pymcl

A Python 3 wrapper for the mcl library. Currently support operations on BLS12-381 curve.

Requirements

• Python 3.10 or higher

If you want to build from source, please check readme of mcl.

Installation

Install from PyPI (recommended):

pip install pymcl

Or install from source:

git clone https://github.com/Jemtaly/pymcl
cd pymcl
pip install .

Supported Platforms

• Linux: x86_64, aarch64 (ARM64)
• macOS: x86_64 (Intel), arm64 (Apple Silicon), universal2
• Windows: AMD64 (x64)

Basic Usage

Here is an example of how to use pymcl:

import pymcl

g1 = pymcl.g1 # generator of G1
g2 = pymcl.g2 # generator of G2
x1 = pymcl.Fr.random() # random element in Fr
x2 = pymcl.Fr.random() # random element in Fr

# check the correctness of the pairing
assert pymcl.pairing(g1 * x1, g2 * x2) == pymcl.pairing(g1, g2) ** (x1 * x2)

Other Operations

There are 4 types of elements in pymcl: Fr, G1, G2, and GT. You can perform operations on these elements as follows:

Fr Class

Fr(s: str) -> Fr

Create an element in Fr from a string, which is the decimal representation of the element. The library does not supply a constructor for Fr from an integer, you can convert an integer to a string and then use this constructor, the integer should be in the range of $[0, r)$, where $r$ is the order of the Fr group.

Fr.__str__(self: Fr) -> str

Convert the element to a string.

Fr.random() -> Fr

Return a random element in Fr.

Fr.__add__(self: Fr, other: Fr) -> Fr
Fr.__sub__(self: Fr, other: Fr) -> Fr
Fr.__neg__(self: Fr) -> Fr
Fr.__mul__(self: Fr, other: Fr) -> Fr
Fr.__truediv__(self: Fr, other: Fr) -> Fr
Fr.__invert__(self: Fr) -> Fr

Perform addition, subtraction, negation, multiplication, division, and inversion on the element.

Fr.__eq__(self: Fr, other: Fr) -> bool
Fr.__ne__(self: Fr, other: Fr) -> bool
Fr.isZero(self: Fr) -> bool
Fr.isOne(self: Fr) -> bool

Check the equality and inequality of the element, and check if the element is the additive identity or the multiplicative identity.

Fr.__hash__(self: Fr) -> int

Return the hash value of the element.

Fr.serialize(self: Fr) -> bytes
Fr.deserialize(b: bytes) -> Fr

Serialize and deserialize the element.

G1 Class

G1(s: str) -> G1

Create an element in G1 from its string representation.

G1.__str__(self: G1) -> str

Convert the element to a string. (check the API of mcl for the format of the string representation)

G1.hash(b: bytes) -> G1

Hash a byte array to an element in G1. (check here)

G1.__add__(self: G1, other: G1) -> G1
G1.__sub__(self: G1, other: G1) -> G1
G1.__neg__(self: G1) -> G1
G1.__mul__(self: G1, other: Fr) -> G1

Perform addition, subtraction, negation, and multiplication on the element. Note that for the multiplication of G1 and Fr, the Fr element should be on the right-hand side.

G1.__eq__(self: G1, other: G1) -> bool
G1.__ne__(self: G1, other: G1) -> bool
G1.isZero(self: G1) -> bool

Check the equality and inequality of the element, and check if the element is the additive identity.

G1.__hash__(self: G1) -> int

Return the hash value of the element.

G1.serialize(self: G1) -> bytes
G1.deserialize(b: bytes) -> G1

Serialize and deserialize the element (in compressed form).

G2 Class

The G2 class has the same methods as the G1 class.

GT Class

GT(s: str) -> GT

Create an element in GT from its string representation.

GT.__str__(self: GT) -> str

Convert the element to a string.

GT.__mul__(self: GT, other: GT) -> GT
GT.__truediv__(self: GT, other: GT) -> GT
GT.__invert__(self: GT) -> GT
GT.__pow__(self: GT, other: Fr) -> GT

Perform multiplication, division, inversion, and exponentiation on the element.

GT.__eq__(self: GT, other: GT) -> bool
GT.__ne__(self: GT, other: GT) -> bool
GT.isZero(self: GT) -> bool
GT.isOne(self: GT) -> bool

Check the equality and inequality of the element, and check if the element is the additive identity or the multiplicative identity.

GT.__hash__(self: GT) -> int

Return the hash value of the element.

GT.serialize(self: GT) -> bytes
GT.deserialize(b: bytes) -> GT

Serialize and deserialize the element.

Other Function and Constants

pairing(a: G1, b: G2) -> GT

Compute the pairing of two elements in G1 and G2, note that the first argument should be in G1 and the second argument should be in G2.

g1: G1
g2: G2

The generator of G1 and G2.

r: int

The order of the G1, G2, Fr, and GT groups.