I finally finished typing my notes from the Algebraic Geometry course by Dr C. Birkar last Michaelmas term. As usual, they are available on the mathematics page. This is the first revision of the notes and they might still change a lot. Like most of my texts, the notes are under a Creative Commons license and you can also download the LaTeX source code. Additionally, I uploaded the Bazaar branch to Launchpad. So if you want to help me improve the text, you can just branch from lp:~caramdir/+junk/PartIII-AG. Of course, any feedback and corrections sent by e-mail (or any other way) are also always welcome.

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**Tags:** math.AG

Today I finally submitted my diploma thesis. It is titled *Mathematical Foundations of Elliptic Curve Cryptography* and contains the following topics:

- A short introduction to algebraic curves (including Riemann-Roch, but without proofs);
- some parts of the general theory elliptic curves (including basics about the Tate module and the Weil and Tate pairings);
- elliptic curves over the complex numbers;
- elliptic curves over finite fields (Weil conjectured for elliptic curves);
- elliptic curves over local fields (and the canonical lift);
- division polynomials;
- modular polynomials (also over finite fields);
- an introduction to elliptic curve cryptography;
- point counting (SEA and Satoh’s algorithm);
- cryptoanalysis: MOV/Frey-Rück, anomalous curve and Weil descent attacks
- and some connections to elliptic divisibility sequences.

Now all that is left to do is to prepare for the diploma examination…

**Tags:** cryptography, diploma thesis, ECC, elliptic curve, math.AG, math.NT