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EE720 Postgraduate

An Introduction to Number Theory and Cryptography

Credits
6
Type
Theory
Lecture
6 hr
Half sem
No

Course Content

SOME TOPICS IN ELEMENTARY NUMBER THEORY: Time estimates for doing arithmetic. Divisibility and the Euclidean algorithm. Congruences. Some applications to factoring.

FINITE FIELDS AND QUADRATIC RESIDUES: Finite fields. Quadratic residues and reciprocity.

CRYPTOGRAPHY: some simple cryptosystems. Enciphering matrices.

PUBLIC KEY: The idea of public key cryptography. RSA. Discrete log.

ELLPTIC CURVES: Basic facts. Elliptic curve cryptosystems.

Text / References

  1. 1 Text/references:
  2. 2 Neal Koblitz, A Course in Number and Theory and Cryptography, GraduateTexts in Mathematics No.114, Springer-Verlag, New York/Berlin/Heidelberg,1987.
  3. 3 Alan Baker, A Concise Introduction to the Theory of Numbers,Cambridge University Press, New York/Port Chester/Melbourne/Sydney, 1990.
  4. 4 A.N. Parshin and I.R. Shafarevich (Eds.), Number Theory,Encyclopaedia of Mathematics Sciences, Volume 49, Springer-Verlag, NewYork/Berlin/Heidelberg, 1995.
  5. 5 John Stillwell, Elements of Number Theory, Undergraduate Texts inMathematics, Springer-Verlag, New York/Berlin/Heidelberg, 2003.
  6. 6 Henk C.A. van Tilborg, An Introduction to Cryptology, KluwerAcademic Publishers, Boston/Dordrecht/Lancaster, 1988.
  7. 7 Andre Weil, Number Theory for Beginners, Additional references:
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