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Qudratic field based cryptography
dc.contributor.advisorStanovský, David
dc.creatorStraka, Milan
dc.date.accessioned2017-04-20T04:48:27Z
dc.date.available2017-04-20T04:48:27Z
dc.date.issued2010
dc.identifier.urihttp://hdl.handle.net/20.500.11956/24699
dc.description.abstractNazev prace: Kryptografie zalozena na kvadratickych telesech Autor: Milan Straka Katedra (ustav): Katedra algebry Vedouci diplomove prace: RNDr. David Stanovsky, Ph.D. E-mail vedouciho: David.Stanovsky@mff.cuni.cz Abstrakt: Iraaginarni kvadraticka telesa byla navrzena pro pouziti v asyrnetricke kryptografii Buchmannem a Williamsern jiz v roce 1988 a od te doby vznikly i dalsi kryptograficke protokoly. I kdyz tyto protokolynejsou tak efektivni jako podobna schemata s eliptickyrni kfivkami, mohou konku- rovat schematum zalozenyrn na RSA, a navic je jejich bezpecnost pova- zovana za nezavislou na bezpecnosti beznych kryptosystemu jako RSA, DSA aEGG. Tato prace shrnuje dosavadni vysledky v oboru kvadraticke kryptografie. Jednak popisuje algebraickou teorii nutnou pro zavedeni tndove grupy imaginarnich kvadratickych teles a dale studuje algoritmy operaci v tri- dove grupe, jak asymptoticky, tak prakticky efektivni. Take rozebira vhodna kryptograficka schemata a utoky na ne. Soucasti teto prace je knihovna, ktera popsane protokoly efektivne im- plementuje. Klicova slova: tridova grupa imaginarniho kvadratickeho telesa, diskretni logaritmus, asymetricka kryptografie, sifrovaci a podpisove schema Title: Qudratic field based cryptography Author: Milan Straka Department: Department ofAlgebra Supervisor: RNDr. David...cs_CZ
dc.description.abstractImaginary quadratic fields were first suggested as a setting for public-key cryptography by Buchmann and Williams already in 1988 and more cryptographic schemes followed. Although the resulting protocols are currently not as efficient as those based on elliptic curves, they are comparable to schemes based on RSA and, moreover, their security is believed to be independent of other widely-used protocols including RSA, DSA and elliptic curve cryptography. This work gathers present results in the field of quadratic cryptography. It recapitulates the algebraic theory needed to work with the class group of imaginary quadratic fields. Then it investigates algorithms of class group operations, both asymptotically and practically effective. It also analyses feasible cryptographic schemes and attacks upon them. A library implementing described cryptographic schemes is a part of this work.en_US
dc.languageČeštinacs_CZ
dc.language.isocs_CZ
dc.publisherUniverzita Karlova, Matematicko-fyzikální fakultacs_CZ
dc.titleKryptografie založená na kvadratických tělesechcs_CZ
dc.typerigorózní prácecs_CZ
dcterms.created2010
dcterms.dateAccepted2010-01-27
dc.description.departmentDepartment of Applied Mathematicsen_US
dc.description.departmentKatedra aplikované matematikycs_CZ
dc.description.facultyFaculty of Mathematics and Physicsen_US
dc.description.facultyMatematicko-fyzikální fakultacs_CZ
dc.identifier.repId82058
dc.title.translatedQudratic field based cryptographyen_US
dc.identifier.aleph000967055
thesis.degree.nameRNDr.
thesis.degree.levelrigorózní řízenícs_CZ
thesis.degree.disciplineMatematické metody informační bezpečnostics_CZ
thesis.degree.disciplineMathematical methods of information securityen_US
thesis.degree.programMatematikacs_CZ
thesis.degree.programMathematicsen_US
uk.faculty-name.csMatematicko-fyzikální fakultacs_CZ
uk.faculty-name.enFaculty of Mathematics and Physicsen_US
uk.faculty-abbr.csMFFcs_CZ
uk.degree-discipline.csMatematické metody informační bezpečnostics_CZ
uk.degree-discipline.enMathematical methods of information securityen_US
uk.degree-program.csMatematikacs_CZ
uk.degree-program.enMathematicsen_US
thesis.grade.csProspělcs_CZ
thesis.grade.enPassen_US
uk.abstract.csNazev prace: Kryptografie zalozena na kvadratickych telesech Autor: Milan Straka Katedra (ustav): Katedra algebry Vedouci diplomove prace: RNDr. David Stanovsky, Ph.D. E-mail vedouciho: David.Stanovsky@mff.cuni.cz Abstrakt: Iraaginarni kvadraticka telesa byla navrzena pro pouziti v asyrnetricke kryptografii Buchmannem a Williamsern jiz v roce 1988 a od te doby vznikly i dalsi kryptograficke protokoly. I kdyz tyto protokolynejsou tak efektivni jako podobna schemata s eliptickyrni kfivkami, mohou konku- rovat schematum zalozenyrn na RSA, a navic je jejich bezpecnost pova- zovana za nezavislou na bezpecnosti beznych kryptosystemu jako RSA, DSA aEGG. Tato prace shrnuje dosavadni vysledky v oboru kvadraticke kryptografie. Jednak popisuje algebraickou teorii nutnou pro zavedeni tndove grupy imaginarnich kvadratickych teles a dale studuje algoritmy operaci v tri- dove grupe, jak asymptoticky, tak prakticky efektivni. Take rozebira vhodna kryptograficka schemata a utoky na ne. Soucasti teto prace je knihovna, ktera popsane protokoly efektivne im- plementuje. Klicova slova: tridova grupa imaginarniho kvadratickeho telesa, diskretni logaritmus, asymetricka kryptografie, sifrovaci a podpisove schema Title: Qudratic field based cryptography Author: Milan Straka Department: Department ofAlgebra Supervisor: RNDr. David...cs_CZ
uk.abstract.enImaginary quadratic fields were first suggested as a setting for public-key cryptography by Buchmann and Williams already in 1988 and more cryptographic schemes followed. Although the resulting protocols are currently not as efficient as those based on elliptic curves, they are comparable to schemes based on RSA and, moreover, their security is believed to be independent of other widely-used protocols including RSA, DSA and elliptic curve cryptography. This work gathers present results in the field of quadratic cryptography. It recapitulates the algebraic theory needed to work with the class group of imaginary quadratic fields. Then it investigates algorithms of class group operations, both asymptotically and practically effective. It also analyses feasible cryptographic schemes and attacks upon them. A library implementing described cryptographic schemes is a part of this work.en_US
uk.publication-placePrahacs_CZ
uk.grantorUniverzita Karlova, Matematicko-fyzikální fakulta, Katedra aplikované matematikycs_CZ


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