Multiparty Unconditionally Secure Protocols

Assume n participants P 1,P 2, . . . , Pn share the knowledge of a multivariable function F and that they want to publicly compute z =F (x1,x2, . . . , xn ), where xi is a secret input provided by Pi . The difficulty is to simultaneously provide the secrecy of each xi and to guarantee the correctness of the common result z . Such a task has been accomplished in [GMW] under the assumption that trapdoor permutations exist. The result we propose in this extended abstract is that, under the assumption that each pair of participants can communicate secretly, any reasonable function can be computed if at least 3 2n _ __ of the participants are honest and this is proved without any cryptographic assumption. Our result is based on a non-cryptographic verifiable secret sharing protocol that we also introduce in this paper.