Cryptography

Lecture

Tutorial

Time & Place

Lecture 1: Mo 16¹⁵-17⁴⁵, Cosec meeting room (1.25).
Lecture 2: Tu 12⁰⁰-12⁴⁵, Cosec meeting room (1.25).
Tutorial : Mo 14³⁰-16⁰⁰, Cosec meeting room (1.25).
First meeting: We 31.10.2007.

Allocation

3+2 SWS, 6 credits.

Media Informatics: Computer and Communication Technology.
Recommendation for University of Bonn - Computer Science: A or A1, respectively.

Prerequisites

None.

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.

Lecture notes

Current version available here: pdf.

Tutorials

Tutorial 1: From paleo-cryptography to AES.
- Exercise sheet: pdf.
- Solution: pdf.
Tutorial 2: Finite fields - Cultivating polynomials.
- Exercise sheet: pdf.
- Solution: pdf.
Tutorial 3: Euler and RSA.
- Exercise sheet: pdf.
- Solution: pdf.
Tutorial 4: Discrete logarithms.
- Exercise sheet: pdf.
- Solution: pdf.
Tutorial 5: Discrete logarithms (2).
- Exercise sheet: pdf.
Tutorial 6: Cryptographic hash functions.
- Exercise sheet: pdf.
- Solution: pdf.
Tutorial 7: Elliptic curves and group law.
- Exercise sheet: pdf.
- Solution: pdf.
- MuPAD worksheet: here.

Assignments

Assignment 1: From paleo-cryptography to AES. (For November, 15th)
- Exercise sheet: pdf.
Assignment 2: Finite fields in AES. (For November, 26th)
- Exercise sheet: pdf.
- Multiplication over F_2⁸ (in JavaScript): here.
Assignment 3: Security of RSA. (For December, 4th)
- Exercise sheet: pdf.
Assignment 4: Computing discrete logarithms. (For December, 11th)
- Exercise sheet: pdf.

Literature

Mihir Bellare & Shafi Goldwasser (2001). Lecture Notes on Cryptography. PostScript.
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 (2005). Cryptography - Theory and Practice. Discrete Mathematics and its Applications. Chapman \& Hall / CRC Press, Boca Raton FL, 3rd edition. ISBN 1584885084, 600pp.