DM854: Cryptology

Study Board of Science

Teaching language: Danish or English depending on the teacher, but English if international students are enrolled
EKA: N340049112, N340049102
Censorship: Second examiner: None, Second examiner: External
Grading: Pass/Fail, 7-point grading scale
Offered in: Odense
Offered in: Autumn
Level: Master

STADS ID (UVA): N340049101
ECTS value: 10

Date of Approval: 25-03-2019

Duration: 1 semester

Version: Approved - active

Entry requirements

A bachelor degree in computer science, mathematics, applied mathematics, mathematics-economy or comparable.

Academic preconditions

Students taking the course are expected to:

  • Have knowledge of basic linear algebra
  • Be able to understand and write proofs, use basic probability, and analyze algorithms.

Course introduction

The aim of the course is to enable the student to understand and work with the concepts in cryptology, including cryptosystems, cryptanalysis, and protocols, which is important in regard to data, computer, and network security.                 
The purpose of this course is to study cryptology, which is cryptography plus cryptanalysis - the creation of secret codes and the possibilities for breaking them. We will also study cryptographic protocols for the security of information. Many of the newer cryptosystems and cryptographic protocols are based on number theoretic problems, so these number-theoretic problems and algorithms for them will also be discussed in this course, as will some of the algebra necessary for understanding them. Cryptology has many applications including sending private messages, enabling commerce over the Internet (through encryption of credit card numbers, electronic money, secure methods for electronic signatures on documents, etc.), authentication such as PIN codes for Dankort and logins, and secret sharing (requiring that k out of m people participate before some sensitive action can occur).

The course builds on the knowledge acquired in the courses DM549 Discrete Methods for Computer Science or MM537 Introduction to Mathematical Methods, DM551 Algorithms and Probability or MM541 Combinatorial Mathematics, DM507 Algorithms and Data Structures, and DM553 Complexity and Computability or MM539 Algebra 2.

The course gives an academic basis for writing a Master's thesis in cryptology.

In relation to the competence profile of the degree it is the explicit focus of the course to:
  • Describe, analyze and solve advanced problems in cryptology using the learned models
  • Analyze the advantages and disadvantages of various cryptographic methods
  • Be able to understand and with a scientific basis reflect on the principles and mathematics behind cryptologic systems
  • Give expert knowledge about cryptology, which is based on the highest level of international research
  • Give knowlede about a variety of specialized models and methods developed in cryptology, based on the the highest level of international research, including subjects from
  • Develop new variants of the methods learned, where concrete problems require it

Expected learning outcome

The learning objectives of the course is that the student demonstrates the ability to:
  • Decide which symmetric or public key cryptosystem is most appropriate for a given application
  • Analyze and implement cryptosystems, functions, and protokols, together with techniques for breaking them
  • Do the calculations relevant for the cryptographic systems, functions and protocols, which are covered
  • Prove that cryptographic systems, functions and protocols are correct and secure/insecure
  • Do simple proofs involving algebraic objects that are relevant in cryptology


The following main topics are contained in the course:
  • Classical cryptosystems
  • Information theoretic security
  • Stream and block ciphers
  • Hash functions and message authentication codes
  • Public key cryptosystems, digital signatures, key exchange
  • Protocols such as secret sharing and zero-knowledge knowledge
  •  Relevant topics from algebra


See Blackboard for syllabus lists and additional literature references.

Examination regulations

Prerequisites for participating in the exam a)




Mandatory assignments




Second examiner: None




Full name and SDU username


Normally, the same as teaching language

Examination aids

To be announced during the course

ECTS value


Additional information

The prerequisite examination is a prerequisite for participation in exam element a). 

Exam element a)




Type Prerequisite name Prerequisite course
Examination part Prerequisites for participating in the exam a) N340049101, DM854: Cryptology


Oral examination




Second examiner: External


7-point grading scale


Student Identification Card


Normally, the same as teaching language

Examination aids

To be announced during the course 

ECTS value


Additional information

Oral exam as well as three assignments handed in during the course. The grade is based on an overall impression of the elements included in the evaluation.
One assignment must be solved independently, while the other two can be solved in groups of up to 3 people. Assignments, along with selected topics from the course, form the basis for the oral exam. The external examiner will have the opportunity to see the answers to the three assignments.

Indicative number of lessons

72 hours per semester

Teaching Method

At the faculty of science, teaching is organized after the three-phase model ie. intro, training and study phase.

See Danish version

Teacher responsible

Name E-mail Department
Joan Boyar


08 - 09
09 - 10
10 - 11
11 - 12
12 - 13
13 - 14
14 - 15
15 - 16
Show full time table

Administrative Unit

Institut for Matematik og Datalogi (datalogi, fiktiv)

Team at Registration & Legality


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