Original title: Analýza proudové šifry QUAD
Translated title: Analysis of the stream cipher QUAD
Authors: Čurilla, Marcel ; Holub, Štěpán (advisor) ; Příhoda, Pavel (referee)
Document type: Master’s theses
Year: 2012
Language: slo
Abstract: [eng] [cze]
Title: Analysis of the stream cipher QUAD Author: Marcel Čurilla Department: Katedra algebry Supervisor: doc. Mgr. Štěpán Holub, Ph.D. Abstract: Stream cipher QUAD was introduced in 2006 on Eurocrypt by Côme Ber- bain, Henri Gilbert a Jacques Patarin cite quad. The authors showed a reduction of this cipher for the problem of solving m quadratic equations of n variables over finite fields known as the MQ problem. For simplicity, they considered only the case of the field GF(2). In this thesis I introduce this stream cipher. I show the proof (reduction) of safety ciphers QUAD for MQ problem over any finite field GF(q). I describe the basic met- hods for the solution of system of quadratic equations over finite fields, linearization and relinearization. I focus on XL algorithm - which is currently the fastest algo- rithm for solving quadratic systems. This algorithm was designed precisely to deal with overdefined quadratic systems. While analyzing the cipher QUAD I show for what instance is a cipher QUAD breakable and vice versa for what instance is the security guaranteed. Keywords: stream cipher, QUAD, MQ problem, algorithm XL, 1 Název práce: Analýza proudové šifry QUAD Autor: Marcel Čurilla Katedra: Katedra algebry Vedoucí diplomové práce: doc. Mgr. Štěpán Holub, Ph.D. Abstrakt: Prúdová šifra QUAD bola predstavená na Eurocrypte autormi Côme Ber- bain, Henri Gilbert a Jacques Patarin [1]. Ukázali redukciu tejto šifry na problém riešenia m kvadratických rovníc n premenných nad konečným telesom známy, ako MQ problém. Pre zjednodušenie, autori uvažovali len prípad telesa GF(2). V tejto práci predstavím túto prúdovú šifru. Uvidiem dôkaz (redukciu) bezpečnosti šifry QUAD na MQ problém nad l'ubovol'ným konečným telesom GF(q). Popíšem základné metódy pre riešenie systému kvadratických rovníc nad konečným telesom, linearizáciu a reline- arizáciu. Podrobnejšie sa budem venovat' algoritmu XL, momentálne najrýchlejšiemu algoritmu na riešenie kvadratických systémov. V analýze šifry QUAD ukážem pre ktoré instancie je šifra QUAD prelomitel'ná a naopak pre ktoré instancie je bezpečnost' zaručená. Klíčová slova: prúdová šifra , QUAD, MQ problém, algoritmus XL 1

Institution: Charles University Faculties (theses) (web)
Document availability information: Available in the Charles University Digital Repository.
Original record: http://hdl.handle.net/20.500.11956/40849

Permalink: http://www.nusl.cz/ntk/nusl-499457


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