plot_curve_finite.py

import matplotlib.pyplot as plt
import numpy as np
from local.ec.static import XY
from local.ec.core import MAX_COORDINATE, PARAMETER_A, PARAMETER_B


def plot():
    # Initialize the plot
    fig, ax = plt.subplots()
    ax.set_title("Elliptic curve $y^2 \equiv x^3 + {}x + {}$ (mod {})".format(PARAMETER_A.value, PARAMETER_B.value, MAX_COORDINATE))
    ax.set_xlabel("x")
    ax.set_ylabel("y")

    # Initialize an array of zeros (white squares)
    points = np.zeros((MAX_COORDINATE, MAX_COORDINATE))

    # Add points on the curve
    for (dlog, xy) in enumerate(XY):
        if xy:
            # Inverted coordinates
            # because imshow treats first component as rows (y coordinate)
            # and second component as columns (x coordinate)
            points[xy[1], xy[0]] = 1
            ax.text(xy[0], xy[1], str(dlog), ha="center", va="center", color="white")

    # Plot the curve
    # Set origin to the bottom left
    # because imshow places it at the top left by default
    ax.imshow(points, cmap='gray_r', origin='lower')

    # Show plot
    plt.show()


if __name__ == "__main__":
    plot()