This paper shows for the first time that distributed computing can be both reliable and efficient in an environment that is both highly dynamic and hostile. More specifically, we show how to maintain clusters of size $O(log N)$, each containing more
than two thirds of honest nodes with high probability, within a system whose size can vary textit{polynomially} with respect to its initial size. Furthermore, the communication cost induced by each node arrival or departure is polylogarithmic with respect to $N$, the maximal size of the system. Our clustering can be achieved despite the presence of a Byzantine adversary controlling a fraction $bad leq {1}{3}-epsilon$ of the nodes, for some fixed constant $epsilon > 0$, independent of $N$. So far, such a clustering could only be performed for systems who size can vary constantly and it was not clear whether that was at all possible for polynomial variances.
We consider the problem of computing an aggregation function in a emph{secure} and emph{scalable} way. Whereas previous distributed solutions with similar security guarantees have a communication cost of $O(n^3)$, we present a distributed protocol th
at requires only a communication complexity of $O(nlog^3 n)$, which we prove is near-optimal. Our protocol ensures perfect security against a computationally-bounded adversary, tolerates $(1/2-epsilon)n$ malicious nodes for any constant $1/2 > epsilon > 0$ (not depending on $n$), and outputs the exact value of the aggregated function with high probability.
