Can linear minimum storage regenerating codes be universally secure?
Sreechakra Goparaju, Salim El Rouayheb, Robert Calderbank · 2015
We study the problem of making a distributed storage system information-theoretically secure against a passive eavesdropper, and aim to characterize coding schemes that are universally secure for up to a given number of eavesdropped nodes. Specifically, we consider minimum storage regenerating (MSR) codes and ask the following question: For an MSR code where a failed node is repaired using all the remaining nodes, is it possible to simultaneously be optimally secure using a single linear coding scheme? We define a pareto-optimality associated with this simultaneity and show that there exists at least one linear coding scheme that is pareto-optimal.