A Novel and Secure Secret Sharing Algorithm Applied to Insecure Networks

In a traditional (t, n) threshold secret sharing scheme, a secret is divided into n shares and each shareholder keeps one share. Any t or more shareholders can reconstruct the secret if each of them releases its share to the others privately. However, if the communication is over insecure networks, participated shareholders may not be able to verify identities of others and the communicated information may be captured. In these cases, the secret will be obtained by an adversary without a valid share. If an adversary captures messages among shareholders to compute the secret, the attack is passive attack. If an adversary impersonates a legal shareholder to participate in secret reconstruction, the attack is active attack. In order to thwart the two attacks, this paper proposes a novel threshold changeable secret sharing scheme which can realize secure secret reconstruction over insecure networks. In the scheme, legal shareholders use random integers to protect their original shares to resist active attack. Besides, a shareholder is required to keep two shares. It keeps one share private to recover the secret for itself and uses the other share to send to other shareholders. In this way, the scheme can also thwart passive attack.