Wurzelziehen in endlichen Körpern: Die Algorithmen von Tonelli und Cipolla
Permutationen und ihr Vorzeichen
Das Jacobi-Symbol und das quadratische Reziprozitätsgesetz
Der Lucas-Lehmer-Primzahltest für Mersenne-Zahlen
Das RSA-Verschlüsselungsverfahren
Die Sicherheit des geheimen Schlüssels bei RSA
Das Rabin-Verschlüsselungsverfahren
Pollards (p-1)-Methode zur Faktorisierung
Pollards rho-Methode zur Faktorisierung
Das Quadratische Sieb
Die schnelle Fourier-Transformation
Primitive Einheitswurzeln in Ringen
Multiplikation großer Zahlen nach Karatsuba
Multiplikation großer Zahlen nach Schönhage und Strassen
Division mittels Newton-Verfahren
Der Diffie-Hellman-Schlüsselaustausch
Das ElGamal-Verschlüsselungsverfahren
Shanks Babystep-Giantstep-Algorithmus
Pollards rho-Methode zur Berechnung des diskreten Logarithmus
Der Pohlig-Hellman Algorithmus
Index Calculus
Elliptische Kurven und ihre Anwendung
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
“ which is joint work with Alexei Miasnikov
and Svetla Vassileva.
