Secret Sharing and Statistical Zero Knowledge

We show a general connection between various types of statistical zero-knowledge (SZK) proof systems and (unconditionally secure) secret sharing schemes. Viewed through the SZK lens, we obtain several new results on secret-sharing: • Characterizations: We obtain an almost-characterization of access structures for which there are secret-sharing schemes with an efficient sharing algorithm (but not necessarily efficient reconstruction). In particular, we show that for every language L ∈ SZKL (the class of languages that have statistical zero knowledge proofs with log-space verifiers and simulators), a (monotonized) access structure associated with L has such a secretsharing scheme. Conversely, we show that such secret-sharing schemes can only exist for languages in SZK. • Constructions: We show new constructions of secret-sharing schemes with both efficient sharing and efficient reconstruction for access structures associated with languages that are in P, but are not known to be ...

• Type: Journal
• Year: 2015
• Where: ASIACRYPT
• Authors: Vinod Vaikuntanathan, Prashant Nalini Vasudevan
• Keywords: ASIACRYPT 2015, Cryptology