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Generic Secure Repair for Distributed Storage

Huang, Wentao and Bruck, Jehoshua (2017) Generic Secure Repair for Distributed Storage. . (Unpublished)

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This paper studies the problem of repairing secret sharing schemes, i.e., schemes that encode a message into n shares, assigned to n nodes, so that any n−r nodes can decode the message but any colluding z nodes cannot infer any information about the message. In the event of node failures so that shares held by the failed nodes are lost, the system needs to be repaired by reconstructing and reassigning the lost shares to the failed (or replacement) nodes. This can be achieved trivially by a trustworthy third-party that receives the shares of the available nodes, recompute and reassign the lost shares. The interesting question, studied in the paper, is how to repair without a trustworthy third-party. The main issue that arises is repair security: how to maintain the requirement that any colluding z nodes, including the failed nodes, cannot learn any information about the message, during and after the repair process? We solve this secure repair problem from the perspective of secure multi-party computation. Specifically, we design generic repair schemes that can securely repair any (scalar or vector) linear secret sharing schemes. We prove a lower bound on the repair bandwidth of secure repair schemes and show that the proposed secure repair schemes achieve the optimal repair bandwidth up to a small constant factor when n dominates z, or when the secret sharing scheme being repaired has optimal rate. We adopt a formal information-theoretic approach in our analysis and bounds. A main idea in our schemes is to allow a more flexible repair model than the straightforward one-round repair model implicitly assumed by existing secure regenerating codes. Particularly, the proposed secure repair schemes are simple and efficient two-round protocols.

Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription Paper
Huang, Wentao0000-0003-0963-3624
Bruck, Jehoshua0000-0001-8474-0812
Record Number:CaltechAUTHORS:20191004-142514161
Persistent URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:99094
Deposited By: Tony Diaz
Deposited On:04 Oct 2019 21:40
Last Modified:04 Oct 2019 21:40

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