An ECDLP-Based Verifiable Multi-Secret Sharing Scheme

Secret sharing is an important issue in cryptography which has many applications. In a secret sharing scheme, a secret is shared by a dealer among several participants in such a way that any authorized subset of participants can recover the secret by pooling their shares. Recently, several schemes based on elliptic curves and bilinear maps have been presented. Some of these schemes need a secure channel, there are restrictions on the number of secrets, or the participants or the dealer are unable to verify the validity of the shares. In this paper, we present a new verifiable $(t, n)$-threshold multi-secret sharing scheme based on elliptic curves and pairings that does not have any of the above restrictions. The hardness of a discrete logarithm problem on elliptic curves guarantees the security of the proposed scheme.