Applications of Finite Fields in Cryptography and Coding Theory

• Grant number: 24/15717-2
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: December 01, 2024
• End date: November 30, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Sara Díaz Cardell
• Grantee: Daniel Souto da Silva
• Host Institution: Instituto de Geociências e Ciências Exatas (IGCE). Universidade Estadual Paulista (UNESP). Campus de Rio Claro. Rio Claro , SP, Brazil

Abstract

inite fields are a branch of algebra with scientific applications, such as in information theory. Information Theory is a very active and popular field of Mathematics. Two of its main areas are cryptography and coding theory, which stand out both for their role as an interface between algebra, geometry, combinatorics, statistics, and computation, and for their numerous applications in communication technologies.In this project, we will explore the main applications of finite fields in cryptography. For instance, we will examine the use of finite fields in widely used block ciphers today, such as AES and Camellia, as well as their role in elliptic curve cryptography. Additionally, we will provide an introduction to coding theory, covering basic concepts of linear codes, well-known types of codes, and some decoding algorithms.One of the main objectives of this project is to familiarize the student with the applications of finite fields, aiming to stimulate their interest in pursuing further studies in this area in a pos-graduation program.