Verifiable multi-secret sharing schemes for multiple threshold access structures

A multi-secret sharing scheme allows several secrets to be shared amongst a group of participants. In 2005, Shao and Cao developed a verifiable multi-secret sharing scheme where each participant’s share can be used several times which reduces the number of interactions between the dealer and the group members. In addition some secrets may require a higher security level than others involving the need for different threshold values. Recently Chan and Chang designed such a scheme but their construction only allows a single secret to be shared per threshold value. In this article we combine the previous two approaches to design a multiple time verifiable multi-secret sharing scheme where several secrets can be shared for each threshold value. Since the running time is an important factor for practical applications, we will provide a complexity comparison of our combined approach with respect to the previous schemes.