On the Power of the Adversary to Solve the Node Sampling Problem

Abstract

Abstract. We study the problem of achieving uniform and fresh peer sampling in large scale dynamic systems under adversarial behaviors. Briefly, uniform and fresh peer sampling guarantees that any node in the system is equally likely to appear as a sample at any non malicious node in the system and that infinitely often any node has a non-null probability to appear as a sample of honest nodes. This sample is built locally out of a stream of node identifiers received at each node. An important issue that seriously hampers the feasibility of node sampling in open and large scale systems is the unavoidable presence of malicious nodes. The objective of malicious nodes mainly consists in continuously and largely biasing the input data stream out of which samples are obtained, to prevent (honest) nodes from being selected as samples. First, we demonstrate that restricting the number of requests that malicious nodes can issue and providing a full knowledge of the composition of the system is a necessary and sufficient condition to guarantee uniform and fresh sampling. We also define and study two types of adversary models: (1) an omniscient adversary that has the capacity to eavesdrop on all the messages that are exchanged within the system, and (2) a blind adversary that can only observe messages that have been sent or received by nodes it controls. The former model allows us to derive lower bounds on the impact that the adversary has on the sampling functionality while the latter one corresponds to a more realistic setting. Given any sampling strategy, we quantify the minimum effort exerted by both types of adversary on any input stream to prevent this sampling strategy from outputting a uniform and fresh sample.

Lightweight Metric Computation for Distributed Massive Data Streams

“…The authors have proposed estimators of the frequency moments F k of a stream, which are important statistical tools that allow to quantify specificities of a data stream. Subsequently, a lot of attention has been devoted to the strongly related notion of the entropy [15] of a stream [16,17,18], and all notions based on entropy as the quantification of the amount of randomness of a stream (e.g, [17,19,20,21]). The construction of synopses or sketches of the data stream have been proposed for different applications (e.g, [22,23,24,25]).…”

Estimating the Frequency of Data Items in Massive Distributed Streams

“…However, accuracy of this computation with respect to the stream in its entirety fully depends on the volume of data items that has been sampled and their order in the stream. Furthermore, an adversary may easily take advantage of the sampling policy to hide its attacks among data items that are not sampled, or in a way that prevents its "malicious" data items from being correlated [1]. In contrast, the streaming approach consists in scanning each piece of data of the input stream on the fly, and in locally keeping only compact synopses or sketches that contain the most important information about these data.…”

Deviation Estimation between Distributed Data Streams

“…Most of the research done so far with this approach has focused on computing functions or statistics measures with error ε using poly(1/ε, log n) bits of space where n is the domain size of the data items. These include the computation of the number of different data items in a given stream [8], [9], [10], the frequency moments [11], the most frequent data items [11], [12], the entropy of the stream [13], [14], [15], or the information divergence over streams [16].…”