eccrypto: Elliptic Curve Cryptography from Scratch

A pure Python library for Elliptic Curve Cryptography (ECC), built from scratch with a focus on security, clarity, and modern Python practices.

This library provides the essential cryptographic primitives for digital signatures and key exchange, implemented with secure, constant-time algorithms and a clean, object-oriented API. It's an excellent tool for learning the fundamentals of ECC or for projects that require a clear and auditable cryptographic implementation.

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✨ Features

• Secure by Default:
  • Constant-Time scalar multiplication (Montgomery Ladder) to prevent timing side-channel attacks.
  • Deterministic Signatures (RFC 6979) to eliminate risks from faulty random number generators.
  • Non-Malleable Signatures ("low-s" normalization) to prevent signature tampering.
• Modern API: A clean, object-oriented interface for key management, signing, and verification.
• Key Exchange: Built-in support for Elliptic Curve Diffie-Hellman (ECDH) key exchange with a standard HKDF.
• Core Primitives: Includes all necessary building blocks, such as FieldElement and Point arithmetic.
• Standard Curves: Comes with built-in support for the secp256k1 curve.

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📦 Installation

Install the library from PyPI using uv:

uv add eccrypto

or by using pip:

pip install eccrypto

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🚀 Quick Start

Here are some examples of how to use the library for common cryptographic tasks.

🔑 Key Generation

First, import the secp256k1 curve and the generate_keypair helper function.

from ecc import secp256k1
from ecc import generate_keypair

# Generate a new private and public key pair
private_key, public_key = generate_keypair(secp256k1)

print("Private Key:", private_key)
print("Public Key:", public_key)

✍️ ECDSA Signing & Verification

Use the key pair to create and verify a digital signature.

# Assume `private_key` and `public_key` from the step above
message = b":D"

# Alice signs the message with her private key
signature = private_key.sign(message)
print(f"Signature: {signature}")

# Bob verifies the signature with Alice's public key
is_valid = public_key.verify(message, signature)

if is_valid:
    print("✅ Signature is valid!")
else:
    print("❌ Signature is invalid!")

🤝 ECDH Key Exchange

Establish a shared secret between two parties (Alice and Bob).

# Alice and Bob both generate their own key pairs
alice_priv, alice_pub = generate_keypair(secp256k1)
bob_priv, bob_pub = generate_keypair(secp256k1)

# Alice computes the secret using her private key and Bob's public key
secret_by_alice = alice_priv.ecdh(bob_pub)

# Bob computes the secret using his private key and Alice's public key
secret_by_bob = bob_priv.ecdh(alice_pub)

# The secrets must be identical
assert secret_by_alice == secret_by_bob
print(f"\n✅ Shared secret derived successfully: 0x{secret_by_alice.hex()}")

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📚 Documentation

For a deeper dive into the mathematical concepts behind finite fields, elliptic curve group theory, and the discriminant, please see our detailed documentation:

• Mathematical Foundations

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🛠️ Development & Testing

To set up the project for development, clone the repository and install the test dependencies:

# clone the repo
git clone [email protected]:drtoxic/ECC.git
cd ECC

# source the venv
source .venv/bin/activate

# sync
uv sync

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🤝 Contributions

Contributions, issues, and feature requests are welcome. Please feel free to open an issue or submit a pull request.

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📄 License

This project is licensed under the GPL-3.0 License. See LICENSE.

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📞 Contact

Author: Shivakumar Email: [email protected] GitHub: drtoxic69

For questions, bug reports, or feature requests, please open an issue on the GitHub repository or contact me directly via email.