Course content

An introduction to computational methods in modern algebra, primarily motivated by cryptographic problems. The course will contain an overview of the number field sieve for factoring, techniques for solving lattice problems and Gröbner basis methods for commutative rings. In order to present this material, there will also be an introduction to general algebraic number theory, including relevant computational algorithms. There will also be an introduction to basic lattice theory, the ideas of reduced lattice bases, and the relation of classical lattice theory to modern cryptography. There will also be an introduction to Gröbner basis theory, including its motivating problems in cryptography and general mathematics.

Learning outcome

1. Knowledge. The student has sufficient knowledge about algebraic number theory, lattices and Gröbner basis theory to be able to understand the relevant algorithms and their analysis, as well as their application in cryptography and general mathematics.

2. Skills. The student is able to use computational algorithms in algebraic number theory, lattices and Gröbner basis theory in order to solve important cryptographic and computational mathematical problems.

3. General competence. The course will allow students to participate in research and scientific discussions on an international level and be able to learn new topics in computational algebra.

Learning methods and activities

Lectures and mandatory exercises, including a programming project.

Compulsory assignments

• Exercises

Recommended previous knowledge

MA3201 Rings and modules and TMA4160 Cryptography or equivalent are recommended. Knowledge about programming is necessary for the exercises and the project.

Course materials

The course material will be announced at semester start.