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The detection of information flows by timing analysis is considered. Given transmission timestamps of monitored nodes, the problem is to decide whether there is an information flow through these nodes by analyzing the transmission patterns. Due to constraints that packets from an information flow need to be delivered within certain delay or the relay nodes have bounded memory, transmission patterns of an information flow are statistically different from those of independent traffic. The main result of this paper is a tight characterization of the maximum amount of chaff noise such that Chernoff-consistent detection is achievable. The direct part of the result is an explicit construction of a detector that has vanishing false alarm and miss probabilities as the sample size increases whenever the noise level is below certain threshold. Conversely, when the noise level is above this threshold, there exist means to hide the information flow such that it is indistinguishable from independent traffic. Explicit characterization of the noise threshold is provided for Poisson transmission schedules. It is also shown that while information flows can be hidden among chaff noise for a small number of hops, the rate of information flow diminishes as the number of hops increases.