Elliptic Curve Theory and Applications (Seminar 3: Elliptic Curves Over Finite Fields)

​Introductory course on elliptic curves, free and open to the public. This is a technical course, a light background in math will be useful but not necessary.

​Seminar 3: Elliptic Curves over Finite Fields

1. ​Finding points on E(Fp​)

2. ​Addition modulo p

3. ​Modular inverses in the slope formula

4. ​Point doubling

5. ​Orders of points

6. ​Subgroups generated by a point P

7. ​Cardinality

8. ​Hasse's theorem

9. ​Cofactors and prime-order subgroups

10. ​Scalar multiplication

11. ​Computational complexity

​Readings:

1. ​Whitfield Diffie & Martin Hellman, “New Directions in Cryptography” (1976)

2. ​Joseph H. Silverman & John T. Tate, "Rational Points on Elliptic Curves" textbook chapters 1-3

3. ​Neal Koblitz, “Elliptic Curve Cryptosystems,” Mathematics of Computation 48 (1987), 203–209.

4. ​Victor S. Miller, “Use of Elliptic Curves in Cryptography,” CRYPTO '85, pp. 417–426.