178 research outputs found

    Qudratic field based cryptography

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    Imaginary 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.Nazev prace: Kryptografie zalozena na kvadratickych telesech Autor: Milan Straka Katedra (ustav): Katedra algebry Vedouci diplomove prace: RNDr. David Stanovsky, Ph.D. E-mail vedouciho: [email protected] 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...Department of Applied MathematicsKatedra aplikovan√© matematikyFaculty of Mathematics and PhysicsMatematicko-fyzik√°ln√≠ fakult

    Funkcionální datové struktury a algoritmy

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    Title: Functional Data Structures and Algorithms Author: Milan Straka Institute: Computer Science Institute of Charles University Supervisor of the doctoral thesis: doc. Mgr. Zdenńõk DvoŇô√°k, Ph.D, Computer Science Institute of Charles University Abstract: Functional programming is a well established programming paradigm and is becoming increasingly popular, even in industrial and commercial appli- cations. Data structures used in functional languages are principally persistent, that is, they preserve previous versions of themselves when modified. The goal of this work is to broaden the theory of persistent data structures and devise efficient implementations of data structures to be used in functional languages. Arrays are without any question the most frequently used data structure. Despite being conceptually very simple, no persistent array with constant time access operation exists. We describe a simplified implementation of a fully per- sistent array with asymptotically optimal amortized complexity őė(log log n) and especially a nearly optimal worst-case implementation. Additionally, we show how to effectively perform a garbage collection on a persistent array. The most efficient data structures are not necessarily based on asymptotically best structures. On that account, we also focus on data structure...N√°zev pr√°ce: Funkcion√°ln√≠ datov√© struktury a algoritmy Autor: Milan Straka √östav: Informatick√Ĺ √ļstav Univerzity Karlovy Vedouc√≠ doktorsk√© pr√°ce: doc. Mgr. Zdenńõk DvoŇô√°k, Ph.D, Informatick√Ĺ √ļstav Univerzity Karlovy Abstrakt: Funkcion√°ln√≠ programov√°n√≠ je rozŇ°√≠Ňôen√© a st√°le v√≠ce obl√≠ben√© programo- vac√≠ paradigma, kter√© nach√°z√≠ sv√© uplatnńõn√≠ i v prŇĮmyslov√Ĺch aplikac√≠ch. Datov√© struktury pouŇĺ√≠van√© ve funkcion√°ln√≠ch jazyc√≠ch jsou pŇôev√°Ňĺnńõ perzistentn√≠, coŇĺ znamen√°, Ňĺe pokud jsou zmńõnńõny, zachov√°vaj√≠ sv√© pŇôedchoz√≠ verze. C√≠lem t√©to pr√°ce je rozŇ°√≠Ňôit teorii perzistentn√≠ch datov√Ĺch struktur a navrhnout efektivn√≠ implementace tńõchto datov√Ĺch struktur pro funkcion√°ln√≠ jazyky. Bezpochyby nejpouŇĺ√≠vanńõjŇ°√≠ datovou strukturou je pole. Ańćkoli se jedn√° o vel- mi jednoduchou strukturu, neexistuje jeho perzistentn√≠ protńõjŇ°ek s konstantn√≠ sloŇĺitost√≠ pŇô√≠stupu k prvku. V t√©to pr√°ci pop√≠Ň°eme zjednoduŇ°enou implementaci perzistentn√≠ho pole s asymptoticky optim√°ln√≠ amortizovanou ńćasovou sloŇĺitost√≠ őė(log log n) a pŇôedevŇ°√≠m t√©mńõŇô optim√°ln√≠ implementaci se sloŇĺitost√≠ v nejhorŇ°√≠m pŇô√≠padńõ. Tak√© uk√°Ňĺeme, jak efektivnńõ rozpoznat a uvolnit nepouŇĺ√≠van√© verze per- zistentn√≠ho pole. Nejv√ĹkonnńõjŇ°√≠ datov√© struktury nemus√≠ b√Ĺt vŇĺdy ty, kter√© jsou zaloŇĺeny na asymptoticky nejlepŇ°√≠ch struktur√°ch. Z toho dŇĮvodu se tak√© zamńõŇô√≠me na imple- mentaci...Informatick√Ĺ √ļstav Univerzity KarlovyComputer Science Institute of Charles UniversityFaculty of Mathematics and PhysicsMatematicko-fyzik√°ln√≠ fakult
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