Byzantine Fault Tolerance of Regenerating Codes
  Recent years have witnessed a slew of coding techniques custom designed for networked storage systems. Network coding inspired regenerating codes are the most prolifically studied among these new age storage centric codes. A lot of effort has been invested in understanding the fundamental achievable trade-offs of storage and bandwidth usage to maintain redundancy in presence of different models of failures, showcasing the efficacy of regenerating codes with respect to traditional erasure coding techniques. For practical usability in open and adversarial environments, as is typical in peer-to-peer systems, we need however not only resilience against erasures, but also from (adversarial) errors. In this paper, we study the resilience of generalized regenerating codes (supporting multi-repairs, using collaboration among newcomers) in the presence of two classes of Byzantine nodes, relatively benign selfish (non-cooperating) nodes, as well as under more active, malicious polluting nodes. We give upper bounds on the resilience capacity of regenerating codes, and show that the advantages of collaborative repair can turn to be detrimental in the presence of Byzantine nodes. We further exhibit that system mechanisms can be combined with regenerating codes to mitigate the effect of rogue nodes. 
Fr\'ed\'erique Oggier and Anwitaman Datta
cs.DC cs.CR