in Coding Theory 03.08.2015 Daejon, Korean Republic (South Korea) Rosenthal Joachim;
7th Workshop on Coding and Systems Talk given at a conference Variants of McEliece type Cryptosystems based on Subspace Codes and Rank Metric Codes 01.07.2015 Salamanca, Spain Rosenthal Joachim;
7th Workshop on Coding and Systems Talk given at a conference Subspace codes and symmetric codes 01.07.2015 Salamanca, Spain Randrianarisoa Tovohery Hajatiana;
Algebraic Combinatorics and Applications (ALCOMA 15) Talk given at a conference McEliece type Cryptosystem based on Gabidulin Codes 15.03.2015 Kloster Banz, Germany Rosenthal Joachim;
SPCodingSchool Poster Using Eigenvectors in the McEliece cryptosystems 19.01.2015 Campinas, Brazil Randrianarisoa Tovohery Hajatiana;
Expanders Everywhere Talk given at a conference Codes based on Expander Graphs and Ramanujan Graphs 01.12.2014 Neuchatel, Switzerland Rosenthal Joachim;
4th International Castle Meeting in Coding Theory Talk given at a conference Convolutional Codes over Large Alphabets and their Decoding over the Erasure Channel 15.09.2014 Palmela, Portugal Rosenthal Joachim;
Workshop on Communication Security Talk given at a conference The Semigroup Action Problem, a Cryptographic Primitive to build Asymmetric Cryptographic Protocols 11.09.2014 Ancona, Italy Rosenthal Joachim;
MTNS 2014 Talk given at a conference Limitations of Polynomial-Size List-Decoding of Projective Space Codes 07.07.2014 Groningen, Netherlands Rosenthal Joachim;
2014 European School of Information Theory Poster Using Eigenvectors in the McEliece cryptosystems 14.04.2014 Tallin, Estonia Randrianarisoa Tovohery Hajatiana;
Workshop On Coding and Information Theory Talk given at a conference Subspace Codes and Orbit Codes 11.12.2013 The University of Hong Kong, Hongkong Rosenthal Joachim;


Associated projects

Number Title Start Funding scheme
138080 Algebraic Constructions and Decoding of Network Codes 01.10.2011 Project funding
169510 Algebraic Constructions and Decoding of Rank Metric Codes with Applications to Network Coding and Code based Cryptography 01.10.2016 Project funding
138080 Algebraic Constructions and Decoding of Network Codes 01.10.2011 Project funding
169510 Algebraic Constructions and Decoding of Rank Metric Codes with Applications to Network Coding and Code based Cryptography 01.10.2016 Project funding

Abstract

Coding theory has emerged out of the need for bettercommunication and has rapidly developed as a mathematical theoryin strong relationship with algebra, combinatorics and algebraicgeometry. Nowadays error-correcting-codes are used in everydaypractical applications such as digital-storage media, wire-lineand wireless networks, and satellite and deep-space communicationsystems. Example of simple block codes are the internationalstandard book numbers (ISBN), the ASCII code and various encodingschemes used to identify bank accounts.Network coding theory is concerned with the encoding andtransmission of information where there may be many informationsources and possibly many receivers. R. Kötter andF. Kschischang identified a fundamental mathematicalquestion which lies at the heart of network coding. Thisformulation seeks the construction of good subsets of thefinite Grassmann variety and it is the intended plan of theproposed research to use algebraic techniques to come up with newnetwork codes which have better performance.
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