چكيده به لاتين
A (t,n) secret sharing scheme (SSS) enables a dealer to divide a secret into n shares in such a way that (i) the secret can be recovered successfully with t or more than t shares, and (ii) the secret cannot be recovered with fewer than t shares. A verifiable secret sharing scheme (VSSS) has been proposed to allow shareholders to verify that their shares are generated by the dealer consistently without compromising the secrecy of both shares and the secret. So far, there is only one secure Chinese remainder theorem-based VSSS using the RSA assumption. In third season is mentioned a Chinese remainder theorem-based VSS scheme without making any computational assumptions, which is a simple extension of Azimuth–Bloom (t,n) SSS. Just like the most well-known Shamir’s SSS, the proposed VSSS is unconditionally secure. In addition, no information is leaked when there are fewer than t shares in the secret reconstruction. In secret sharing, a Multi-Level threshold Secret Sharing scheme (MLSSS) divides shares into different levels. Shares at higher levels can be used at lower ones but shares of lower levels are invalid at higher ones. However, MLSSS is limited in applications and vulnerable to Illegal Participant (IP) attack and t- Share Capture (SC) attack. Therefore, forth season,first extends the notion of MLSSS to multi-group threshold secret sharing (MGSSS) to accommodate wider application scenarios. In order to cope with the 2 attacks, then proposes a tightly coupled MGSS scheme based on Chinese Remainder Theorem. In the scheme, a shareholder, with only one private share, is allowed to participate in secret reconstruction of different groups. Moreover, only if each participant has valid share and actually participates in secret reconstruction.
