This is Enric Florit's personal homepage.
Here you will find a growing (and at times, incomplete) list of my projects. In the materials section you'll find some slides for talks I have given. This website is updated once every few months, mostly when I have some new material to share.
A short list of places to go from here:
- The biggest and most serious project I've taken part in: Skibeta
- My when-you-got-some-time, giving-back-to-the-community, have-fun-with-some-friends project: Hacking Lliure
- The SIMBa Seminar: informal mathematics seminar in Barcelona
- My github and gitlab accounts
- My twitter account: @enricflorit (don't expect many witty words, I retweet things most of the time)
I think this will be about it for the introduction.
Oh, let me include a .png with my favourite avatar!
- February 2020. Isogeny-based cryptography. Talk given at the STNB2020 (Barcelona Number Theory Seminar).
Abstract: The SIDH protocol was presented in 2011 by Jao and De Feo, giving an alternative to the key exchange of Diffie-Hellman which is resistent to quantum cryptanalysis. Its security is based in the difficulty of finding isogenies between two supersingular elliptic curves. The main concept used is quotienting a curve by a finite subgroup, so that private keys are cyclic subgroups of a certain initial curve, and public keys are the respective quotient curves. These are computed with the Vélu formulas, although the computation of high-degree isogenies must be optimized to make the protocol effective. After explaining the protocol and justifying the choice of parameters, we will see two attacks with which we can try to break keys. You can find the slides here (pdf).
- January 2020. Isogeny Explorer: Understanding isogeny-based cryptography through visualization. Visualizations of supersingular isogeny graphs.
The topic of my Bachelor's thesis was isogeny-based cryptography. More specifically, I studied the SIDH protocol and its basic cryptanalysis. To better understand isogeny graphs and to be able to explain them, I made a way to save isogeny graphs in JSON files for visualization with D3.js. Access the final product here. The graph data was generated by my custom implementation of SIDH and its attacks in Sage, which can be found here.
- November 2019. Postquantum Cryptography: what, why, and how? Talk given at the SIMBa Seminar.
Abstract: The key agreement scheme proposed by Diffie and Hellman in 1976 relies on the problem of finding discrete logarithms. One can choose appropriate groups where the best algorithms for solving this problem are too slow, such as certain elliptic curves over finite fields. There are already proposed quantum algorithms that break discrete logarithms in polynomial time. For this reason multiple "postquantum" cryptography primitives have appeared in the last years, while trying to find harder computational problems. One of the proposed protocols using elliptic curves is SIDH/SIKE, candidate to the NIST Post-Quantum Cryptography Competition. You can find the slides here (pdf) and a recording of the talk here.
- July 2019. Elliptic curves, Pairings, and the ECDLP.
I had the opportunity to attend to a Summer School named "Cryptography meets Graph Theory" (more info here) where we were encouraged to present a poster. Mine was about the MOV attack, an algorithm that tries to simplify Discrete Logarithms over Elliptic Curves. You can find the poster here. I also wrote some study notes, although they are very incomplete. The material is fairly technical, but accessible once one has some basic knowledge on groups, arithmetic and elliptic curves.
- April 2019. p-adic attacks on elliptic curves.
The people at the Overdrive Hacking Conference asked me to do some talk on cryptograpy, and so I started studying about elliptic curve theory and ECC. During the actual talk I didn't have much time to explain the attack, but it is partially detailed in the slides. The main reference for study was Lawrence Washington's "Elliptic Curves: Number theory and Cryptography". You can find the slides here (pdf).