Elliptic Curves in Cryptography
IAM 505 - Fall 2013
Exams
Textbook and References
- Washington - Elliptic Curves: Number Theory and Cryptography
- D. Hankerson, A. Menezes, S. Vanstone - Guide to Elliptic Curve Cryptography
- I. Blake, G. Seroussi, N. Smart - Elliptic curves in Cryptography
Course Policy and Exams
There will two midterms and one final exam with contibution %30, %30 and %40 respectively.
If you attend less than %60 percent of classes than you may receive NA.
Only one make-up examination will be offered. The excuse for not attending an examination must be proved with documents. The make-up examination will take place shortly after the final exam.
Course Outline
The aim of this course is to introduce the Elliptic Curves in Cryptography. After introducing the basic facts about the elliptic curves, we shall discuss the implementation of Elliptic Curves and Algorithms to compute group order. The emphasis will be given the elliptic curve cryptosystems and the related algorithms. The other applications of Elliptic Curves in Cryptography such as primality and factorization tests will also be discussed.
- Basic theory. (3 weeks)
- Torsion points. (1 week)
- Elliptic curves over finite fields. (3 weeks)
- The discrete logarithm problem. (2 weeks)
- Elliptic curve cryptography. (2 weeks)
- Primality testing. (1 week)
- Elliptic curves over complex numbers. (1 week)
- Complex multiplication. (1 week)