# Selected Topics in Cryptology

## Objectives and Content

Topic for autumn 2024: Cryptographic Boolean Functions

Objectives:

This course aims to educate in the field of cryptographic Boolean functions, providing both classical notions and results, as well as recent developments. It will train to solve problems, prepare scientific articles and presentations, and, possibly, also to contribute to Boolean functions wiki:

Content:

The course is dedicated to Boolean functions, in particular, those with special properties for applications in cryptography. Some related discrete functions and structures, such as permutation polynomials and planar functions over finite fields, will be studied too.

The course covers a collection of cencepts and theoretical results, bounds, and techniques essential for the area of cryptographic Boolean functions. Among these topics are:

• Classical notions and results related to cryptographic Boolean functions, such as nonlinearity and differential uniformity;
• Discrete structures related to cryptographic Boolean functions;
• Recent developments for cryptographic Boolean functions.

## Learning Outcomes

After completing the course the student should have following learning outcomes defined in terms of knowledge, skills and general competence:

Knowledge:

The students should have nowledge of:

• Different representations of Boolean functions;
• Basic cryptographic criteria for Boolean functions;
• Construction of optimal cryptographic functions;
• Different equivalence relations for Boolean functions;
• Permutation polynomials over finite fields;
• Planar functions and commutative semifields and other related discrete structures.
• Also recent developments in the field of cryptographic Boolean functions will be discussed. The related content will be renewed every year.

Skills:

The students are able to

• solve problems related to cryptographic Boolean functions;
• present results on the topic of cryptographic Boolean functions as if for scientific events;
• write a scientific article on some of the solved problems, or, in case of PhD students, instead of the last two points, creating webpages with information on Boolean functions for Boolean wiki.

General competence:

The students

• are familiar with foundations and recent developments in the field of cryptographic Boolean functions and related discrete structures;
• can exchange opinions with others with relevant background and participate in discussions concerning the subject.

10 ECTS

Master/PhD

## Semester of Instruction

Autumn
Required Previous Knowledge
At least 60 ECTS in computer science, preferably including basic knowledge in descrete mathematics: INF240A and MAT121
Recommended Previous Knowledge
Access to the Course

Access to the course requires admission to a program of study at The Faculty of Mathematics and

Natural Sciences

Teaching and learning methods

The teaching comprises lectures and some of these lectures will be dedicated to practical issues

Lectures: 4 hours pr. week

Compulsory Assignments and Attendance
Compulsory assignments are valid for one subsequent semester.
Forms of Assessment
Oral exam.
Grading Scale
The grading scale used is A to F. Grade A is the highest passing grade in the grading scale, grade F is a fail.
Examination Support Material
None