Swap 2 Secrets via Homomorphic Properties of Shamir Secret Sharing-Toy模板网

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The Description of the problem

I have 2 secrets denoted as $s_1, s_2$ and they are in different vector with same dimensions. Now all the vector are encrypted by the Shamir Secret Sharing. What is I really want is to swap the $s_1, s_2$ in their shares format via the homomorphic properties of Secret Sharing. I need you give me a python implementation.
To accomplish the task of swapping the secrets $s_1$ and $s_2$ without revealing them, you can use the additive homomorphic properties of Shamir’s Secret Sharing. I’ll provide a Python implementation using the secretsharing library:

The Solution from GPT-4

Install the secretsharing library if you haven’t already:

pip install secret-sharing

Here’s a Python implementation that demonstrates swapping the secrets $s_1$ and $s_2$ in their shares format:

import random
from secretsharing import PlaintextToHexSecretSharer as Sharer

def generate_shares(secret, n_shares, threshold):
    shares = Sharer.split_secret(secret, threshold, n_shares)
    return shares

def swap_shares(shares_s1, shares_s2):
    swapped_shares_s1 = []
    swapped_shares_s2 = []

    for share_s1, share_s2 in zip(shares_s1, shares_s2):
        int_share_s1 = int(share_s1.split('-')[1], 16)
        int_share_s2 = int(share_s2.split('-')[1], 16)

        # Swap the secrets using additive homomorphism
        swapped_int_share_s1 = (int_share_s1 - int_share_s2) % Sharer.prime
        swapped_int_share_s2 = (int_share_s2 + int_share_s1) % Sharer.prime
        
        swapped_share_s1 = share_s1.split('-')[0] + '-' + format(swapped_int_share_s1, 'x')
        swapped_share_s2 = share_s2.split('-')[0] + '-' + format(swapped_int_share_s2, 'x')

        swapped_shares_s1.append(swapped_share_s1)
        swapped_shares_s2.append(swapped_share_s2)

    return swapped_shares_s1, swapped_shares_s2

def recover_secret(shares):
    secret = Sharer.recover_secret(shares)
    return secret

def main():
    s1 = hex(random.randint(1, 1_000_000))[2:]  # Example secret 1
    s2 = hex(random.randint(1, 1_000_000))[2:]  # Example secret 2
    n_shares = 5
    threshold = 3

    shares_s1 = generate_shares(s1, n_shares, threshold)
    shares_s2 = generate_shares(s2, n_shares, threshold)

    print(f"Original shares:\nSecret 1: {shares_s1}\nSecret 2: {shares_s2}")

    swapped_shares_s1, swapped_shares_s2 = swap_shares(shares_s1, shares_s2)

    print(f"\nSwapped shares:\nSecret 1: {swapped_shares_s1}\nSecret 2: {swapped_shares_s2}")

    recovered_s2 = recover_secret(swapped_shares_s1[:threshold])
    recovered_s1 = recover_secret(swapped_shares_s2[:threshold])

    print(f"\nRecovered secrets after swapping:\nSecret 1: {recovered_s1}\nSecret 2: {recovered_s2}")

if __name__ == "__main__":
    main()

This implementation generates shares for two secrets, $s_1$ and $s_2$ , and then swaps them using homomorphic properties without revealing the secrets. Finally, it recovers the secrets from the swapped shares. Note that this implementation assumes the secrets are in hexadecimal format.文章来源地址https://www.toymoban.com/news/detail-463807.html