A secret sharing scheme is a method to store information securely and
reliably. Particularly, in a threshold secret sharing scheme, a secret is
encoded into n shares, such that any set of at least t1 shares suffice to
decode the secret, and any set of at most t2<t1 shares reveal no
information about the secret. Assuming that each party holds a share and a user
wishes to decode the secret by receiving information from a set of parties; the
question we study is how to minimize the amount of communication between the
user and the parties. We show that the necessary amount of communication,
termed "decoding bandwidth", decreases as the number of parties that
participate in decoding increases. We prove a tight lower bound on the decoding
bandwidth, and construct secret sharing schemes achieving the bound.
Particularly, we design a scheme that achieves the optimal decoding bandwidth
when d parties participate in decoding, universally for all t1≤d≤n. The scheme is based on Shamir's secret sharing scheme and preserves its
simplicity and efficiency. In addition, we consider secure distributed storage
where the proposed communication efficient secret sharing schemes further
improve disk access complexity during decoding.Comment: submitted to the IEEE Transactions on Information Theory. New
references and a new construction adde