Elliptic Curve Utils (ecutils)

Elliptic Curve Utils, or ecutils, is a Python package that provides utilities for working with elliptic curves, particularly in the context of cryptography. It includes functionality for operations like point addition and scalar multiplication on curves, as well as higher-level protocols like key exchange and digital signatures.

Features

• Implements common elliptic curve operations such as point addition and multiplication.
• Provides classes for encoding/decoding textual messages to and from elliptic curve points (e.g., Koblitz encoding).
• Supports several standardized elliptic curves including secp192k1, secp256r1, and secp521r1.
• Includes an implementation of the Elliptic Curve Digital Signature Algorithm (ECDSA) for signing messages and verifying signatures.
• Features key exchange protocols like Diffie-Hellman and Massey-Omura over elliptic curves.

Installation

You can install the ecutils package using pip:

pip install ecutils

Usage

Encoding and Decoding Messages with Koblitz

from ecutils.algorithms import Koblitz

# Initialize Koblitz with a specific curve
koblitz = Koblitz(curve_name="secp256k1")

# Encode a message to a curve point
point, j = koblitz.encode("Hello, World!")

# Decode the curve point back to a message
decoded_message = Koblitz.decode(point, j)

Digital Signatures with ECDSA

from ecutils.algorithms import DigitalSignature

# Create a DigitalSignature instance with your private key
ds = DigitalSignature(private_key=123456)

# Hash of your message
message_hash = hash('your message')

# Generate signature
r, s = ds.generate_signature(message_hash)

# Verify signature (typically on the receiver's side)
is_valid = ds.verify_signature(ds.public_key, message_hash, r, s)

Diffie-Hellman Key Exchange

from ecutils.protocols import DiffieHellman

# Alice's side
alice = DiffieHellman(private_key=12345)

# Bob's side
bob = DiffieHellman(private_key=67890)

# Alice computes her shared secret with Bob's public key
alice_shared_secret = alice.compute_shared_secret(bob.public_key)

# Bob computes his shared secret with Alice's public key
bob_shared_secret = bob.compute_shared_secret(alice.public_key)

# alice_shared_secret should be equal to bob_shared_secret

MasseyOmura Key Exchange

from ecutils.protocols import MasseyOmura
from ecutils.algorithms import Koblitz

# Initialize the Koblitz instance for the elliptic curve 'secp192k1'
koblitz = Koblitz(curve_name='secp192k1')

# Sender's side
# -------------
# Sender chooses their private key
private_key_sender = 123456789
# Initialize Massey-Omura protocol with the sender's private key
mo_sender = MasseyOmura(private_key_sender, curve_name='secp192k1')

# Encode the message using the Koblitz method
# `j` is used to handle the ambiguity in the decoding process
message, j = koblitz.encode("Hello, world!")

# Perform the first encryption step with Massey-Omura protocol
encrypted_msg_sender = mo_sender.first_encryption_step(message)

# The encoded message is now sent to the receiver...
# (transmission of encrypted_msg_sender)

# Receiver's side
# ---------------
# Receiver chooses their private key
private_key_receiver = 987654321
# Initialize Massey-Omura protocol with the receiver's private key
mo_receiver = MasseyOmura(private_key_receiver, curve_name='secp192k1')

# Perform the second encryption step with Massey-Omura protocol
encrypted_msg_receiver = mo_receiver.second_encryption_step(encrypted_msg_sender)

# The double-encrypted message is sent back to the sender...
# (transmission of encrypted_msg_receiver)

# Sender's side again
# -------------------
# Perform the partial decryption step with Massey-Omura protocol
partial_decrypted_msg = mo_sender.partial_decryption_step(encrypted_msg_receiver)

# The partially decrypted message is sent back to the receiver...
# (transmission of partial_decrypted_msg)

# Receiver's final decryption
# ---------------------------
# Finish decryption with Massey-Omura protocol to get the original message
original_message = mo_receiver.partial_decryption_step(partial_decrypted_msg)

# Decode the message using the Koblitz method
# `j` is used to resolve the mapping from the elliptic curve point back to the message
decoded_message = koblitz.decode(original_message, j)

# The decoded_message contains the original plaintext message
print(decoded_message)

Documentation

For more in-depth use and examples, check out the official documentation.

Support

For issues, questions, or contributions, please refer to the project's GitHub repository.

License

This project is licensed under the MIT License.

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Cross-Platform Compiled Library

In addition to this Python module, there exists a cross-platform compiled library that offers similar functionalities. This library is available under the Apache Version 2.0 license and can be found on the official website:

ecutils - software distribution

If you need an implementation outside of the Python environment or seek integration with other programming languages, this library might be an excellent alternative.