minicurve

A very simple library developed by Marek Narozniak 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
2. Eliptic Curve Digital Signature Algorithm
3. Schnorr Signature
4. Pedersen Commitments and Confidential Transactions

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.

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

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.

Thanks!

Code for computing quadratic residues from this gist. Thanks to Nakov.