SCHEDULE
| # | Date | Topic (references) | Materials |
|---|---|---|---|
| 1 | 2/17 | Introduction | notes, slides |
| 2 | 2/22 | The group law, Weierstrass and Edwards equations (Washington 2.1-3, 2.6.3, Bernstein-Lange 2007, Bernstein-Lange 2010) | notes, worksheet 1, worksheet 2 |
| 3 | 2/24 | Finite field arithmetic (Modern Computer Algebra 3.2, 8.1-4, 9.1, 11.1, 14.2-6, HEHCC 9.1-2, Rabin 1980, Cantor-Zassenhaus 1981) | notes, slides, worksheet, bonus video |
| 4 | 3/1 | Isogenies (Washington 2.9, Silverman III.4) | notes, slides |
| 5 | 3/3 | Isogeny kernels and division polynomials (Washington 3.2, 12.3, Silverman III.4) | notes, slides, worksheet |
| 6 | 3/9 | Endomorphism rings (Washington 4.2, , Silverman III.6) | notes, slides |
| 7 | 3/10 | Hasse's Theorem, point counting (Washington 4.3) | notes, slides |
| 8 | 3/15 | Schoof's algorithm (Washington 4.2, 4.5, Schoof 1985) | notes worksheet |
| 9 | 3/17 | Generic algorithms for the discrete logarithm problem (Washington 5.2, Pohlig-Hellman 1978, Pollard 1978, Shor 1994, Shoup 1997) | notes |
| 10 | 3/24 | Index calculus, smooth numbers, factoring integers (Washington 5.1, 7.1, Granville, Lenstra) | notes, slides, worksheet 1, worksheet 2, worksheet 3 |
| 11 | 3/29 | Elliptic curve primality proving (ECPP) (Washington 7.2, Goldwasser-Kilian, Pomerance) | notes |
| 12 | 3/31 | Endomorphism algebras (Silverman III.9) | notes, slides |
| 13 | 4/5 | Ordinary and supersingular curves (Silverman III.1,V, Washington 2.7, 4.6) | notes |
| 14 | 4/7 | Elliptic curves over C (part I) (Cox Sec. 10, Silverman VI.2-3, Washington 9.1-2) | notes |
| 15 | 4/12 | Elliptic curves over C (part II) (Cox Sec. 10-11, Silverman VI.4-5, Washington 9.2-3) | notes |
| 16 | 4/14 | Complex multiplication (CM) (Cox Sec. 11, Silverman VI.5, Washington 9.3) | notes |
| 17 | 4/21 | The CM torsor (Cox Sec. 7, Silverman (advanced topics) II.1.1) | notes |
| 18 | 4/26 | Riemann surfaces and modular curves (Silverman (advanced topics) I.2, Milne V.1) | notes |
| 19 | 4/28 | The modular equation (Cox Sec. 11, Milne V.2, Washington pp. 273-274) | notes |
| 20 | 5/3 | The Hilbert class polynomial (Cox Sec. 8, 11) | notes |
| 21 | 5/5 | Ring class fields and the CM method (Cox 8, 11) | notes |
| 22 | 5/10 | Isogeny volcanoes (Sutherland) | notes |
| 23 | 5/12 | The Weil pairing (Miller, Washington 11, Silverman III.8) | notes |
| 24 | 5/17 | Modular forms and L-functions (Milne V.3-4) | slides, notes |
| 25 | 5/19 | Fermat's last theorem (Milne V.7-9, Washington 15, Cornell-Stevens-Silverman I) | notes |
