Secret Sharing and Statistical Zero Knowledge

This work shows a general connection between various types of statistical zero-knowledge (SZK) proof systems and (unconditionally secure) secret sharing schemes, and shows that universally-efficient secret-sharing schemes cannot exist for all (monotone languages in) $\mathbf {P}$, unless there is a polynomial q such that ${\mathbf{P}} \subseteq {\ mathbf {DSPACE}}(q(n))$.