On the secure conditions for distributed storage systems

Abstract

The problem of secure distributed storage systems (DSS) with regenerating codes is concerned in this paper. We consider an eavesdropper model where an eavesdropper wiretaps a subset of storage nodes, and either their repairing data or stored data can be wiretapped. We focus on two typical and special cases, the Minimum Bandwidth Repair (MBR) and the Minimum Storage Repair (MSR). Our main contribution is to draw a connection between this problem and secure network coding theory introduced by Cai and Yeung, and the secrecy capacity can be determined in this method. We prove that for both MBR and MSR cases, if the maximal wiretapped information rate can be determined, the secrecy capacity can be achieved by linear secure network coding. Particularly, a static exact regenerating code can be transformed into a secure regenerating code for the MBR and MSR cases.

Weakly secure regenerating codes for distributed storage

“…Note that G e can be considered as a generator matrix of PM-MBR code for node e. To ensure weak security against g guesses, we need to design H such that for each node e ∈ [n], its generator matrix G e satisfies (8).…”

“…The main idea of our solution is to construct H such that it has the same structure as that of the generator matrix G e of a node for the PM-MBR code. The same structure of G e and H would enable us to ensure the condition (8).…”

“…Eve observes α = d symbols stored on node e given by E = ψ e M, where ψ e is the e-th row of Ψ. To use condition (8), we need to find a matrix G e such that E = G e X. This is carried out by a simple linear transformation that guarantees E = (ψ e M) T = G e X.…”

“…Information-theoretic model for securing regenerating codes was introduced by Pawar et al [5], [6]. Since then, a number of investigations have been carried out on characterizing outer-bounds on secrecy capacity and the associated achievable schemes (see [7], [8], [9]). All these results are focussed on the paradigm of information-theoretic perfect secrecy.…”

“…This is because the condition (8) must be satisfied for all sub-matrices of H, the number of which are exponentially large. Moreover, for each sub-matrix H G ′ , we must ensure(8) for each node e ∈ [n], since Eve can observe any storage node. Therefore, we explicitly construct H that requires small field size.…”