Secret Verification Method Suitable for the Asymmetric Secret Sharing Scheme

Conventional secret sharing schemes, such as Shamir's secret sharing scheme, cannot prevent the leak of shares when they are deposited on servers. In contrast, in an asymmetric secret sharing scheme, the owner of the secret has a stronger authority than the server, and the number of servers storing the share can be set to less than k. Therefore, even if all the shares stored in the server leak, the secret is not leaked. This can prevent the leakage of secrets from attacks on servers. In the conventional secret sharing scheme, a correct secret cannot be reconstructed if the attacker outputs a false share at the time of reconstruction by hijacking the server. This problem cannot be addressed even if asymmetric secret sharing is used. Therefore, we extend the asymmetric secret sharing scheme in a manner enabling the owner to detect a secret when an attacker outputs a false share. In the proposed scheme, a server is not required to store information other than the share if n > k. In other words, no burden is imposed on the server for verification. In addition, the hijacked servers can be identified under certain conditions, realizing an efficient verification method for secrets that is suitable for the asymmetric secret sharing scheme.