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Course syllabus - Cryptography

Scope

7.5 credits

Course code

MAA063

Valid from

Autumn semester 2024

Education level

First cycle

Progressive Specialisation

G2F (First cycle, has at least 60 credits in first-cycle course/s as entry requirements)

Main area(s)

Mathematics/Applied Mathematics

Organisation

School of Education, Culture and Communication

Ratified

2023-12-12

Literature lists

Course literature is preliminary up to 8 weeks before course start. Course literature can be valid over several semesters.

    • Ratified date: 2024-12-17
    • Latest update: 2025-05-27

    Books

    Koblitz, Neal

    A Course in Number Theory and Cryptography

    ISBN: 1468403109, 9781468403107

    Volume 114 of Graduate Texts in Mathematics. Springer Science & Business Media,

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 disability study support, can request adaptions for the examination. It is the examiner who takes decisions on any adaptions, based on the certificate and other conditions.

Grade

Grading scale: 5, 4, 3