Verifiable Secret Sharing Scheme Using Merkle Tree

Abstract

In Shamir’s (k,n) secret sharing scheme, the distributor splits a secret into n shares(shadows), and sends the shares to n participants. Each participant has a different share. In the phase of secret reconstruction, only K or more participants with their shares can reconstruct the secret together, less than K participants can’t reconstruct the secret, and know nothing about the secret. Shamir’s scheme is unconditionally secure in theory. However, this scheme can’t prevent adversaries from cheating. In asynchronous communication, a dishonest participant or a foreign adversary sends a fake share to the honest participants after he gets the shares from other participants and will reconstruct the secret alone while the other honest participants cannot reconstruct the secret. This scheme does not verify the share and identify the participants. In this paper, an efficient share verification method based on Merkel tree will be discussed, in which the root and authentication paths of a Merkel tree are used to verify shares between the participants, so that they can reconstruct secrets correctly after verifying and eliminating the fake shares. This method does not need complex algorithms and estimating the number of cheaters in advance, and will not increase the size of each share.