Kryptologie

K. Köhler: Cryptology
[4 h, 3h Lectures + 1h Practical Exercises (Lab)]

PowerPoint Foils     PowerPoint Foils with notes

Goal

The students understand the mathematical background of cryptographic algorithms, can implement them, assess their strengths and weaknesses, and can select appropriate measures to establish secure and authentic communication.

Content

  • Mathematical Foundations of cryptography (finite groups, rings and fields; elementary number theory; probability theory and information theory; finite automata)
  • Classic ciphers
  • Theoretical and practical security
  • Cryptographic building blocks (random generators, prime number generators, hash functions)
  • Block ciphers (AES)
  • Stream ciphers and operation modes of block ciphers
  • Asymmetric ciphers (RSA, DH, ElGamal, Elliptic Curves)
  • Quantum cryptography
  • Protocols
  • Cryptographic applications and their practical use
Most algorithms are implemented in a high-level programming language (C++, Java, Maple, or Mathematica) and their complexity is determined.
Students are expected to give a presentation of a cryptographic application or a selected topic of cryptography.

Kryptologie

Vorlesungsskript     Mathematica Notebooks bitte laden

Kap. Thema MC-Questions Praktikum Lösung
1 Ziele der Kryptologie


2 Grundbegriffe


3 Klassische Chiffren MC-Classic UtilitiesStudents.nb
classicStudents.nb
Aufgaben		 Lclassic.pdf
4 Sicherheit von Kryptosystemen

Lsecurity.pdf
5 Stromchiffren MC-Stream GaloisUsage.nb
FPSUsage.nb
shiftregStudents.nb
Aufgaben
Ciphertexts 		Lstream.pdf
6 Symmetrische Blockchiffren
AESStudents.nb Lblock1.pdf
Lblock2.pdf
7 Asymmetrische Chiffren MC-Asymmetric primes.nb
Diffie-Hellman.nb
ElGamal.nb
RSAStudents.nb
Aufgaben
ciphertexts
utilities 		Lasymmetric1.pdf
Lasymmetric2.pdf
8 Protokolle


9 Praktische Anwendungen


10 Anhang: Mathematische Grundlagen MC-Algebra
Lmath.pdf
11 Anhang: Häufigkeiten der Zeichen, Bigramme und Trigramme


12 Anhang: Kryptologische Begriffe


13 Literatur


14 Prüfungen



Quantum cryptography:
Vortrag Göran Pulkkis 31.5.05
Vortrag Göran Pulkkis 01.6.05
Vortrag Göran Pulkkis 02.6.05
quant_ex_mu.html

Referate im SS 2007

PrüfungWS02/03