Optimal Weakly Secure Minimum Storage Regenerating Codes Scheme

In a distributed storage system, regenerating codes can be utilized to ensure data availability. This reduces the repair bandwidth but increases the risk of data eavesdropping on each node. Previous studies in this area generally only provided an approximate analysis of the security of schemes with information-theoretic security or weak security. Some researchers have further divided weak security into block security; however, they only analyzed several the regenerating codes schemes and proposed improved schemes with specific eavesdropping capabilities. In this study, we analyze the block security of a Cauchy-matrix-based product-matrix minimum storage regenerating(MSR) scheme and determine the optimal block security of MSR codes. Lastly, an improved MSR codes scheme for achieving optimal block security is proposed, and the relevant proof is provided.

[1]  Adi Shamir,et al.  How to share a secret , 1979, CACM.

[2]  Frank R. Kschischang,et al.  Universal Secure Network Coding via Rank-Metric Codes , 2008, IEEE Transactions on Information Theory.

[3]  Nihar B. Shah,et al.  Information-Theoretically Secure Regenerating Codes for Distributed Storage , 2011, 2011 IEEE Global Telecommunications Conference - GLOBECOM 2011.

[4]  Sriram Vishwanath,et al.  Optimal Locally Repairable and Secure Codes for Distributed Storage Systems , 2012, IEEE Transactions on Information Theory.

[5]  Chau Yuen,et al.  On block security of regenerating codes at the MBR point for distributed storage systems , 2014, 2014 IEEE International Symposium on Information Theory.

[6]  Rui Zhu,et al.  On the secure conditions for distributed storage systems , 2013, 2013 International Symposium on Network Coding (NetCod).

[7]  Krishna R. Narayanan,et al.  Weakly Secure Network Coding , 2005 .

[8]  Hirosuke Yamamoto,et al.  Secret sharing system using (k, L, n) threshold scheme , 1986 .

[9]  Kannan Ramchandran,et al.  Explicit construction of optimal exact regenerating codes for distributed storage , 2009, 2009 47th Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[10]  Kenneth W. Shum,et al.  Cooperative repair of multiple node failures in distributed storage systems , 2016, Int. J. Inf. Coding Theory.

[11]  Kannan Ramchandran,et al.  Securing Dynamic Distributed Storage Systems Against Eavesdropping and Adversarial Attacks , 2010, IEEE Transactions on Information Theory.

[12]  Muriel Médard,et al.  Coding for Trusted Storage in Untrusted Networks , 2012, IEEE Transactions on Information Forensics and Security.

[13]  Patrick P. C. Lee,et al.  Double Regenerating Codes for hierarchical data centers , 2016, 2016 IEEE International Symposium on Information Theory (ISIT).

[14]  Minghua Chen,et al.  BASIC Codes: Low-Complexity Regenerating Codes for Distributed Storage Systems , 2016, IEEE Transactions on Information Theory.

[15]  Swanand Kadhe,et al.  On a weakly secure regenerating code construction for minimum storage regime , 2014, 2014 52nd Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[16]  Jiwu Shu,et al.  Cross-Rack-Aware Single Failure Recovery for Clustered File Systems , 2020, IEEE Transactions on Dependable and Secure Computing.

[17]  Alexandros G. Dimakis,et al.  Network Coding for Distributed Storage Systems , 2007, IEEE INFOCOM 2007 - 26th IEEE International Conference on Computer Communications.

[18]  Arman Fazeli,et al.  Minimum Storage Regenerating Codes for All Parameters , 2017, IEEE Transactions on Information Theory.

[19]  Kannan Ramchandran,et al.  Having Your Cake and Eating It Too: Jointly Optimal Erasure Codes for I/O, Storage, and Network-bandwidth , 2015, FAST.

[20]  Jian Li,et al.  Secure regenerating code , 2014, 2014 IEEE Global Communications Conference.

[21]  Nihar B. Shah,et al.  Optimal Exact-Regenerating Codes for Distributed Storage at the MSR and MBR Points via a Product-Matrix Construction , 2010, IEEE Transactions on Information Theory.