## Forster: Cryptography

Course (4 hours weekly + 2 hours Problem sessions) by O. Forster
Summer Semester 2007, Department of Mathematics, LMU München

Time and Room: Wed, Fri 14-16, B006

Problem sessions: Wed 16-18, B006

About this course: In the past, cryptography was mainly used by the military, secret service and diplomatic service. Today, in the age of internet, almost everybody is confronted directly or indirectly with cryptography. In this course, after a brief look on classical cryptography, we will study modern block cipher crypto systems (DES, AES) and public key cryptography. Public key cryptography plays an important role in electronic commerce, electronic banking and other kinds of modern data communication. It deals not only with secret coding of messages but also with digital signatures and authentification. Public key cryptography uses interesting mathematical methods from number theory and algebraic geometry (e.g. elliptic curves over finite fields)

Prerequisites: Basic notions of algebra, number theory and analysis

For: Studierende der Mathematik und/oder Informatik nach dem Vordiplom,
Students of the International Master Program in Mathematics,
und andere Interessenten

Contents:

1. Monoalphabetic substitutions
2. Structure of the ring Z/mZ
3. Hill ciphers
4. Vigenère cipher
5. Rotor machines, Enigma
6. Shannon's notion of perfect secrecy. One-Time-Pads
7. Pseudo random number generators
8. Feistel networks, DES
10. The RSA cipher system
11. Primality tests
12. The discrete logarithm
13. Message digests, digital signatures
14. Elliptic curves

ARIBAS code for some cryptographic algorithms

• Advanced Encryption Standard (AES): AES.ari
• Secure Hashing Algorithm (SHA-1): SHA1.ari

Literature

• J. Buchmann: Introduction to Cryptography (also a German edition is available). Springer Verlag
• D. R. Stinson: Cryptography: Theory and Practice. CRC Press
• Menezes, van Oorschot, Vanstone: Handbook of Applied Cryptography. CRC Press
• S. Wagstaff: Cryptanalysis of Number Theoretic Ciphers. CRC Press
• O. Forster: Algorithmische Zahlentheorie, Vieweg-Verlag

Otto Forster (), 2007-02-03