A Verifiable Multi-Secret Sharing Scheme with Elliptic Curve Cryptography

Abstract

In a multi-secret sharing scheme (MSS) more than one secrets are shared among a set of authorized participants on a public channel. A multi-secret sharing scheme is verifiable, if the secrecy of both secrets and shares are maintained such that the participants and the combiner both can verify the correctness of the shares transferred to them and also the correctness of the secrets obtained after executing the reconstruction process of the secret sharing scheme. We propose a verifiable (k, t, n) threshold multi-secret sharing scheme based on MSS proposed by Shao (2014). In a typical (k, t, n) threshold MSS scheme, the dealer shares $k$ secrets among $n$ participants secretly (in encoded way) so that all the $k$ secrets can be revealed if any $t$ or more (≤ n) participants submit their shares, whereas none of the secrets can be revealed by any less than $t$ participants. At the same time the shares obtained and secrets reconstructed are verifiable by participants and combiner. We propose to use public channel for distribution process rather than private channel used in Shao's MSS scheme. In the proposed scheme the distribution over public channel is made secure using Elliptic Curve Deffie-Hellman (ECDH) protocol.