Optimal Locally Repairable and Secure Codes for Distributed Storage Systems (1210.6954v2)

Abstract: This paper aims to go beyond resilience into the study of security and local-repairability for distributed storage systems (DSS). Security and local-repairability are both important as features of an efficient storage system, and this paper aims to understand the trade-offs between resilience, security, and local-repairability in these systems. In particular, this paper first investigates security in the presence of colluding eavesdroppers, where eavesdroppers are assumed to work together in decoding stored information. Second, the paper focuses on coding schemes that enable optimal local repairs. It further brings these two concepts together, to develop locally repairable coding schemes for DSS that are secure against eavesdroppers. The main results of this paper include: a. An improved bound on the secrecy capacity for minimum storage regenerating codes, b. secure coding schemes that achieve the bound for some special cases, c. a new bound on minimum distance for locally repairable codes, d. code construction for locally repairable codes that attain the minimum distance bound, and e. repair-bandwidth-efficient locally repairable codes with and without security constraints.

• The paper introduces secure coding schemes that significantly improve secrecy capacity using Gabidulin pre-coding, achieving optimal protection against eavesdropping.
• It derives upper bounds for local repairability and constructs efficient codes that balance fault tolerance with minimal repair bandwidth.
• The research presents practical constructions that integrate regenerating code principles with multiple local parities, ensuring robust and efficient distributed storage.

Optimal Locally Repairable and Secure Codes for Distributed Storage Systems

The paper addresses two critical challenges in distributed storage systems (DSS): ensuring security against eavesdropping and enabling local-repairability, where efficient data recovery within small node groups minimizes bandwidth usage. The authors detail novel approaches to enhance the performance of DSS using coding schemes that optimally balance these constraints with storage and bandwidth requirements.

Key results presented include:

1. Secrecy Bounds and Secure Coding Schemes: The paper derives an improved upper bound on secrecy capacity specific to minimum storage regenerating (MSR) codes, considering both direct node observation and downloaded data during repairs by colluding eavesdroppers. An explicit secure MSR coding scheme is introduced, utilizing Gabidulin codes for initial data secrecy pre-coding, which demonstrates improved rate and attains secrecy capacity for specific eavesdropping scenarios. Especially, the zigzag construction allows optimal secrecy while supporting efficient repair in the presence of adversaries.
2. Local Repairability Bounds and Construction: The paper presents an upper bound on the minimum distance for vector codes with locality parameters and details a construction method leveraging Gabidulin codes and MDS array codes. This ensures a balance between repair efficiency and fault tolerance, offering optimal codes for given parameters (e.g., node locality, parity). The introduction of multiple local parities per group signifies advancements over prior scalar LRC approaches, accomplishing improved resilience and reduced repair costs.
3. Repair Bandwidth Considerations: Extending the concept of LRCs, the paper examines the trade-off between local repairs and repair bandwidth. An upper bound on stored data is established for bandwidth-efficient codes that employ inside group repairs using MSR code methods. Repair bandwidth-efficient LRCs attained by integrating regenerating code characteristics exhibit performance gains in practical deployments.
4. Security in Locally Repairable Systems: In light of multiple parities, the research demonstrates that LRCs with optimized local repairs significantly mitigate information leakage during repairs vis-a-vis single-parity per group setups. The authors provide a theoretical framework to quantify secure storage capacity and practical constructions that achieve these limits, illustrating improvements over classical single-parity configurations.
5. Potential Future Directions: While the advancements proposed are significant for specific cases, further explorations are suggested for code designs that might combine cooperative repairs with locality and security. Another avenue is achieving secure LRCs with alternative parameters or lower field sizes.

Overall, the paper makes a substantial contribution to the state of distributed storage by presenting feasible and mathematically grounded methods for optimizing security and efficiency. These findings are pivotal in advancing the design of robust and efficient storage solutions in an era where data integrity and accessibility are paramount. Future implementations may benefit notably from the technical prowess of these theoretical constructs.