On Secrecy Capacity of Minimum Storage Regenerating Codes

In this paper, we revisit the problem of characterizing the secrecy capacity of minimum storage regenerating (MSR) codes under the passive <inline-formula> <tex-math notation="LaTeX">$(l_{1},l_{2})$ </tex-math></inline-formula>-eavesdropper model, where the eavesdropper has access to data stored on <inline-formula> <tex-math notation="LaTeX">$l_{1}$ </tex-math></inline-formula> nodes and the repair data for an additional <inline-formula> <tex-math notation="LaTeX">$l_{2}$ </tex-math></inline-formula> nodes. We study it from the information-theoretic perspective. First, some general properties of MSR codes as well as a simple and generally applicable upper bound on secrecy capacity are given. Second, a new concept of <italic>stable</italic> MSR codes is introduced, where the stable property is shown to be closely linked with secrecy capacity. Finally, a comprehensive and explicit result on secrecy capacity in the linear MSR scenario is present, which generalizes all related works in the literature and also predicts certain results for some unexplored linear MSR codes.