### Install LightECC Package

Source: https://github.com/serengil/lightecc/blob/main/README.md

Install the LightECC library using pip. This command fetches and installs the package from the Python Package Index (PyPI).

```shell
pip install lightecc
```

--------------------------------

### Import LightECC Library

Source: https://github.com/serengil/lightecc/blob/main/README.md

Import the LightECC class from the installed library to begin using its functionalities in your Python script.

```python
from lightecc import LightECC
```

--------------------------------

### Initialize and Use Elliptic Curve Arithmetic

Source: https://github.com/serengil/lightecc/blob/main/README.md

Initialize a LightECC object with a specified form and curve name. Perform basic arithmetic operations like addition, subtraction, multiplication, and division on the curve's base point (G).

```python
from lightecc import LightECC

# build an elliptic curve
ec = LightECC(
    form_name = "edwards", # or weierstrass, koblitz. default is weierstrass.
    curve_name = "ed25519", # check out supported curves section
)

# get the base point
G = ec.G

# addition
_2G = G + G
_3G = _2G + G
_5G = _3G + _2G
_10G = _5G + _5G

# subtraction
_9G = _10G - G

# multiplication
_20G = 20 * G
_50G = 50 * G

# division
_25G = _50G / G
```

--------------------------------

### Demonstrate Neutral Element and Cyclic Group Properties

Source: https://github.com/serengil/lightecc/blob/main/README.md

Illustrates the neutral element (point at infinity) and cyclic group properties of an elliptic curve. The neutral element does not change a point when added, and adding the order 'n' to a scalar results in the same point.

```python
ec = LightECC()

# order of elliptic curve
n = ec.n

# neutral element
neutral = n * G

# scalar multiplication
_17G = 17 * G
minus17G = -1 * _17G

# proof of work for neutralism
assert _17G == _17G + neutral
assert _17G + minus17G == neutral

# proof of work for cyclic group
assert (n + 1) * G == G
assert (n + 2) * G == 2 * G
```

--------------------------------

### LightECC Citation (BibTeX)

Source: https://github.com/serengil/lightecc/blob/main/README.md

BibTeX entry for citing the LightECC library in academic publications. This format is commonly used in LaTeX documents.

```BibTeX
@misc{serengil2025lightecc
    author       = {Serengil, Sefik Ilkin},
    title        = {LightECC: A Lightweight Elliptic Curve Cryptography Arithmetic Library for Python with Support for Prime and Binary Fields},
    year         = {2025},
    publisher    = {GitHub},
    howpublished = {https://github.com/serengil/LightECC},
}
```

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