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

On Epsilon-MSCR Codes for Two Erasures

Cooperative regenerating codes are regenerating codes designed to tradeoff storage for repair bandwidth in case of multiple node failures. Minimum storage cooperative regenerating (MSCR) codes are a class of cooperative regenerating codes which achieve the minimum storage point of the tradeoff. Recently, these codes have been constructed for all possible parameters $(n,k,d,h)$, where $h$ erasures are repaired by contacting any $d$ surviving nodes. However, these constructions have very large sub-packetization. $\epsilon$-MSR codes are a class of codes introduced to tradeoff subpacketization level for a slight increase in the repair bandwidth for the case of single node failures. We introduce the framework of $\epsilon$-MSCR codes which allow for a similar tradeoff for the case of multiple node failures. We present a construction of $\epsilon$-MSCR codes, which can recover from two node failures, by concatenating a class of MSCR codes and scalar linear codes. We give a repair procedure to repair the $\epsilon$-MSCR codes in the event of two node failures and calculate the repair bandwidth for the same. We characterize the increase in repair bandwidth incurred by the method in comparison with the optimal repair bandwidth given by the cut-set bound. Finally, we show the subpacketization level of $\epsilon$-MSCR codes scales logarithmically in the number of nodes.Comment: 14 pages, Keywords: Cooperative repair, MSCR Codes, Subpacketizatio

Functional broadcast repair of multiple partial failures in wireless distributed storage systems

We consider a distributed storage system with n nodes, where a user can recover the stored file from any k nodes, and study the problem of repairing r partially failed nodes. We consider broadcast repair , that is, d surviving nodes transmit broadcast messages on an error-free wireless channel to the r nodes being repaired, which are then used, together with the surviving data in the local memories of the failed nodes, to recover the lost content. First, we derive the trade-off between the storage capacity and the repair bandwidth for partial repair of multiple failed nodes, based on the cut-set bound for information flow graphs. It is shown that utilizing the broadcast nature of the wireless medium and the surviving contents at the partially failed nodes reduces the repair bandwidth per node significantly. Then, we list a set of invariant conditions that are sufficient for a functional repair code to be feasible. We further propose a scheme for functional repair of multiple failed nodes that satisfies the invariant conditions with high probability, and its extension to the repair of partial failures. The performance of the proposed scheme meets the cut-set bound on all the points on the trade-off curve for all admissible parameters when k is divisible by r , while employing linear subpacketization, which is an important practical consideration in the design of distributed storage codes. Unlike random linear codes, which are conventionally used for functional repair of failed nodes, the proposed repair scheme has lower overhead, lower input-output cost, and lower computational complexity during repair