How to Publicly Verifiably Expand a Member without Changing Old Shares in a Secret Sharing Scheme

摘要

Publicly verifiable secret sharing is a kind of special verifiable secret sharing, in which the shares of a secret can be verified by everyone, not only shareholders. Because of the property of public verifiability, it plays an important role in key-escrow, electronic voting, and so on. In this paper, we discuss a problem of how to publicly verifiably expand a member without changing old shares in a secret sharing scheme and present such a scheme. In the presented scheme, a new member can join a secret sharing scheme based on discrete logarithms to share the secret with the help of old shareholders. Furthermore, everyone besides the new member can verify the validity of the new member's share and any old shareholder doesn't need to change her old share. That means it is very convenient for key management.