Elliptic Curve Theory and Applications: The Geometry of Elliptic Curves

​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 2: The Geometry of Elliptic Curves

1. ​Why does the group law work?

2. ​Projective geometry and the point at infinity

3. ​Bézout's Theorem

4. ​Singularities and nonsingular curves

5. ​Associativity and the group law

6. ​The complex picture: elliptic curves and the torus

​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.