This was my TIPE for the year 2017/2018. By publishing it I hoped to make high level implementations of common algorithms related to elliptic curves more easily available, including the CM method and the Pollard-rho attack on discrete logarithms. If it can be an example to anyone that'd be great too.
The productions are all there: slides, MCOT, DOT, abstract... There are also many useless documents I produced during the year, but the important content is certainly the code in the algo folder (and the attacks folder, though it is less relevant to this TIPE). Nearly all functions in there are documented, and example usage can be found in tests.sage.
The distinction between the articles and resources directories is blurry, but surely there is one.
To generate a secure elliptic curve of a given security n with cofactor smaller than k, load the files rd_approach.sage and/or cm_approach.sage in the sage interpreter and call either gen_random or gen_cm with parameters 2^{2n} and k. See the documentation of each for details.
To generate graphs, you first need to generate performance files using the bench_* functions in tests.sage. Modify them to suit your needs, but keep in mind that generating curves of large order can take a very long time, as the implementations given here are not optimized.
Then you can call the plot_* functions to get the actual graphs, and don't forget to modify the bits array according to the computed benchmarks.
I thought after a while that this subject was far too deep for me to understand and be productive in. And I was certainly right for the maths part, of which I understood only the tiny portion shown in my slides. For this reason I focused on programming, something I could do. It paid off, especially once I realised I could actually implement the CM method, allowing me to compare two approaches. This was at the very end of the school year, when I was really questionning the interest of my work. Fake it 'till you make it. -- C. Nolan