IAM729 - Special Topics: Normal Bases in Finite Fields

Credit: 3(3-0); ECTS: 8.0
Instructor(s): Ferruh Özbudak
Prerequisites: Consent of Instructor(s)

Course Catalogue Description

This course introduces some fundamental results in normal bases of low complexity together with its connections to cryptography and related areas.

Course Objectives

The aim of this course is to study some recent developments in representation of elements of finite fields. The main topics are construction of normal bases, optimal normal bases, normal bases of low complexity and the existence and nature of completely free elements in finite fields. The emphasis will be given on the

• some properties of characterization of normal elements,
• composition of normal bases and constructions of optimal bases.
• We will also study how to obtain good complexity normal elements in finite fields.

Course Learning Outcomes

This course will be beneficial for students interested in finite fields and their applications in cryptography and coding theory. At the end of this course, it is expected that students should have a good overview of recent approaches in normal bases over finite fields.

Tentative (Weekly) Outline

This course introduces some fundamental results in normal bases of low complexity together with its connections to cryptography and related areas.

More Info on METU Catalogue

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