The communication complexity of secret sharing for general access structures is a basic open problem in the study of information-theoretic cryptography.
In this talk, we explore the potential power of \emph{amortization} in the context of secret sharing.
In particular, we will show that for some natural family of access structures the information rate required for supporting very long secrets is significantly better than the best known achievable rate for short secrets.
Our main result is based on a new construction of multi-party Conditional Disclosure of Secrets (CDS) for arbitrary predicates in which each party communicates less than four bits per secret bit.
