Communication efficient secret sharing

Document Type

Article

Publication Date

12-1-2016

Abstract

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 a generalization of Shamir's secret sharing scheme and preserves its simplicity and efficiency. In addition, we consider the setting of secure distributed storage where the proposed communication efficient secret sharing schemes not only improve decoding bandwidth but further improve disk access complexity during decoding.

Identifier

84999106904 (Scopus)

Publication Title

IEEE Transactions on Information Theory

External Full Text Location

https://doi.org/10.1109/TIT.2016.2616144

ISSN

00189448

First Page

7195

Last Page

7206

Issue

12

Volume

62

Grant

CCF-1218005

Fund Ref

National Science Foundation

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