Fundamental limits of secure exact-repair regenerating codes

Ph.D.In a distributed storage system, where a file is stored, there may exist illegitimate users who want to obtain information about the file. In this work, we consider secure distributed storage systems against eavesdropping attack. In particular, the secure distributed storage system we consider is based on an exact-repair regenerating code, and the eavesdropping model is that the eavesdropper has the capability to observe the data involved in the repair of a subset of ℓ nodes. An (n, k, d, ℓ) secure exact-repair regenerating code is an (n, k, d) exact-repair regenerating code that is secure under this eavesdropping model. We are interested in understanding the fundamental limits of the secure exact-repair regenerating codes.For the (n, k, d, ℓ = 0) exact-repair regenerating code problem, it was known that there is a tradeoff between the stor-age and the repair bandwidth, that is, the optimal storage-bandwidth tradeoff curve must have multiple corner points. How-ever, it has been shown that for some parameters (n, k, d, ℓ), the associated optimal storage-bandwidth tradeoff curve has only one corner point, which contradicts with the problem without security sharply.The focus of this work is on characterizing parameters such that the optimal tradeoff curve can be determined by a single Pareto optimal point. Specifically, we establish a lower bound ℓˆ on the number of wiretap nodes, and show that this bound is tight for the case k = d = n-1. This lower bound subsumes all previous results.在分佈式存儲系統中，當一個文件被儲存的時候，可能存在一些非法用戶想得到此文件的信息。在本文中，我們考慮抗竊聽攻擊的安全分佈式存儲系統方案。本文著重考慮基於精確修復再生碼的安全分佈式存儲系統，即存在竊聽者可以獲取ℓ.個被修復節點在修復過程中下載的數據。(n, k, d, ℓ.) 安全精確修復再生碼定義為在此竊聽模型下安全的(n, k, d) 精確修復再生碼。本文中我們希望確定安全精確修復再生代碼的基本理論界限。對於不考慮安全性的精確修復再生碼問題，其節點存儲量與修復帶寬之間存在最優折衷曲線，且該最優存儲帶寬折衷曲線上具有多個重要參數頂點。然而，對於一些參數下的(n, k, d, ℓ.) 安全精確修復再生碼，我們知道最優的存儲帶寬折衷曲線只有一個頂點，這與不考慮安全性的最優折衷曲線非常不同。本文的重點在於確定所有參數，使得這些參數對應的最優折衷曲線可以由一個帕雷托最優點確定。具體而言，我們給出一個竊聽節點數量的下界，並且證明這個下界對於k = d = n - 1 的情況是緊的。同時本文所給出的這個下界包含了此前所有的已知結果。Ye, Fangwei.Thesis Ph.D. Chinese University of Hong Kong 2018.Includes bibliographical references (leaves 151-157).Abstracts also in Chinese.Title from PDF title page (viewed on …)