The Description of the problem

I have 2 secrets denoted as s 1 , s 2 s_1, s_2 s1,s2 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 s_1, s_2 s1,s2 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 s_1 s1 and s 2 s_2 s2 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 s_1 s1 and s 2 s_2 s2 in their shares format:

import random
from secretsharing import PlaintextToHexSecretSharer as Sharerdef generate_shares(secret, n_shares, threshold):shares = Sharer.split_secret(secret, threshold, n_shares)return sharesdef 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 homomorphismswapped_int_share_s1 = (int_share_s1 - int_share_s2) % Sharer.primeswapped_int_share_s2 = (int_share_s2 + int_share_s1) % Sharer.primeswapped_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_s2def recover_secret(shares):secret = Sharer.recover_secret(shares)return secretdef main():s1 = hex(random.randint(1, 1_000_000))[2:]  # Example secret 1s2 = hex(random.randint(1, 1_000_000))[2:]  # Example secret 2n_shares = 5threshold = 3shares_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 s_1 s1 and s 2 s_2 s2, 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.

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Swap 2 Secrets via Homomorphic Properties of Shamir Secret Sharing

The Description of the problem

The Solution from GPT-4

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