ecc-pycrypto

This Python package provides simple and user-friendly implementation of ECC, supporting ElGamal encryption, ECDH and ECDSA algorithms.

Introduction

• Elliptic-curve cryptography (ECC) is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields.

  • SafeCurves provides a list of safe elliptic curves.
  • The three common types of elliptic curves are: Weierstrass Curve, Montgomery Curve and Twisted Edwards Curve.

• ElGamal encryption is a public-key cryptosystem that enables secure communication between two parties. The ElGamal elliptic curve variant can be explored further in the paper Architectural Evaluation of Algorithms RSA, ECC and MQQ in Arm Processors.

• Elliptic Curve Diffie–Hellman (ECDH) is a key agreement protocol that allows two parties, each having an elliptic-curve public–private key pair, to establish a shared secret over an insecure channel.

• Elliptic Curve Digital Signature Algorithm (ECDSA) offers a variant of the Digital Signature Algorithm (DSA) which uses elliptic-curve cryptography.

Warning

This project is intended as an educational tool to help you learn and understand the concepts of ECC and how the algorithm works. Do not use it in production environments!

Installation

git clone git@github.com:lc6chang/ecc-pycrypto.git
cd ecc-pycrypto
pip3 install .

or

pip3 install git+https://github.com/lc6chang/ecc-pycrypto.git

Usages

Elliptic curve operations

from ecc import curve, registry

# Choose a curve from registry
P256 = registry.P256
# Define a point on the curve
P = curve.AffinePoint(
    curve=P256,
    x=0x9d8b7f25322574b60f9914b240d79bf35ba7284d0c93a0b76acac49b931cbde6,
    y=0x2aae8628ed337a97cecead2e61d0c188a979a4d1383382a3696b29b449072069,
)
# The base point
G = P256.G  # AffinePoint(curve=P256, x=484395..., y=361342...)
# The neutral point
O = P256.O  # InfinityPoint(curve=P256)
# Operations
assert P + O == P
assert P - P == O
assert 100 * O == O
assert P + P == 2 * P
print(20 * P - 5 * G)  # >>> AffinePoint(curve=P256, x=280875..., y=737429...)
# Define a custom curve
MY_CURVE = curve.ShortWeierstrassCurve(
    name="MY_CURVE",
    a=...,
    b=...,
    p=...,
    n=...,
    G_x=...,
    G_y=...,
)

ElGamal encryption

from ecc import curve, registry, key, cipher

# Plaintext bytes
plaintext_bytes = b"I am plaintext."
# Generate a key pair
pri_key, pub_key = key.gen_key_pair(registry.Curve25519)
# Encode plaintext bytes into a point on the curve
plaintext_point = curve.encode(plaintext_bytes, registry.Curve25519)
# Encrypt using ElGamal algorithm
C1, C2 = cipher.elgamal_encrypt(plaintext_point, pub_key)
# Decrypt
plaintext_point_decrypted = cipher.elgamal_decrypt(pri_key, C1, C2)
# Decode the decrypted point back to plaintext bytes
plaintext_bytes_decrypted = curve.decode(plaintext_point_decrypted)
# Verify
assert plaintext_bytes_decrypted == plaintext_bytes

ECDH shared secret

from ecc import registry, key, cipher

alice_pri_key, alice_pub_key = key.gen_key_pair(registry.Curve25519)
bob_pri_key, bob_pub_key = key.gen_key_pair(registry.Curve25519)
alice_shared = cipher.ecdh_shared(alice_pri_key, bob_pub_key)
bob_shared = cipher.ecdh_shared(bob_pri_key, alice_pub_key)
assert alice_shared == bob_shared

ECDSA sign and verify

from ecc import registry, key, cipher

plaintext_bytes = b"I am plaintext."
pri_key, pub_key = key.gen_key_pair(registry.Curve25519)
signature = cipher.ecdsa_sign(plaintext_bytes, pri_key, registry.Curve25519)
assert cipher.ecdsa_verify(plaintext_bytes, signature, pub_key)
assert not cipher.ecdsa_verify(plaintext_bytes[:-1], signature, pub_key)