Cryptography I (4+2)

Responsible:

Prof. Dr. Joachim von zur Gathen

Course:

• Tue 17:15 - 18:45, b-it-max (Hörsaal), Start: 24.10.2005, Prof. Dr. Joachim von zur Gathen
• Wed 17:30 - 19:00, Rheinsaal, Start: 26.10.2005, Prof. Dr. Joachim von zur Gathen

Exercises:

• Mon 18:00 - 19:30, Rheinsaal, Start: 31.10.2005, Michael Nüsken

Prerequisite:

Linear Algebra or the bridging course

Summary:

Cryptography deals with methods for secure data transfer. In earlier times this was the domain of military and intelligence agencies, but today modern cryptography has grown into a key technology, enabling e-commerce and secure internet communications. Its many applications range from credit and debit cards, mobile phones, tv decoders, and electronic money to unforgeable electronic signatures under orders and contracts in the internet. In the course, we first discuss two of the current standard tools, namely AES and RSA. Further topics are key exchange, including group cryptography and discrete logarithm, digital signatures and identification, and cryptographic hash functions.

Exercises

• Exercise sheet 1 (PDF), due to 2005/11/07.
  • Some definitions basic to AES (MuPAD note book).
• Exercise sheet 2 (PDF), due to 2005/11/14.
• Exercise sheet 3 (PDF), due to 2005/11/21, 14:00.
• Exercise sheet 4 (PDF), due to 2005/11/28, 14:00.
• Exercise sheet 5 (PDF), due to 2005/12/05, 14:00.
• Exercise sheet 6 (PDF), due to 2005/12/12, 14:00.
  • Dixon's random squares method (MuPAD note book).
• Exercise sheet 7 (PDF), due to 2005/12/19, 14:00.
• Exercise sheet 8 (PDF), due to 2006/01/09, 14:00 (updated 2005/12/19, 15:25).
• Exercise sheet 9 (PDF), due to 2006/01/23, 14:00.
  • A buggy long hash function (MuPAD note book).
• Exercise sheet 10 (PDF), due to 2006/01/30, 14:00.
• Exercise sheet 11 (PDF), due to 2006/02/06, 14:00.

Literature

• Mihir Bellare & Shafi Goldwasser (2001). Lecture Notes on Cryptography. PostScript .
• Johannes Buchmann (1999). Einführung in die Kryptographie. Springer Lehrbuch. Springer-Verlag, Berlin. ISBN 3540405089.
• Johannes A. Buchmann (2004). Introduction to Cryptography. Birkhäuser Verlag, 2nd edition. ISBN 0-387-21156-X (hardcover), 0-387-20756-2.
• Alfred J. Menezes, Paul C. van Oorschot & Scott A. Vanstone (1997). Handbook of Applied Cryptography. CRC Press, Boca Raton FL. ISBN 0-8493-8523-7. Its homepage includes a lot of free sample chapters.
• Douglas R. Stinson (1995). Cryptography, Theory and Practice. CRC Press, Boca Raton~FL. ISBN 0849385210.
• Douglas R. Stinson (2002). Cryptography - Theory and Practice, volume~1. Chapman & Hall / CRC Press, 2nd edition. ISBN 1584882069, 360pp.
• Douglas R. Stinson (2005). Cryptography - Theory and Practice. Discrete Mathematics and its Applications. Chapman \& Hall / CRC Press, Boca Raton~FL, 3rd edition. ISBN 1584885084, 600pp.

Links

• A visualisation of AES flows (needs Java). Each "wire" carries one byte encoded as a color.