Secure Cooperative Regenerating Codes for Distributed Storage Systems

Regenerating codes enable trading off repair bandwidth for storage in distributed storage systems (DSS). Due to their distributed nature, these systems are intrinsically susceptible to attacks, and they may also be subject to multiple simultaneous node failures. Cooperative regenerating codes allow bandwidth efficient repair of multiple simultaneous node failures. This paper analyzes storage systems that employ cooperative regenerating codes that are robust to (passive) eavesdroppers. The analysis is divided into two parts, studying both minimum bandwidth and minimum storage cooperative regenerating scenarios. First, the secrecy capacity for minimum bandwidth cooperative regenerating codes is characterized. Second, for minimum storage cooperative regenerating codes, a secure file size upper bound and achievability results are provided. These results establish the secrecy capacity for the minimum storage scenario for certain special cases. In all scenarios, the achievability results correspond to exact repair, and secure file size upper bounds are obtained using min-cut analyses over a suitable secrecy graph representation of DSS. The main achievability argument is based on an appropriate pre-coding of the data to eliminate the information leakage to the eavesdropper

Explicit Construction of Optimal Exact Regenerating Codes for Distributed Storage

Erasure coding techniques are used to increase the reliability of distributed storage systems while minimizing storage overhead. Also of interest is minimization of the bandwidth required to repair the system following a node failure. In a recent paper, Wu et al. characterize the tradeoff between the repair bandwidth and the amount of data stored per node. They also prove the existence of regenerating codes that achieve this tradeoff. In this paper, we introduce Exact Regenerating Codes, which are regenerating codes possessing the additional property of being able to duplicate the data stored at a failed node. Such codes require low processing and communication overheads, making the system practical and easy to maintain. Explicit construction of exact regenerating codes is provided for the minimum bandwidth point on the storage-repair bandwidth tradeoff, relevant to distributed-mail-server applications. A subspace based approach is provided and shown to yield necessary and sufficient conditions on a linear code to possess the exact regeneration property as well as prove the uniqueness of our construction. Also included in the paper, is an explicit construction of regenerating codes for the minimum storage point for parameters relevant to storage in peer-to-peer systems. This construction supports a variable number of nodes and can handle multiple, simultaneous node failures. All constructions given in the paper are of low complexity, requiring low field size in particular.Comment: 7 pages, 2 figures, in the Proceedings of Allerton Conference on Communication, Control and Computing, September 200

Interference Alignment in Regenerating Codes for Distributed Storage: Necessity and Code Constructions

Regenerating codes are a class of recently developed codes for distributed storage that, like Reed-Solomon codes, permit data recovery from any arbitrary k of n nodes. However regenerating codes possess in addition, the ability to repair a failed node by connecting to any arbitrary d nodes and downloading an amount of data that is typically far less than the size of the data file. This amount of download is termed the repair bandwidth. Minimum storage regenerating (MSR) codes are a subclass of regenerating codes that require the least amount of network storage; every such code is a maximum distance separable (MDS) code. Further, when a replacement node stores data identical to that in the failed node, the repair is termed as exact. The four principal results of the paper are (a) the explicit construction of a class of MDS codes for d = n-1 >= 2k-1 termed the MISER code, that achieves the cut-set bound on the repair bandwidth for the exact-repair of systematic nodes, (b) proof of the necessity of interference alignment in exact-repair MSR codes, (c) a proof showing the impossibility of constructing linear, exact-repair MSR codes for d < 2k-3 in the absence of symbol extension, and (d) the construction, also explicit, of MSR codes for d = k+1. Interference alignment (IA) is a theme that runs throughout the paper: the MISER code is built on the principles of IA and IA is also a crucial component to the non-existence proof for d < 2k-3. To the best of our knowledge, the constructions presented in this paper are the first, explicit constructions of regenerating codes that achieve the cut-set bound.Comment: 38 pages, 12 figures, submitted to the IEEE Transactions on Information Theory;v3 - The title has been modified to better reflect the contributions of the submission. The paper is extensively revised with several carefully constructed figures and example

Improving the Secrecy of Distributed Storage Systems using Interference Alignment

Regenerating codes based on the approach of interference alignment for wireless interference channel achieve the cut-set bound for distributed storage systems. These codes provide data reliability, and perform efficient exact node repair when some node fails. Interference alignment as a concept is especially important to improve the repair efficiency of a failed node in a minimum storage regenerating (MSR) code. In addition it can improve the stored data security in presence of passive intruders. In this paper we construct a new code resilient against a threat model where a passive eavesdropper can access the data stored on a subset of nodes and the downloaded data during the repair process of a subset of failed nodes. We achieve an optimal secrecy capacity for the new explicit construction of MSR interference alignment code. Hence, we show that the eavesdropper obtains zero information from the original message stored across the distributed storage, and that we achieve a perfect secrecy.Comment: 20 pages, 3 figure