keum 0.2.0

Modular elliptic curve library implementation in Python for experimentations

py-keum

This is a work in progress

Keum is a modular implementation of cryptographic components which can be used as a toolbox to bootstrap projects and experimentations. The library aims to be the building block of higher level cryptographic protocols like Plonk, Groth16, folding schemes, recursion layer, etc.

It is not supposed to be used in production! It is inefficient and not audited (and will never be).

For instance, keum includes (or will include):

• Finite field implementation
• Elliptic curve operations in different forms (Edwards, Montgomery, Weierstrass) and different coordinates (affine, jacobian, projective)
• Arithmetisation oriented hash functions (Poseidon, Griffin, Anemoi, Rescue)
• Polynomial operations
• Polynomial commitments

The generic primitives are instantiated with standard parameters. For instance, the following elliptic curves are currently supported:

• pallas
• vesta
• grumpkin
• tweedledee
• tweedledum
• secp256k1
• secp256r1
• bn254

API

Finite fields

For a more complete documentation, have a look at ff.py.

from keum import PrimeFiniteField

# Instantiate a finite field is easy as creating a subclass of PrimeFiniteField and define the class attribute ORDER to the actual order of the prime finite field
class F13(PrimeFiniteField):
    ORDER = 13

# generate random values
a = F13.random()
b = F13.random()

# add two field element
a + b

Elliptic curves

For a more complete documentation, have a look at ec.py.

The following curves are currently supported:

• pallas
• vesta
• grumpkin
• tweedledee
• tweedledum
• secp256k1
• secp256r1
• bn254

Add a new curve

New elliptic curves can be instantiated easily. See the files given above for the structure to use. When a new curve is added, it must be exposed in __init__.py, and added in the test environment in test_ec.py. The CI will take care of running the tests for the newly added curve.

from keum import pallas

# generate random values
p1 = pallas.AffineWeierstrass.random()
p2 = pallas.AffineWeierstrass.random()

# add two points
p1 + p2

How to contribute

Python 3.11 is required. Use pyenv to install it.

Install the dependencies using

poetry install

Run the tests with

poetry run pytest tests/

Format with

poetry run black keum/*.py tests/*.py