DM854: Cryptology (10 ECTS)

STADS: 15018901

Level
Master's level course

Teaching period
The course is offered in the autumn semester.

Teacher responsible
Email: joan@imada.sdu.dk

Timetable
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Prerequisites:
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 DM508 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

Subject overview
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

Literature
There isn't any litterature for the course at the moment.

Website
This course uses e-learn (blackboard).

Prerequisites for participating in the exam
Project assignments. Pass/fail, internal marking by teacher.

Assessment and marking:
Oral exam without exam aids. External marking, Danish 7-mark scale.

Expected working hours
The teaching method is based on three phase model.
Intro phase: 36 hours
Skills training phase: 36 hours, hereof:
 - Tutorials: 36 hours

Educational activities

Educational form
Activities during the study phase:

• Using the acquired knowledge in projects.
• Discussing the scientific articles/book chapters
• Eksperiments in Maple.

Language
This course is taught in Danish or English, depending on the lecturer. However, if international students participate, the teaching language will always be English.

Course enrollment
See deadline of enrolment.

Tuition fees for single courses
See fees for single courses.