Cryptology, 7.5 credits

Contents

Cryptography is essential in today’s digital society which is founded on secure and confidential communication. In practice, when implementing a system building on cryptography it is important to be aware of and to understand different methods’ strengths, limitations and theoretical backgrounds which often rely on modern mathematics.

The course covers a variety of encryption methods and protocols with a focus on foundational pillars of modern communication and those at the forefront of active research such as cryptographic algorithms safeguarded against quantum computers. The course includes both symmetric encryption (where the same key is used to both encrypt and decrypt messages), and asymmetric encryption (where a public key can be used by others to send you encrypted messages, but only you have the private key to decrypt them).

The course introduces different cryptographic tools and applications such as digital signatures, authentication, and cryptocurrencies. Basic cryptoanalysis will also be covered where strengths and weaknesses of different methods and protocols are discussed.

The course combines theory with practical activities including programming exercises.

Expected learning outcomes

For a passing grade, the student must be able to

Knowledge and understanding
• explain the theoretical foundations of cryptology
• describe well-established cryptographic methods and protocols

Skills and abilities
• implement a selection of encryption algorithms
• use a selection of standard tools within cryptography

Judgment and approach
• evaluate the applicability of different encryption methods and protocols for different scenarios
• critically assess strengths and weaknesses of different methods and protocols

Required Knowledge

The course requires 90 ECTS including a course in Linear Algebra, a course in Programming and either a course in Discrete Mathematics or 45 ECTS in total in Mathematics.

Form of instruction

The teaching is mainly in the form of lectures and interactive activities.

Examination modes

The course is assessed through assignments (including computer lab assignments) and a written exam.

The final grade for the course is based on a weighted assessment of the results from the various examination components.

For the whole course, one of the following grades is assigned: Fail (U), Pass (G) or Pass with distinction (VG). The grade is only set once all compulsory elements have been assessed.

A student who has been awarded a passing grade for the course cannot be reassessed for a higher grade. Students who do not pass a test or examination on the original date are given another date to retake the examination. A student who has sat two examinations for a course or a part of a course, without passing either examination, has the right to have another examiner appointed, provided there are no specific reasons for not doing so (Chapter 6, Section 22, HEO). The request for a new examiner is made to the Head of the Department of Mathematics and Mathematical Statistics. Examinations based on this course syllabus are guaranteed to be offered for two years after the date of the student's first registration for the course.

Examiners may decide to deviate from the modes of assessment in the course syllabus. Individual adaption of modes of assessment must give due consideration to the student's needs. The adaption of modes of assessment must remain within the framework of the intended learning outcomes in the course syllabus. Students who require an adapted examination must submit a request to the department holding the course no later than 10 days before the examination. The examiner decides on the adaption of the examination, after which the student will be notified.

Credit transfer
All students have the right to have their previous education or equivalent, and their working life experience evaluated for possible consideration in the corresponding education at Umeå university. Application forms should be adressed to Student services/Degree evaluation office. More information regarding credit transfer can be found on the student web pages of Umeå university, http://www.student.umu.se, and in the Higher Education Ordinance (chapter 6). If denied, the application can be appealed (as per the Higher Education Ordinance, chapter 12) to Överklagandenämnden för högskolan. This includes partially denied applications.

Other regulations

In a degree, this course may not be included together with another course with a similar content. If unsure, students should ask the Director of Studies in Mathematics and Mathematical Statistics. The course can also be included in the subject area of computational science and engineering.

Transitional provisions

In the event that the syllabus ceases to apply or undergoes major changes, students are guaranteed at least three examinations (including the regular examination opportunity) according to the regulations in the syllabus that the student was originally registered on for a period of a maximum of two years from the time that the previous syllabus ceased to apply or that the course ended.