Selected Areas in Cryptology


The goal of this course is to provide insight into cryptography secure against quantum computers (post-quantum cryptography) as well as various methods for the mathematical cryptanalysis of cryptographic systems


Cryptology deals with mathematical techniques for design and analysis of algorithms and protocols for digital security in the presence of malicious adversaries. For example, encryption and digital signatures are used to construct private and authentic communication channels, which are instrumental to secure Internet transactions.

This course in cryptology consists of two main topics:

The first part focuses on post-quantum cryptography dealing with cryptographic systems that are secure even given the existence of quantum computers and the second part focuses on cryptanalysis, the analysis of the security of cryptographic systems.

After a general introduction to cryptography (the constructive side of cryptology) and cryptanalysis the course introduces the main contenders for secure systems: lattice-based encryption, code-based encryption, hash-based signatures, and multivariate-quadratic-based signatures. These systems are examples of public-key systems and this is the main area affected by quantum computers; symmetric-key systems, such as hash functions and block and stream ciphers) are used as building blocks inside them and for the transmission of data in bulk.

The second part of the course will cover various generic attacks against common cryptographic primitives (e.g., block ciphers, hash functions) and cover important cryptanalytic attack techniques like time-memory tradeoffs, linear cryptanalysis, differential cryptanalysis and algebraic cryptanalysis.


Basics of linear algebra (simple bachelor level), probability theory (simple bachelor
level), knowledge of number theory and algebra matching at least and

It is recommended but not mandatory to follow the MasterMath course on Cryptology first; that course is available as video lectures for self study.


Tanja Lange and Marc Stevens.


The exam is planned for 17 June and will be offered as an oral ezam. Therefore we are a bit more flexible with the ate. The same holds for the retake.

Each exam will take 30 min and will have Marc and Tanja both asking some questions. These cover general concepts as well as showing some expam-type exercises and asking the student to explain how they would solve it, without doing any of the computational steps.
After the quesstioning part they will retreat to discuss the grade and return to the student to announce the grade.