Verifiable secret sharing schemes based on non-homogeneous linear recursions and elliptic curves

In this paper, we propose two secure verifiable multi-secret sharing schemes that are based on non-homogeneous linear recursions and elliptic curves over ZNZN. Such schemes have simple construction and verification phases. Moreover these have various techniques for the reconstruction phase. The security of the proposed schemes is based on the security of the ECRSA cryptosystem and the intractability of the ECDLP.