Original title: Kryptografie založená na polookruzích
Translated title: Cryptography based on semirings
Authors: Mach, Martin ; Korbelář, Miroslav (advisor) ; El Bashir, Robert (referee)
Document type: Master’s theses
Year: 2019
Language: eng
Abstract: [eng] [cze]
Cryptography based on semirings can be one of the possible approaches for the post-quantum cryptography in the public-key schemes. In our work, we are interested in only one concrete semiring - tropical algebra. We are examining one concrete scheme for the key-agreement protocol - tropical Stickel's protocol. Although there was introduced an attack on it, we have implemented this attack and more importantly, stated its complexity. Further, we propose other variants of Stickel's protocol and we are investigating their potential for practical usage. During the process, we came across the theory of tropical matrix powers, thus we want to make an overview of it due to the use in cryptography based on matrices over the tropical algebra semiring. 1 Kryptografie založená na polookruzı́ch je jednı́m z možných řešenı́, jak přistu- povat k schématům s veřejným klı́čem v postkvantové kryptografii. V našı́ práci se budeme zabývat jednı́m konkrétnı́m polookruhem - tropickou algebrou. Pro- zkoumáme jedno konkrétnı́ schéma dohody na klı́či - Stickelův protokol upravený pro použitı́ v polookruzı́ch. Přestože na toto schéma byl již navržen útok, tak jsme tento algoritmus naimplementovali a předevšı́m určili jeho složitost. Dále navrhujeme dalšı́ varianty Stickelova protokolu a zkoumáme jejich potenciál pro praktické využitı́. Během tohoto výzkumu jsme narazili na teorii chovánı́ mocnin tropických matic, proto jsme se snažili udělat jejı́ přehled pro použitı́ v krypto- grafii založené na maticı́ch nad tropickou algebrou. 1
Keywords: public key cryptography; semigroup action; semiring; tropical algebra; akce pologrupy; kryptografie s veřejným klíčem; polookruh; tropická algebra

Institution: Charles University Faculties (theses) (web)
Document availability information: Available in the Charles University Digital Repository.
Original record: http://hdl.handle.net/20.500.11956/109954

Permalink: http://www.nusl.cz/ntk/nusl-405824


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Universities and colleges > Public universities > Charles University > Charles University Faculties (theses)
Academic theses (ETDs) > Master’s theses