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Reed-Solomon-koder i ett McElieceskryptosystem: En kodteoretisk genomgång
Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.
2009 (Swedish)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
Abstract [sv]

Detta arbete är ett examensarbete i matematik på kandidatnivå vid Växjö universitet. Det är en studie av kodningsteori i allmänhet med fokusering på cykliska koder och Reed-Solomon-koder i synnerhet. Reed-Solomon-koderna används för att skapa McElieces kryptosystem. En kortfattad analys av McElieces kryptosystems säkerhet görs tillsammans med en genomgång av kända sätt att forcera denna typ av kryptosystem. Här visar det sig att användning av Reed-Solomon-kod försvagar kryptosystemet i förhållande till om den ursprungligt föreslagna Goppa-koden används. För att kunna göra denna säkerhetsanalys görs också en kortfattad genomgång av komplexitetsteori och vad det innebär att ett problem är NP-fullständigt.

Nyckelord: Kodningsteori, Kodteori, Cykliska koder, BCH-koder, Reed-Solomon-koder, McElieces kryptosystem, Kryptering, Kodforcering, Komplexitetsteori, NP-fullständigt

Abstract [en]

This work is produced on bachelor level in mathematics at University of Växjö. It is a study of coding theory with focus on cyclic codes in general and Reed-Solomon codes in detail. Reed-Solomon codes are used for implementing McEliece's crypto system. A short analysis of McEliece's crypto system security is also made together with a description of some known ways to break this type of cryptosystem. It is shown that using Reed-Solomon codes weaken this cryptosystem compared to using the original supposed Goppa codes. The security analyse also need a short summary of complexity theory and what it means that a problem is NP-complete.

Keywords: Coding theory, Cyclic codes, BCH codes, Reed-Solomon codes, McEliece's cryptography system, Cryptography, Code breaking, Complexity theory, NP-complete

Place, publisher, year, edition, pages
2009. , p. 58
Series
Reports from MSI, ISSN 1650-2647 ; 09068
Keywords [en]
Coding theory, Cyclic codes, BCH codes, Reed-Solomon codes, McEliece's cryptography system, Cryptography, Code breaking, Complexity theory
Keywords [sv]
Kodningsteori, Kodteori, Cykliska koder, BCH-koder, Reed-Solomon-koder, McElieces kryptosystem, Kryptering, Kodforcering, Komplexitetsteori
National Category
Mathematics
Identifiers
URN: urn:nbn:se:vxu:diva-6055ISRN: VXU/MSI/MA/E/–09068–SEOAI: oai:DiVA.org:vxu-6055DiVA, id: diva2:272020
Presentation
(English)
Uppsok
Physics, Chemistry, Mathematics
Supervisors
Examiners
Available from: 2009-10-14 Created: 2009-10-13 Last updated: 2010-03-10Bibliographically approved

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CiteExportLink to record
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