Secret sharing with secure secret reconstruction

Threshold secret sharing is a fundamental building block in information security to provide secrecy and robustness services for various cryptographic protocols. According to the definition of (t, n) threshold secret sharing, the secret is divided into n shares, such that any t or more than t of these shares allow the secret to be reconstructed; but less than t shares reveal no information of the secret. In other words, this definition only considers protection of the secret from colluded insiders but not outsiders. In this paper, we propose an extended secret sharing scheme, called secret sharing with secure secret reconstruction, in which the secret can be protected in the reconstruction phase from both attacks of insiders and outsiders. In traditional secret sharing schemes, when more than t shares are presented in the secret reconstruction, outsiders only need to intercept t shares to recover the secret. But in our proposed basic scheme, outsiders need to intercept all the released shares to recover the secret. Obviously, requiring more shares in the reconstruction contributes to security enhancement for this process. The limitation of this basic scheme is that it cannot prevent outsiders from learning the secret if they intercept all the released shares. To address this issue, we further extend the basic scheme so that the reconstructed secret is only accessible to shareholders, but not to outsiders. To the best of our knowledge, our extended scheme is the first secret sharing scheme that satisfies this property with information theoretical security. (C) 2020 Published by Elsevier Inc.