This short note revisits the problem of designing secure minimum storage regenerating (MSR) codes for distributed storage systems. A secure MSR code ensures that a distributed storage system does not reveal the stored information to a passive eavesdropper. The eavesdropper is assumed to have access to the content stored on @math number of storage nodes in the system and the data downloaded during the bandwidth efficient repair of an additional @math number of storage nodes. This note combines the Gabidulin codes based precoding [18] and a new construction of MSR codes (without security requirements) by Ye and Barg [27] in order to obtain secure MSR codes. Such optimal secure MSR codes were previously known in the setting where the eavesdropper was only allowed to observe the repair of @math nodes among a specific subset of @math nodes [7, 18]. The secure coding scheme presented in this note allows the eavesdropper to observe repair of any @math ouf of @math nodes in the system and characterizes the secrecy capacity of linear repairable MSR codes.
In this section we formally define the underlying eavesdropper model and the associated secrecy capacity. We then present a brief description two key components of our secure coding schemes: 1) Gabidulin precoding scheme and 2) a code construction from @cite_14 . We conclude the section with a discussion on the prior work in the area of designing secure coding schemes for distributed storage systems.
@cite_14
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In this paper, we investigate secure and reliable transmission strategies for multi-cell multi-user massive multiple-input multiple-output systems with a multi-antenna active eavesdropper. We consider a time-division duplex system where uplink training is required and an active eavesdropper can attack the training phase to cause pilot contamination at the transmitter. This forces the precoder used in the subsequent downlink transmission phase to implicitly beamform toward the eavesdropper, thus increasing its received signal power. Assuming matched filter precoding and artificial noise (AN) generation at the transmitter, we derive an asymptotic achievable secrecy rate when the number of transmit antennas approaches infinity. For the case of a single-antenna active eavesdropper, we obtain a closed-form expression for the optimal power allocation policy for the transmit signal and the AN, and find the minimum transmit power required to ensure reliable secure communication. Furthermore, we show that the transmit antenna correlation diversity of the intended users and the eavesdropper can be exploited in order to improve the secrecy rate. In fact, under certain orthogonality conditions of the channel covariance matrices, the secrecy rate loss introduced by the eavesdropper can be completely mitigated.