2017/01/11 by Shuo Shao, Shao, Shuo, Tie Liu +5
Computer Science · Mathematics · #Advanced Data Storage Technologies #Cryptography and Data Security #Distributed systems and fault tolerance #FOS: Computer and information sciences #Information Theory (cs.IT) #cs.IT #math.IT
paper · pdf · doi:10.48550/arxiv.1701.03023
12 pages, 3 figures
arxiv created 2017/01/11 · openalex publication_date 2017/01/11 · arxiv updated 2017/01/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the (n,k,d,ℓ) 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 ℓ 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 (ℓ≥ 1) immediately reduces the tradeoff region to one with a single corner point. In this work, we first show that when the secrecy parameter ℓ is sufficiently large, the SRK point is indeed the only corner point of the tradeoff region. However, when ℓ 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.