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Winter Semester

Lecture Series (no. 19324501) + Exercise (no. 19324502)

Foundations of Information-Theoretic Security (Grundlagen der informationstheoretischen Sicherheit), 10 LP


Schedule:  WS, 4+2 SWS

Instructors: Gerhard Wunder, Richard Schöffauer, Benedikt Groß


Description:

The lecture series Information-theoretic Foundations of Security (Wintersemester) as well as Privacy and Identity (Sommersemester) provides a comprehensive treatment of the information-theoretic priciples of security and privacy engineering by exploiting (common) randomness vs. classical computational complexity. It is also an excellent guidance for solving statistical decision problems in data science and machine learning.

An intriguing application is "Physical Layer Security", i.e. implementation of security algorithms already on the physical layer of (wireless) communication systems exploiting physical properties such as noise, fading etc. for symmetric key generation and wiretap channel coding ("wiretap codes").


Outline:

Chapter 1    What is information-theoretic security?    1 VL

--Scope and models

--Attack scenarios (RSA weaknesses, secret key management etc.)

--Diffie-Hellman vs. Key reconcilliation

Chapter 2    Probability spaces    3 VL

--Set theory, sample spaces, random variables, Bayes theorem

--Channels (Markov, conditions for stochastical degradedness)

--Random processes and convergence

--Basic inequality and large deviations (Jensen, log-sum, Caratheodory, bounded distance)


Chapter 3    Information theory    7 VL

--Entropy and conditional entropy, basic rules

--Typicality, AEP and types, Kullback-Leibler distance

--Conditional AEP theorems

--Shannon source coding theorem, Slepian-Wolf

--Mutual information, data processing inequality, mismatch lemma

--Channel coding theorem, broadcast theorem

--Distances (Hamming etc.), spheres, decoding principles

Chapter 4    Crypto metrics    7 VL

--Shannon cypher system, fundamental theorem, crypto lemma

--Pure cyphers and residue classes

--Weak/strong-, distinguising-, semantic- security and their relations

--Conditional min-entropy, guessing probability, separation lemma

--Statistical difference, Pinskers inequality, Csiszar/Körner Lemma

--Optimal tests and attacks, Neyman-Pearson

--Binary/Multiple hyphothesis testing, Fano's inequality and converse


Chapter 5    Wiretap coding    8 VL

--Wiretap coding scheme, secrecy capacity

--Secrecy capacity characterization (noisier, more capable, stochastically degraded)

--Degraded wiretap channel: Achievable rate region and converse

--Non-degraded wiretap channel: Achievable rate region and converse

--Classical wiretap codes (Co-set codes, deterministic model, polar codes)

--Crypto designs (Universal hashes, generalized left-over hash lemma, extractors


Chapter 6    Key generation    8 VL

--Maurer's scheme, key destillation strategies, key capacity

--Key capacity characterization, upper and lower bounds

--Advantage destillation protocols and limits

--Key reconciliation protocols and limits, practical examples (CASCADE, code offset)

--Privacy amplification and limits, universal hash function

--Average case -extractor, -secure sketch, Fuzzy extractor, practical BCH designs

--"From weak to strong security!"





Exercise Materials

Übungsblatt 1

Übungsblatt 2 (Corona-related)

Übungsblatt 3

Übungsblatt 4

Übungsblatt 5 (Corona-related)

Übungsblatt 6

Übungsblatt 7

Übungsblatt 8

Übungsblatt 9