IAMINSTITUTE OF APPLIED MATHEMATICS


IAM503

Code IAM503
Name APPLICATIONS OF FINITE FIELDS
Credits 3(3-0)
ECTS 8.0
Objective The primary focus of this course is to give structure theory of Finite Fields and the related mathematical tools that are needed in Cryptography Graduate Program of IAM.
Content - Algebraic Foundations 1) Groups 2) Rings and Fields 3) Polynomials 4) Field Extensions - Structure of Finite Fields 1) Characterization of finite fields 2) Roots of irreducible polynomials 3) Traces, norms and bases 4) Roots of unity and cyclotomic polynomials 5) Representation of elements of finite fields 6) Wedderburn’s theorem (without proof) - Polynomials over finite fields 1) Order of polynomials and primitive polynomials 2) Irreducible polynomials 3) Construction of irreducible polynomials
Outcomes

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