Password-protected secret sharing scheme with the same threshold in distribution and restoration

Conventional password-protected secret sharing (PPSS) based on Shamir's (k, n) secret sharing scheme requires 2k - 1 shares for reconstructing a search result. However, it can reconstruct the secret by leveraging k shares, because it performs secure multiplication. In this case, it is easier to restore the secret than the search result. In this paper, we propose a novel PPSS with the same distribution threshold for the secret as well as the restoration of the search result. We use the TUS2 method proposed by Aminuddin et al. However, it cannot include 0 as a secret. Therefore, we improve the TUS2 method such that it can include 0 as secret. In addition, we evaluate the security of our scheme, and prove that it is secure. Furthermore, we compare the computational cost of the conventional PPSS and our scheme.