Introduction to Modern Cryptography

Course content

  • Brief review of basic concepts from probability theory and the theory of computation;
  • Basic principles of modern cryptography; security definitions
  • One-way functions, pseudorandom generators, pseudorandom functions, pseudorandom permutations
  • Private-key encryption, block and stream ciphers, security against chosen plaintext attacks
  • Authentication
  • Public-key cryptography 


We will also describe some example constructions; how many we cover depends on interest and time.

If time permits, we may also explore some current topics, such as fully-homomorphic encryption, or quantum cryptography.


MSc Programme in Mathematics

MSc Programme in Mathematics w. a minor subject 

Learning outcome
  • Knowledge: the students will have an understanding of the theoretical and mathematical basis of modern cryptographic systems.
  • Skills: the students will be able to give rigorous security proofs of basic cryptographic systems, and connect various cryptographic primitives with rigorous reductions.
  • Competencies: understanding theorems about theoretical cryptography; proving security reductions; reasoning about the limits of computationally-bounded adversaries.

4 hours of lectures and 3 hours of tutorials per week. Tutorials will be split into project presentations and problem sessions. The exact split depends on the number of enrolled students (time needed for presentations).

Ability to produce rigorous mathematical proofs. Basic knowledge of discrete probability theory. Basic understanding of theory of computation (algorithms and rudimentary complexity theory) OR some experience with writing programs/​algorithm-design.

This course is about the mathematical and theoretical basis of modern cryptography. Within this area, our focus will be on mathematical theorems, proofs and rigorous constructions. We will not discuss computer security in practice. There will be no mandatory programming.

The course is appropriate for students in both Mathematics and Computer Science.

7,5 ECTS
Type of assessment
Continuous assessment
Written examination, 3 hours under invigilation
There will be graded
- [20%] Project with a 15-minute presentation and a 4-5 page write-up;
- [40%] 4 assignments. The one with the lowest grade will be dropped and won't affect the final grade; the other three will contribute towards the final grade equally;
- [40%] Written final exam.
Only certain aids allowed

All aids allowed for the project and assignments.  

No aids for the first hour of the exam. Personally hand-written notes on paper  allowed during the last 2 hours.

Marking scale
7-point grading scale
Censorship form
No external censorship
Several internal examiners
Criteria for exam assessment

The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.

Single subject courses (day)

  • Category
  • Hours
  • Preparation
  • 83
  • Lectures
  • 28
  • Practice Class
  • 21
  • Exam
  • 30
  • Project work
  • 20
  • Exercises
  • 24
  • English
  • 206