Abstract: Multiplicative monotone span program (or multiplicative linear secret sharing scheme)
is a important tool for building a multi-party computation protocol。In this paper, we give a necessary
and su±cient condition for a monotone span program (or linear secret sharing scheme) to be multiplica-
tive，i.e., we can decide whether a monotone span program is multiplicative by judging if a system of
linear equations is solvable. As examples, we study Shamir’s threshold secret sharing scheme and the
extended threshold scheme with weights, pointing out when they are multiplicative, respectively.