Title: Goppa codes and their applications Author: Bc. Jaroslav Kotil Department: Department of algebra Supervisor: prof. RNDr. Aleš Drápal, CSc., DSc. Abstract: In this diploma paper we introduce Goppa codes, describe their para- metres and inclusion in Alternant codes, which are residual Generalized Reed- Solomon codes, and Algebraic-geometry codes. Aftewards we demonstrate deco- ding of Goppa codes and introduce Wild Goppa codes. We also describe post- quantum cryptography member: McEliece cryptosystem for which no effective attacks with quantum computers are known. We outline a usage of this crypto- system with Goppa codes and describe the security of the cryptosystem together with possible attacks of which the most effective ones are based on information- set decoding. Keywords: Goppa codes, Generalized Reed-Solomon codes, Algebraic-geometry codes, Post-quantum cryptography, McEliece cryptosystem 1
Identifer | oai:union.ndltd.org:nusl.cz/oai:invenio.nusl.cz:321400 |
Date | January 2013 |
Creators | Kotil, Jaroslav |
Contributors | Drápal, Aleš, Šťovíček, Jan |
Source Sets | Czech ETDs |
Language | Czech |
Detected Language | English |
Type | info:eu-repo/semantics/masterThesis |
Rights | info:eu-repo/semantics/restrictedAccess |
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