Public Verifiability from Pairings in Secret Sharing Schemes

摘要

In this paper we propose a new publicly verifiable secret sharing scheme using pairings with close relations to Shoenmakers' scheme. This scheme is efficient, multiplicatively homomorphic and with unconditional verifiability in the standard model. We formalize the notion of lndistinguishability of Secrets and prove that out, scheme achieves it under the Decisional Bilinear Square (DBS) Assumption that, is a natural variant of the Decisional Bilinear Dime Hellman Assumption. Moreover, our scheme tolerates active and adaptive adversaries.