Applied mathematics: Cryptology (3 cr)

Evaluation scale

Pass/Fail

Objective

Course purpose
Cryptology is an alternative to the applied mathematics course in information and communication technology. In this course, you will focus your knowledge on the mathematics needed in information security and especially encryption methods.

Course competences
EUR-ACE Knowledge and understanding
• knowledge and understanding of mathematics needed in information and communication technology
• knowledge and understanding of engineering fundamentals underlying the specialisation, at a level necessary to achieve the other programme outcomes, including some awareness at their forefront
EUR-ACE Engineering Practice
• understanding of applicable techniques and methods of analysis, design and investigation and of their limitations in their field of study

Learning outcomes
You know and understand the mathematical principles of the most common encryption methods. You can solve simple linear congruences. You know how to choose the encryption method that suits the situation and you have the skills to deepen your knowledge independently.

Content

Properties of functions (surjection, injection, bijection), number theory (divisibility, prime numbers, congruence, modular arithmetic), random number generation, classical encryption methods, symmetric and asymmetric encryption, elliptic curves

Location and time

The course is implemented between 25.8. and 17.12.2025.

Materials

The written, video and other course material are to be published in the course learning environment.

Teaching methods

Virtual course, self-paced and independently studied.
No scheduled classes in the timetable; guidance is available through weekly support sessions on the course’s Teams channel.
Exercises to be submitted.
Weekly tests in the learning environment.

Lecture videos are available for independent study.

Exam schedules

Published in the learning environment at the beginning of the course.

Student workload

Independent study and exam preparation: 49 h
Returnable exercises: 2 × 9 h = 18 h
Weekly tests: 5 × 1 h = 5 h
Exam: 3 h

The workload is evenly distributed throughout the course, totaling 81 hours.

Assessment criteria, approved/failed

You know and understand the key mathematical concepts and calculation rules related to cryptology. You can solve simple linear congruences. You understand the mathematical principles of encryption methods and know the purposes of different encryption methods. After the course, you will be able to study more about the subject on your own.

Qualifications

You know the basics of set theory and combinatorics, you understand the concept of divisibility and congruence.

Further information

The course is assessed based on the exam, returnable exercises, and weekly tests. All components are scored. To pass the course, students must achieve at least half of the total maximum points for the course and at least one third of the maximum points for the exam.

The course exam is organized twice during the autumn semester, in October and December. Students can choose which session to attend.

This course is a make-up implementation for students studying under the curricula OPS2020–OPS2023.