IAM503 - Applications of Finite Fields
Instructor(s): Ferruh Özbudak
Prerequisites: Consent of Instructor(s)
Course Catalogue DescriptionStructure of Finite Fields, Polynomials over Finite Fields, Factorization of Polynomials, Construction of Irreducible Polynomials, Normal and Optimal Normal Basis.
Course ObjectivesThe 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.
Course Learning OutcomesThis is one of the core courses of the Cryptography Graduate Program which gives the mathematical background on Finite Fields and Their Applications to Cryptography. The contents discussed in this course will be needed throughout various courses including Stream ciphers and various Public Key cryptosystems. So one can understand through these courses whether the outcome of this course is achieved or not.
Tentative (Weekly) Outline- 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
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