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Ergänzungen zu Mathematik II
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Konkrete Mathematik
Kryptographische Verfahren
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Kryptographische Verfahren

Organisatorisches

Dozenten:
Manfred Kufleitner (Raum 1.160, Tel. 0711 / 685 88231)
Volker Diekert (Raum 1.125, Tel. 0711 / 685 88329)

Zeit Raum Termine Vorlesung
Mo 11:30–13:00 0.108 wöchentlich ab 08.04.2013
Fr 11:30–13:00 0.108 bis auf Weiteres wöchentlich ab 12.04.2013

Bitte beachten Sie kurzfristige Termin- und Raumänderungen, die an dieser Stelle veröffentlicht werden.

Übungen

Zeit Raum Bemerkung
Fr 11:30–13:00 0.108 Ausweichtermin Fr 14:00-15:30, Raum V38.03

Übungsblätter

Themen

  • Verschlüsselung
  • Steganographie und Kryptographie
  • Klassische Verschlüsselungsverfahren
  • Blockchiffren
  • Monoalphabetische Verschiebung
  • Monoalphabetische Substitution
  • Polyalphabetische Substitution
  • Vigenèrechiffre
  • Kryptoanalyse
  • Perfekte Sicherheit
  • Vernam-One-Time-Pad
  • Das DES-Verfahren
  • Mehrfachverschlüsselung
  • Symmetrische und asymmetrische Kryptosysteme
  • Das RSA-Verschlüsselungsverfahren
  • Das Rabin-Verschlüsselungsverfahren
  • Der Diffie-Hellman-Schlüsselaustausch
  • Das ElGamal-Verschlüsselungsverfahren
  • Das McEliece-Verschlüsselungsverfahren
  • Das Merkle-Hellman-Verschlüsselungsverfahren
  • Der Miller-Rabin-Primzahltest
  • Wurzelziehen in endlichen Körpern
  • Die schnelle Fourier-Transformation
  • Multiplikation großer Zahlen
  • Pollards (p-1)-Methode zur Faktorisierung
  • Pollards rho-Methode zur Faktorisierung
  • Das Quadratische Sieb
  • Pollards rho-Methode zur Berechnung des diskreten Logarithmus
  • Der Pohlig-Hellman Algorithmus
  • Index Calculus
  • Elliptische Kurven
  • Kryptographische Hashfunktionen
  • Digitale Signaturen
  • Protokolle
  • Teilen von Geheimnissen
  • Zero-Knowledge Beweise

Materialien (nur für den internen Gebrauch, bitte nicht an Dritte weitergeben!)

  • Folien vom 12. April 2013 (PDF)
  • Folien vom 15. April 2013 (PDF)
  • Skript (Stand 2. August 2011) (PDF)
  • Baustelle zur Diskreten Mathematik (Vorgänger des unter Literatur angegebenen Buches von Diekert, Kufleitner, Rosenberger): (PDF)

Literatur

  • Volker Diekert, Manfred Kufleitner, Gerhard Rosenberger: Diskrete algebraische Methoden, Walter de Gruyter, 2013
  • Friedrich Ludwig Bauer: Entzifferte Geheimnisse: Methoden und Maximen der Kryptologie. Springer-Verlag, 1995.
  • Johannes Buchmann: Einführung in die Kryptographie. Springer, 2010 (5. Auflage).
  • Henri Cohen: A Course in Computational Algebraic Number Theory. Springer-Verlag, 1993.
  • Richard Crandall, Carl Pomerance: Prime Numbers: A Computational Perspective. Springer-Verlag, 2005 (2nd edition).
  • Joachim von zur Gathen, Jürgen Gerhard: Modern Computer Algebra. Cambridge University Press, 2003 (2nd edition).
  • Neil Koblitz: A Course in Number Theory and Cryptography. Springer-verlag, 1994 (2nd edition).
  • Bruce Schneier: Applied Cryptography: Protocols, Algorithms, and Source Code in C. John Wiley and Sons, 1996 (2nd edition).
  • Douglas Robert Stinson: Cryptography: Theory and Practice. CRC Press, 1995.

