Elliptic Curve Theory and Applications (Seminar 4: Elliptic Curve Cryptography)

​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 4: Elliptic Curve Cryptography

1. ​EC Diffie-Hellman

2. ​Public/private key pairs

3. ​ECDSA

4. ​Nonces

5. ​Why ECC achieves comparable security with smaller keys

6. ​Examples (secp256k1, Curve25519/X25519, etc)

7. ​What makes a curve cryptographically suitable

8. ​Invalid points subgroup issues

9. ​Side-channel considerations

10. ​Quantum threat, Shor's algorithm

11. ​Why ECC is not post-quantum secure

​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.