Multiparty computation unconditionally secure against Q^2 adversary structures

We present here a generalization of the work done by Rabin and Ben-Or in [RBO89]. We give a protocol for multiparty computation which tolerates any Q active adversary structure based on the existence of a broadcast channel, secure communication between each pair of participants, and a monotone span program with multiplication tolerating the structure. The secrecy achieved is unconditional although we allow an exponentially small probability of error. This is possible due to a protocol for computing the product of two values already shared by means of a homomorphic commitment scheme which appeared originally in [CEvdG87].