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https://github.com/marekyggdrasil/minicurve
A simple library for elliptic curve visualization.
https://github.com/marekyggdrasil/minicurve
cryptography education visualisation visualization
Last synced: about 1 month ago
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A simple library for elliptic curve visualization.
- Host: GitHub
- URL: https://github.com/marekyggdrasil/minicurve
- Owner: marekyggdrasil
- License: mit
- Created: 2021-09-10T14:23:51.000Z (about 3 years ago)
- Default Branch: main
- Last Pushed: 2021-09-14T15:17:55.000Z (about 3 years ago)
- Last Synced: 2024-09-22T12:35:18.602Z (about 2 months ago)
- Topics: cryptography, education, visualisation, visualization
- Language: Python
- Homepage:
- Size: 49.8 KB
- Stars: 2
- Watchers: 3
- Forks: 1
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
Awesome Lists containing this project
README
# minicurve
A very simple library developed by [Marek Narozniak](https://mareknarozniak.com/) for visualizing finite field over elliptic curve. The idea of making this library originates in a cryptography-related tutorial series
1. [Elliptic Curve Cryptography and Diffie-Hellman Key Exchange](https://mareknarozniak.com/2020/11/30/ecdh/)
2. [Eliptic Curve Digital Signature Algorithm](https://mareknarozniak.com/2021/03/16/ecdsa/)
3. [Schnorr Signature](https://mareknarozniak.com/2021/05/25/schnorr-signature/)
4. [Pedersen Commitments and Confidential Transactions](https://mareknarozniak.com/2021/06/22/ct/)
Disclaimer. This library is NOT secure and NOT efficient. It is meant for purely educational purposes for visualizing tutorials. Do NOT use it for any cryptography applications!
## Installation
Super simple!
```
pip install minicurve
```
## Tutorial
Points addition is as simple as `R=P+Q`, you can visualize parent points using arrows as follows.
```python
from minicurve import MiniCurve as mc
from minicurve import Visualizer
# curve parameters
a = 1
b = 7
p = 13
P = mc(a, b, p, x=10, y=4, label='P', color='tab:orange')
Q = mc(a, b, p, x=9, y=11, label='Q', color='tab:orange')
# addition of curve points
R = P + Q
R.setColor('tab:red')
R.setLabel('R')
R.x_delta = -0.3
R.arrow_thickness = 0.01 # you can control the thickness of the arrow
R.arrow_head = 20 # and its head
# visualize the finite field
vis = Visualizer(a, b, p)
vis.makeField()
vis.points = [P, Q, R]
vis.generatePlot(title='points addition $P+Q=R$ using minicurve', addition=True)
# addition=True option will use arrows to visualize addition parents
vis.plot('images/example_add.png')
```
outputs
Multiplication by scalar works in similar way as you can simply `P=4*G` and visualize the scalar using arrow path
```python
from minicurve import MiniCurve as mc
from minicurve import Visualizer
# curve parameters
a = 0
b = 5
p = 7
G = mc(a, b, p, x=3, y=2, label='G', color='tab:green', tracing=True)
# tracing=True option will enabling plotting the arrows indicating scalar multiplication
# private key
k = 4
# public key
P = k*G
P.setColor('tab:orange')
P.setLabel('P')
P.x_delta = 0.08 # you can control the label placement relative to the point
# visualize the finite field
vis = Visualizer(a, b, p)
vis.makeField()
vis.points = [G, P]
vis.generatePlot(title='scalar multiplication $k \cdot G=P, k=4$ using minicurve')
vis.plot('images/example_mul.png')
```
outputs
## FAQ
### What are the valid values of colors?
We are using [Matplotlib colors](https://matplotlib.org/stable/tutorials/colors/colors.html).
## Thanks!
Code for computing [quadratic residues](https://en.wikipedia.org/wiki/Quadratic_residue) from [this gist](https://gist.github.com/nakov/60d62bdf4067ea72b7832ce9f71ae079). Thanks to [Nakov](https://gist.github.com/nakov).