On the Impact of Pollution Attacks on Coding-Based Distributed Storage Systems

Abstract

Coding-based distributed storage systems (DSS) are employed in many diverse heterogeneous settings, e.g., cloud storage data centers, peer-to-peer systems, wireless sensor networks, fog/edge computing system, to provide better throughput, latency, reliability, scalability, load adaptation, geographical migration and fault tolerance with respect to traditional monolithic enterprise storage systems. Despite the undoubted advantages offered by coding, reliability and security are jeopardized by a pollution attack that can easily disrupt the entire system and degrade performance. In this paper we take an abstract view of a DSS and we investigate by means of mathematical modeling what are the availability, robustness, and timeliness of heterogeneous, coding-based DSS when storage nodes (SN) are unreliable and can be malicious. To this end, we focus on a class of allocations of coded fragments to SNs that we call <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">feasible allocations</i> ; the model takes into account both <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">reliability</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">reactivity</i> of SNs. We define <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">robust availability</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">timeliness</i> of feasible allocations that we use to characterize the overall performance and robustness of the DSS in a reference scenario. Our analysis reveals that code redundancy is a double-edged sword in a DSS where malicious SNs come into play and that there exists an optimal value of code redundancy regardless all system parameters that maximizes the number of malicious SNs that can be tolerated to achieve maximum DSS performance. We also found that larger codes are preferred over short ones as they yield superior DSS performance in the presence of malicious SNs. Furthermore, when multiple feasible allocations yield the highest DSS performance timeliness can be used as a guide for the choice. Finally, heterogeneity plays a role in determining the timeliness of the maximally spread allocations in the case of targeted attacks.