New efficient and practical verifiable multi-secret sharing schemes

In 2006, Zhao et al. proposed a practical verifiable multi-secret sharing based on Yang et al.’s and Feldman’s schemes. In this paper we propose two efficient, computationally secure (t,n), and verifiable multi-secret sharing schemes based on homogeneous linear recursion. The first scheme has the advantage of better performance, a new simple construction and various techniques for the reconstruction phase. The second scheme requires fewer public values with respect to Zhao et al.’s and Shao and Cao schemes. These schemes are easy to implement and provide great capabilities for many applications.