Distributed storage plays a crucial role in the current cloud computing framework. After the theoretical bound for distributed storage was derived by the pioneer work of the regenerating code, Reed-Solomon code based regenerating codes were developed. The RS code based minimum storage regeneration code (RS-MSR) and the minimum bandwidth regeneration code (RS-MBR) can achieve theoretical bounds on the MSR point and the MBR point respectively in code regeneration. They can also maintain the MDS property in code reconstruction. However, in the hostile network where the storage nodes can be compromised and the packets can be tampered with, the storage capacity of the network can be significantly affected. In this paper, we propose a Hermitian code based minimum storage regenerating (H-MSR) code and a minimum bandwidth regenerating (H-MBR) code. We first prove that our proposed Hermitian code based regenerating codes can achieve the theoretical bounds for MSR point and MBR point respectively. We then propose data regeneration and reconstruction algorithms for the H-MSR code and the H-MBR code in both error-free network and hostile network. Theoretical evaluation shows that our proposed schemes can detect the erroneous decodings and correct more errors in hostile network than the RS-MSR code and the RS-MBR code with the same code rate. Our analysis also demonstrates that the proposed H-MSR and H-MBR codes have lower computational complexity than the RS-MSR RS-MBR codes in both code regeneration and code reconstruction.
@cite_16 , the authors discussed the amount of information that can be safely stored against passive eavesdropping and active adversarial attacks based on the regeneration structure. @cite_8 , the authors proposed to add CRC codes in the regenerating code to check the integrity of the data in hostile network. Unfortunately, the CRC checks can also be manipulated by the malicious nodes, resulting in the failure of the regeneration and reconstruction. In @cite_6 , the authors analyzed the error resilience of the RS code based regenerating code in the network with errors and erasures. They provided the theoretical error correction capability. Their result is an extension of the MDS code to the regenerating code and their scheme is unable to determine whether the errors in the network are successfully corrected.
@cite_16 @cite_6 @cite_8
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We address the problem of securing distributed storage systems against eavesdropping and adversarial attacks. An important aspect of these systems is node failures over time, necessitating, thus, a repair mechanism in order to maintain a desired high system reliability. In such dynamic settings, an important security problem is to safeguard the system from an intruder who may come at different time instances during the lifetime of the storage system to observe and possibly alter the data stored on some nodes. In this scenario, we give upper bounds on the maximum amount of information that can be stored safely on the system. For an important operating regime of the distributed storage system, which we call the bandwidth-limited regime, we show that our upper bounds are tight and provide explicit code constructions. Moreover, we provide a way to short list the malicious nodes and expurgate the system. Regenerating codes are a class of codes proposed for providing reliability of data and efficient repair of failed nodes in distributed storage systems. In this paper, we address the fundamental problem of handling errors and erasures during the data-reconstruction and node-repair operations. We provide explicit regenerating codes that are resilient to errors and erasures, and show that these codes are optimal with respect to storage and bandwidth requirements. As a special case, we also establish the capacity of a class of distributed storage systems in the presence of malicious adversaries. While our code constructions are based on previously constructed Product-Matrix codes, we also provide necessary and sufficient conditions for introducing resilience in any regenerating code. Due to the use of commodity software and hardware, crash-stop and Byzantine failures are likely to be more prevalent in today's large-scale distributed storage systems. Regenerating codes have been shown to be a more efficient way to disperse information across multiple nodes and recover crash-stop failures in the literature. In this paper, we present the design of regeneration codes in conjunction with integrity check that allows exact regeneration of failed nodes and data reconstruction in presence of Byzantine failures. A progressive decoding mechanism is incorporated in both procedures to leverage computation performed thus far. The fault-tolerance and security properties of the schemes are also analyzed.