Joint Signature Scheme with Elliptic Curve Cryptography (ECC) for Secure Multi-Party Computation (SMPC)

This is a production-friendly Python implementation of a joint signature scheme using Elliptic Curve Cryptography (ECC) for Secure Multi-Party Computation (SMPC). The implementation utilizes the ecdsa library for ECC operations and the SECP256k1 Elliptic Curve.

Functions

generate_key_pair()

This function generates a key pair consisting of a private key (sk) and a corresponding public key (vk) using the SECP256k1 curve.

Parameters:

• None

Returns:

• sk: A private key generated using the SECP256k1 curve.
• vk: The corresponding public key derived from the private key.

generate_shared_secret(vk_list)

This function generates a shared secret by deriving a key from the given list of public keys (vk_list).

Parameters:

• vk_list: A list of public keys from the participating parties.

Returns:

• sk_derived: A derived secret key based on the shared secret.

joint_sign(sk, vk_list, message)

This function generates a joint signature by deriving a shared secret from the given list of public keys (vk_list) and signing the provided message using the private key sk.

Parameters:

• sk: A private key used for joint signature generation.
• vk_list: A list of public keys from the participating parties.
• message: The message to be signed.

Returns:

• signature: The joint signature generated using the shared secret and the provided message.

joint_verify(vk_list, message, signature)

This function verifies a joint signature by deriving a shared secret from the given list of public keys (vk_list) and using the derived public key to verify the provided signature against the message.

Parameters:

• vk_list: A list of public keys from the participating parties.
• message: The message that was signed.
• signature: The joint signature to be verified.

Returns:

• valid: A boolean value indicating whether the joint signature is valid (True) or not (False).

Example Usage

# Generate key pairs for each party
sk1, vk1 = generate_key_pair()
sk2, vk2 = generate_key_pair()
sk3, vk3 = generate_key_pair()

# Share public keys with each other
vk_list = [vk1, vk2, vk3]

# Generate a joint signature from all parties
message = "Hello, world!"
signature = joint_sign(sk1, vk_list, message)

# Verify the joint signature
valid = joint_verify(vk_list, message, signature)
print("Signature is valid:", valid)

In this example, key pairs are generated for each party using the generate_key_pair() function. The public keys are shared among the parties by creating a vk_list. Then, a joint signature is generated using the joint_sign() function by providing a private key, the vk_list, and the message to be signed. Finally, the joint signature is verified using the joint_verify() function by providing the vk_list, the message, and the signature.

Ensure that the ecdsa library is installed before running the code (pip install ecdsa).

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With this documentation, you should have a clear understanding of the provided example and be able to utilize the joint signature scheme with ECC for Secure Multi-Party Computation in your own applications.