eladkay / ellipticcurve

Elliptic curve cryptography learning aid & visualizer

Elliptic Curve Cryptography Study Tool

Project File contains full information about the project (in Hebrew). This project was written as part of the requirements for the Computer Science - Academy & Industry program at the Davidson Institute in the 2019-2020 school year.

Features:

• Visualization of curves over finite fields as well as over the reals
• Calculation of all basic operations on elliptic curves, both numerically and graphically
• Calculation of various tables of information about the curves, like curve order, points' orders, addition tables, subgroups, lines of symmetry & more!
• Calculation of encoding, decoding, encryption and decryption on elliptic curves
• & more...

This project is written in Kotlin, with Swing.

ellipticcurve's Issues

Security issue in ECC certificates, would be interesting to address

https://portal.msrc.microsoft.com/en-US/security-guidance/advisory/CVE-2020-0601

Smootify curves

https://www.particleincell.com/2012/bezier-splines/

See 3b1b/manim for bezier.py and vectorized_mobject.py and functions.py

There is no need to do anything complex to solve the linear system of equations. Just copy over code from Eladkay/EqSolver, it’ll be okay. It is slow - very slow. It does the actual matrix inversion and all the determinants. Its complexity is off the charts. Maybe it’d be a good idea to do one of the following: 1. Rewrite it to use a more efficient algorithm like Gaussian elimination, 2. Scrap it and use a specialized algorithm like the one described that is specialized to triangular matrices, 3. Find a way to not do the calculations so many times per second.

This is currently the hardest challenge this project is facing. It is important to maintain compatibility and abstractness wrt Field.kt.

To do list & schedules

This issue will detail the general plans and schedules in order to finish the project in time.

[ ] Until Oct 4th - finish curve rendering

Oct 4th - Oct 19th - vacation; no work will be done in practice.

[ ] Until Oct 31st - finish operation calculator

[ ] Until Dec 15th - finish mid-term report and hand it in

[ ] Until Jan 1st - finish encryption/decryption simulator

[ ] Until Feb 29th - polish everything and write presentation & reports

Add diophantine equation solver

https://www.quora.com/What-is-the-significance-of-the-modularity-theorem

Generalize EllipticSimulator to work on any curve

Check out acm graphics