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Python wrapper for the PBC (Pairing-Based Cryptography) library

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# PyPBC

PyPBC is a Python wrapper for the PBC (Pairing-Based Cryptography) library, allowing for easy use of pairing-based cryptography in Python.

## Installation

This project follows the common "system dependency + Python wrapper" pattern:

1) Install system dependencies (GMP + PBC)
2) Install the Python package (pypbc)

### Install GMP and other dependencies

For Debian / Ubuntu systems, you can use the provided script to install the necessary dependencies for PBC:

```bash
sudo scripts/install-pbc-deps-debian
```

For other systems, you will need to manually install [GMP](https://gmplib.org/) and the build tools (gcc, flex, bison) as described in the [PBC installation instructions](https://crypto.stanford.edu/pbc/manual/installation.html).

### Install PBC

You can use the provided script to install the PBC library:

```bash
sudo scripts/install-pbc
```

### Install pypbc

Once GMP and PBC are installed, you can install pypbc via pip (for Python v3):

```bash
python3 -m pip install .
```

## Basic Usage

The library provides a simple interface to the PBC library, allowing for easy use of pairing-based cryptography in Python. Here is are some examples of how to use the library.

```python
from pypbc import *

# Initialize a set of parameters from a string 
# check the PBC documentation (http://crypto.stanford.edu/pbc/manual/) for more information
params = Parameters(
    "type a\n"
    "q 8780710799663312522437781984754049815806883199414208211028653399266475630880222957078625179422662221423155858769582317459277713367317481324925129998224791\n"
    "h 12016012264891146079388821366740534204802954401251311822919615131047207289359704531102844802183906537786776\n"
    "r 730750818665451621361119245571504901405976559617\n"
    "exp2 159\n"
    "exp1 107\n"
    "sign1 1\n"
    "sign0 1\n"
)

# Initialize the pairing
pairing = Pairing(params)

# show the order of the pairing
print(pairing.order())

# Generate random elements
g1 = Element.random(pairing, G1)
g2 = Element.random(pairing, G2)
z1 = Element.random(pairing, Zr)
z2 = Element.random(pairing, Zr)

# Check the properties of the pairing
assert pairing.apply(g1 ** z1, g2 ** z2) == pairing.apply(g1, g2) ** (z1 * z2)
```

## API Reference

### Group Enum

The library defines the following groups:

- `Zr`: The multiplicative group of integers modulo the order of the pairing.
- `G1`: The first source group of the pairing.
- `G2`: The second source group of the pairing.
- `GT`: The target group of the pairing.

The Following classes and methods are available:

### `Parameters`

- `__init__(self, string: str) -> None`: Initialize the parameters from a string.
- `__str__(self) -> str`: Return the string representation of the parameters.

### `Pairing`
    
- `__init__(self, params: Parameters) -> None`: Initialize the pairing from the given parameters.
- `order(self) -> int`: Return the order of the pairing (Zr, G1, G2 and GT).
- `apply(self, e1: Element, e2: Element) -> Element`: Apply the pairing to the given elements.
- `is_symmetric(self) -> bool`: Return whether the pairing is symmetric.

### `Element`
    
#### Constructors

- `__init__(self, pairing: Pairing, type: Group, string: str) -> None`: Initialize the element from a string representation.
- `from_int(pairing: Pairing, value: int) -> Element`: Return an element in Zr from the given integer.
- `random(pairing: Pairing, type: Group) -> Element`: Return a random element of the given type.
- `zero(pairing: Pairing, type: Group) -> Element`: Return the additive identity element of the given type.
- `one(pairing: Pairing, type: Group) -> Element`: Return the multiplicative identity element of the given type.
- `from_hash(pairing: Pairing, type: Group, data: bytes) -> Element`: Return an element from the given hash.

#### Serialize and Deserialize

- `to_bytes(self) -> bytes`: Return the byte representation of the element.
- `to_bytes_compressed(self) -> bytes`: Return the compressed byte representation of the element. (Only for G1 and G2 elements)
- `to_bytes_x_only(self) -> bytes`: Return the x-only byte representation of the element. (Only for G1 and G2 elements)
- `from_bytes(pairing: Pairing, type: Group, data: bytes) -> Element`: Return an element from the given byte representation.
- `from_bytes_compressed(pairing: Pairing, type: Group, data: bytes) -> Element`: Return an element from the given compressed byte representation. (Only for G1 and G2 elements)
- `from_bytes_x_only(pairing: Pairing, type: Group, data: bytes) -> Element`: Return an element from the given x-only byte representation. (Only for G1 and G2 elements)

#### Properties

- `order(self)`: Return the order of the element.
- `__getitem__(self, index: int) -> Element`: Return the i-th item of the element (if it is multidimensional).
- `__len__(self) -> int`: Return the length of the element, returns 0 if the element is one-dimensional.

#### Typecasting

- `__str__(self) -> str`: Return the string representation of the element.
- `__int__(self) -> int`: Return the integer representation of the element (if possible).

#### Hashing

- `__hash__(self) -> int`: Return the hash value of the element.

#### Arithmetic Operations

- `__add__(self, other: Element) -> Element`: Return the sum of the elements.
- `__sub__(self, other: Element) -> Element`: Return the difference of the elements.
- `__mul__(self, other: Element | int) -> Element`: Return the product of the elements, same as `__add__` method if the two operands are both in G1, G2 or GT, and same as `__pow__` if one of the operands is an integer or an element of Zr and another is in G1, G2 or GT.
- `__truediv__(self, other: Element) -> Element`: Return the quotient of the elements, the two operands must be in same field, it is same as `__sub__` if the two operands are both in G1, G2 or GT. ***Notice: Division between elements in G1,G2 or GT and elements in Zr is not allowed.***
- `__pow__(self, other: Element | int) -> Element`: Return the power of the element, the exponent can be an integer or an element of Zr.
- `__neg__(self) -> Element`: Return the additive inverse of the element.
- `__invert__(self) -> Element`: Return the multiplicative inverse of the element, same as `__neg__` if the element is in G1, G2 or GT.

#### Comparison Operations

- `__eq__(self, other: Element) -> bool`: Return whether the elements are equal.
- `__ne__(self, other: Element) -> bool`: Return whether the elements are not equal.
- `is0(self) -> bool`: Return whether the element is the additive identity.
- `is1(self) -> bool`: Return whether the element is the multiplicative identity.

## Acknowledgements

This project is based on the original [PyPBC](https://github.com/debatem1/pypbc) project by [Geremy Condra](https://github.com/debatem1).

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