Elliptic Curve Theory and Applications (Seminar 1: Modular Arithmetic)

​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 1: Modular Arithmetic

1. ​Congruence

2. ​Addition and multiplication mod n

3. ​Multiplicative inverses

4. ​Euclidean and extended Euclidean algorithms

5. ​Primes

6. ​The finite field Fp

7. ​Fermat's little theorem

8. ​Exponentiation in finite fields

9. ​Cyclic groups and generators

10. ​The discrete logarithm problem

11. ​Classical Diffie–Hellman

​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.

​Readings accessible on the slack channel.