Contents |
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Course Code
IAM 503 (9700503)
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Credit
(3-0) 3
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Prerequsites
Consent of the instructor
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Content/Aims
The primary focus of this course is to give structure theory of Finite Fields and the related mathematical tools that are neded in Cryptography Graduate Program of IAM. Structure of Finite Fields, Irreducible and Primitive Polynomials over Finite Fields, Construction of Irreducible Polynomials.
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Learning Outcomes
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Suggested Textbooks/Resources
- R. Lindl and H. Niederreither, Introduction to Finite Fields and Their Applications, Cambridge Univ. Press, 1986.
- A.J. Menezes, Editor: Applications of Finite Fields, Kluwer Academic Publisher, Boston, 1993.
- A.J. Menezes, Paul C. van Oorschot and Scott A. Vanstone: Handbook of Applied Cryptography
CRC Press, 1996.
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Outline
- Groups
- Rings and Fields
- Polynomials
- Field Extensions
- Characterization of Finite fields
- Roots of irreducible polynomials
- Traces, norms and bases
- Roots of unity and cyclotomic polynomials
- Representation of elements of finite fields
- Wedderburn's theorem
- Order of polynomials and primitive polynomials
- Irreducible polynomials
- Constructions of irreducible polynomials