Introduction to Modern Cryptography

Course content

  • 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.

 

Education

MSc Programme in Mathematics
MSc Programme in Mathematics with 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 probability, theory of computation (algorithms and rudimentary complexity theory) OR some experience with writing programs/​algorithm-design.

Academic qualifications equivalent to a BSc degree is recommended.

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.

Written
Oral
Individual
Collective

Written feedback will be given on mandatory, individual assignments in order for students to improve their subsequent assignments.

Collective oral feedback will be given in class when students suggest solutions to the posed problems and questions.

ECTS
7,5 ECTS
Type of assessment
Continuous assessment
Oral examination, 30 minutes
There will be graded
- [20%] Project with a 15-minute presentation;
- [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%] Oral final exam with preparation time of 25min, where the student randomly selects one topic from a previously known list of topics.
Aid
Only certain aids allowed

All aids allowed for the project and assignments.  

No aids allowed during the final exam.

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
  • Lectures
  • 28
  • Preparation
  • 107
  • Theory exercises
  • 21
  • Project work
  • 20
  • Exam
  • 30
  • English
  • 206