Cryptology is a key technology for the security of worldwide computer nets. Modern cryptographic techniques are used to keep data secret, sign electronic messages, control computer network access, secure electronic financial transactions, protect copyrights, among others. In view of these applications users should be able to assess the efficiency and security of these key technologies. For this purpose, it is important not only to know the function of cryptographic processes, it is also important to understand their mathematical basics. Both is explained in this module.

Professional competence
The students:

• identify basic concepts of cryptography and explain them by examples
• know relevant cryptosystems, apply them and assess their security
• are familiar in using mathematical basics of cryptographic algorithms
• implement cryptographic algorithms and prove their correctness and estimations of their complexity

Methodological competence
The students:

• assess the efficiency and security of cryptographic processes
• extend their knowledge about algorithms and their complexity
• develop their implementation skills in particular the handling of very large numbers
• analyze simple encryption using well-known and own techniques

Social competence
The students

• use the language of mathematics to discuss in groups with different knowledge about problems
• present their ideas in an understandable way
• expand and improve their own ideas through the proposals of their fellow students

Self-competence
The students:

• reflect their knowledge about security in IT systems
• reflect their knowledge about algorithms and their complexity
• experience the development of a new field of knowledge within a short amount of time
• discover new applications of mathematical contexts

A) Mathematical Basics: Integers; Polynomials; Congruences; Residue Class Rings
B) Encryption
C) Probability and Perfect Security
D) Symmetric Encryption (DES, AES)
E) Generation of Prime Numbers
F) Public-Key-Encryption
G) Factorisation and Discrete Logarithms
H) Cryptographic Hash Functions and Digital Signatures
I) Identification and Certification

Lecture notes; further literature will be announced in the lecture.
For attunement: Singh, Simon: The Code Book: Science of Secrecy from Ancient Egypt to Quantum Cryptography. Anchor, 2000.

At the end of the lecture periode

Written exam