News

[Jun’23] The paper “Parallel algorithms for power circuits and the word problem of the Baumslag group” by Caroline Mattes and Armin Weiß has been accepted at Computational Complexity.

[Oct’22] The paper “Lower Bounds for Sorting 16, 17, and 18 Elements” by Florian Stober and Armin Weiß has been accepted at ALENEX 2023.

[Sep’22] The paper “Conelikes and Ranker Comparisons” by Viktor Henriksson and Manfred Kufleitner has been accepted at LATIN 2022.

[Sep’22] The paper “Improved Parallel Algorithms for Generalized Baumslag Groups” by Caroline Mattes and Armin Weiß has been accepted at LATIN 2022.

[Apr’22] The paper “Reachability Games and Parity Games” by Volker Diekert and Manfred Kufleitner has been accepted at ICTAC 2022.

[Apr’22] The paper “Satisfiability Problems for Finite Groups” by Pawel M. Idziak, Piotr Kawalek, Jacek Krzaczkowski and Armin Weiß has been accepted at ICALP 2022.

[Mar’22] The paper “The Power Word Problem in Graph Products” by Florian Stober and Armin Weiß was accepted at DLT 2022.

[Nov’20] Volker Diekert is Partner Investigator in the Australian ARC grant “Geodetic groups: foundational problems in algebra and computer science” at University of Technology Sydney.

[Apr’20] The paper “Groups with ALOGTIME-hard word problems and PSPACE-complete circuit value problems” by Laurent Bartholdi, Michael Figelius, Markus Lohrey and Armin Weiß has been accepted at CCC 2020.

[Apr’20] The paper “Hardness of equations over finite solvable groups under the exponential time hypothesis” by Armin Weiß has been accepted at ICALP 2020.

[Dec’19] The paper “An Automaton Group with PSPACE-Complete Word Problem” by Jan Philipp Wächter and Armin Weiß has been accepted at STACS 2020.

[Nov’19] Carlos Camino was awarded the stuvus Special Prize for exceptional commitment in teaching.

[Jun’19] The paper “The power word problem” by Markus Lohrey and Armin Weiß has been accepted at MFCS 2019.

[May’19] The paper “On the Average Case of MergeInsertion” by Florian Stober and Armin Weiß has been accepted at IWOCA 2019.

[Oct’18] The paper “Worst-Case Efficient Sorting with QuickMergesort” by Stefan Edelkamp and Armin Weiß has been accepted at ALENEX 2019.

[Jun’18] At CCC 2018, Lukas Fleischer received a Best Student Paper Award for his submission “On the Complexity of the Cayley Semigroup Membership Problem”.

[Jun’18] The paper “Testing Simon’s congruence” by Lukas Fleischer and Manfred Kufleitner was accepted at MFCS 2018.

[Jun’18] The paper “The Intersection Problem for Finite Semigroups” by Lukas Fleischer was accepted at DLT 2018.

[Apr’18] The paper “The isomorphism problem for finite extensions of free groups is in PSPACE” by Géraud Sénizergues and Armin Weiß was accepted at ICALP 2018.

[Apr’18] The paper “On the Complexity of the Cayley Semigroup Membership Problem” by Lukas Fleischer was accepted at CCC 2018.

[Jan’18] On March 24-29, 2019 Volker Diekert, Markus Lohrey, Olga Kharlampovich and Alexei Miasnikov will organize the Schloss Dagstuhl Seminar “Algorithmic Problems in Group Theory”.

[Dec’17] The paper “The Intersection Problem for Finite Monoids” by Lukas Fleischer and Manfred Kufleitner was accepted at STACS 2018.

[Jun’17] At the 12th International Computer Science Symposium in Russia (CSR), Lukas Fleischer and Manfred Kufleitner received a Best Paper Award for their publication “Green’s Relations in Finite Transformation Semigroups”, and Armin Weiss received a Best Paper Award for “The conjugacy problem in free solvable groups and wreath product of abelian groups is in $\text{TC}^0$ \text{TC}^0 “ which is joint work with Alexei Miasnikov and Svetla Vassileva.