Course syllabus - Cryptography

Objectives

The purpose of the course is to give the student opportunity to learn the foundations of the mathematics of cryptography.

Learning outcomes

After completing the course, the student should be able to
1. describe commonly used cryptosystems and other cryptographic operations, as well as their roles in the cryptographic infrastructure
2. describe the important forms of attack against the various systems and what measures and steps should be taken to prevent these attacks
3. perform the cryptographic operations covered in the course well as the more elementary operations on which they are based
4. explain why the various operations have the properties that make them useful in cryptography
5. account for and carry out the kinds of calculations in the areas of modular arithmetic, finite fields and vector spaces over finite fields and elliptic curves, which are the basis of cryptography

Course content

- Overview of the purpose and history of cryptography
- Symmetric and asymmetric cryptosystems. Block and stream ciphers. Public key cryptography and digital signatures
- Number theory and efficient multiprecision arithmetic: modular arithmetic, prime numbers, integer factorization, the discrete logarithm problem. Applications such as the Miller-Rabin primality test, Diffie-Hellman key exchange, and the RSA cryptosystem
- Finite fields, of both prime and prime power order. Linear algebra and polynomials over finite fields
- Elliptic curves and elliptic curve cryptography
- Hash functions and their roles in cryptographic protocols, in particular message authentication codes
- Perspectives on advanced topics, such as post-quantum encryption and the Håstad attack

Specific requirements

At least 60 credits including Discrete mathematics 7.5 credits, and Programming, 7.5 credits, or equivalent.

Examination

LAB1, Laboratory work, 3 credits, computer laboratory work concerning learning outcomes 1-3 and 5, grades Fail (U) or Pass (G).
TEN1, Written examination, 4.5 credits, individual written examination concerning learning outcomes 1-5, grades Fail (U), 3, 4 or 5.

A student who has a certificate from MDU regarding a disability has the opportunity to submit a request for supportive measures during written examinations or other forms of examination, in accordance with the Rules and Regulations for Examinations at First-cycle and Second-cycle Level at Mälardalen University (2020/1655). It is the examiner who takes decisions on any supportive measures, based on what kind of certificate is issued, and in that case which measures are to be applied.

Suspicions of attempting to deceive in examinations (cheating) are reported to the Vice-Chancellor, in accordance with the Higher Education Ordinance, and are examined by the University’s Disciplinary Board. If the Disciplinary Board considers the student to be guilty of a disciplinary offence, the Board will take a decision on disciplinary action, which will be a warning or suspension.

Grade

Pass with distinction, Pass with credit, Pass, Fail