Secret sharing scheme with inherited characteristic

To assure the shareholders can look for their “legal” attorneys to renew the secret, once the secret sharing scheme is initialized, a secret sharing scheme with inherited characteristic is constructed. In this scheme, each shareholder can produce a new share by his algorithm, which is equivalent to the primary one. Together with other shares, the primary secret can be renewed. Since this scheme is constructed not by replacing the primary share with a new share produced by the dealer in his primitive secret sharing scheme, so no matter how much shares the shareholder produces, these shares can not be gathered together to renew the secret in this scheme. Compared with the existing secret sharing schemes, this scheme provides more agility for the shareholders by investing each of them a function but not affect its security.