In this lecture, the fundamentals and paradigms of information-theoretical security (ITS) are conveyed, i.e. security mechanisms that cannot be traced back to "solving a difficult problem". ITS should come into play in future communication systems (e.g. evolutionary path from 5G to 6G or WiFi-6) and addresses essential aspects of new services such as the IoT, the tactile Internet, etc., especially with regard to scalable, fast and also user-manageable security ("Usability "). Another aspect that is frequently mentioned is security for the post-quantum age. Generally speaking, ITS uses the properties of the transmission channel in a targeted manner, e.g. through tap-proof coding or by generating a shared secret ("common information") about the specific properties of the complex electromagnetic wave propagation in the transmission medium.
- What is perfect security? Attacks on Diffie-Hellman and RSA, key management in scalable systems
--Fundamental inequalities and set characterizations (Jensen, Caratheodory, ...)
- Basics of information theory (conditional entropy, transinformation, AEP, Method of types, Shannon sentences, multi-user systems, Slepian-Wolf, basics of coding, ...)
- Encryption systems and crypto-metrics (fundamental theorems, pure ciphers and residual classes, distance measure for distribtions, Pinsker's inequality, semantic security, min-entropy, optimal hypothesis tests and attacks, ...)