On the Tradeoff Region of Secure Exact-Repair Regenerating Codes
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2017 IEEE. We consider the (n,k,d,) secure exact-repair regenerating code problem, which generalizes the (n,k,d) exact-repair regenerating code problem with the additional constraint that the stored file needs to be kept information-theoretically secure against an eavesdropper, who can access the data transmitted to regenerate a total of different failed nodes. For all known results on this problem, the achievable tradeoff regions between the normalized storage capacity and repair bandwidth have a single corner point, achieved by a scheme proposed by Shah, Rashmi, and Kumar (the SRK point). Since the achievable tradeoff regions of the exact-repair regenerating code problem without any secrecy constraints are known to have multiple corner points in general, these existing results suggest a phase-change-like behavior, i.e., enforcing a secrecy constraint ( 1) immediately reduces the tradeoff region to one with a single corner point. In this paper, we first show that when the secrecy parameter is sufficiently large, the SRK point is indeed the only corner point of the tradeoff region. However, when is small, we show that the tradeoff region can in fact have multiple corner points. In particular, we establish a precise characterization of the tradeoff region for the (7, 6, 6, 1) problem, which has exactly two corner points. Thus, a smooth transition, instead of a phase-change-type of transition, should be expected as the secrecy constraint is gradually strengthened.
