| 1 | Introduction to Elliptic Curves (PDF) | |
| 2 | The Group Law, Weierstrass and Edwards Equations (PDF) |
18.783 Lecture 2: Proof of Associativity (SWS) 18.783 Lecture 2: Group Law on Edwards Curves (SWS)
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| 3 | Finite Fields and Integer Arithmetic (PDF) | |
| 4 | Finite Field Arithmetic (PDF) | |
| 5 | Isogenies (PDF) | |
| 6 | Isogeny Kernels and Division Polynomials (PDF) | 18.783 Lecture 6: Division Polynomials (SWS) |
| 7 | Endomorphism Rings (PDF) | |
| 8 | Hasse's Theorem, Point Counting (PDF) | |
| 9 | Schoof's Algorithm (PDF) | 18.783 Lecture 9: Schoof's Algorithm (SWS) |
| 10 | Generic Algorithms for Discrete Logarithms (PDF) | |
| 11 | Index Calculus, Smooth Numbers, Factoring Integers (PDF) |
18.783 Lecture 11 - Index Calculus (SWS) 18.783 Lecture 11 - Pollard p-1 (SWS) 18.783 Lecture 11 Montgomery ECM (SWS)
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| 12 | Elliptic Curve Primality Proving (ECPP) (PDF) | |
| 13 | Endomorphism Algebras (PDF) | |
| 14 | Ordinary and Supersingular Curves (PDF) | |
| 15 | Elliptic Curves over C (Part 1) (PDF) | |
| 16 | Elliptic Curves over C (Part 2) (PDF) | |
| 17 | Complex Multiplication (PDF) | |
| 18 | The CM Action (PDF) | |
| 19 | Riemann Surfaces and Modular Curves (PDF) | |
| 20 | The Modular Equation (PDF) | |
| 21 | The Hilbert Class Polynomial (PDF) | |
| 22 | Ring Class Fields and the CM Method (PDF) | |
| 23 | Isogeny Volcanoes (PDF) | |
| 24 | The Weil Pairing (PDF) | |
| 25 | Modular Forms and L-series (PDF) | |
| 26 | Fermat's Last Theorem (PDF) | |
