Towards provably invisible network flow fingerprints

Abstract

Network traffic analysis reveals important information even when messages are encrypted. We consider active traffic analysis via flow fingerprinting by invisibly embedding information into packet timings of flows. In particular, assume Alice wishes to embed fingerprints into flows of a set of network input links, whose packet timings are modeled by Poisson processes, without being detected by a watchful adversary Willie. Bob, who receives the set of fingerprinted flows after they pass through the network modeled as a collection of independent and parallel M/M/1 queues, wishes to extract Alice's embedded fingerprints to infer the connection between input and output links of the network. We consider two scenarios: 1) Alice embeds fingerprints in all of the flows; 2) Alice embeds fingerprints in each flow independently with probability p. Assuming that the flow rates are equal, we calculate the maximum number of flows in which Alice can invisibly embed fingerprints while having those fingerprints successfully decoded by Bob. Then, we extend the construction and analysis to the case where flow rates are distinct, and discuss the extension of the network model.

Fundamental Limits of Invisible Flow Fingerprinting

“…Similar to the definition of covertness [28]- [32], we define invisibility [1]: the probability of the failure event satisfies P f ≤ ζ as T → ∞. We term ζ the reliability parameter.…”

“…Construction: Per above, Alice uses a scheme consisting of two phases of lengths T 1 and T 2 , and employs a codebook of fingerprints to embed in the flows. The codebook construction is similar to the one adopted in [1], [29], [30]. In particular, Alice generates m independent instantiations of a Poisson process with parameter λT 2 , where T 2 is the length of the second phase, as follows.…”

“…• For the case where Alice fingerprints a subset of the flows, in [1,Theorem 2], we presented a scenario where Alice fingerprints each flow independently with probability q. Here, we present a slightly different variation of this scheme where instead of a probabilistic selection of flows for fingerprinting, Alice fingerprints a subset of the flows which is known to both Alice and Bob (see Theorem 2).…”

“…Here, we present a slightly different variation of this scheme where instead of a probabilistic selection of flows for fingerprinting, Alice fingerprints a subset of the flows which is known to both Alice and Bob (see Theorem 2). Furthermore, the results of [1,Theorem 2] were applicable only for specific values of q and the total number of flows that yield a close to a maximal number of traceable flows. Here, we present the results for arbitrary q and number of flows (see Theorem 4.3).…”

Fundamental Limits of Covert Packet Insertion

“…Similar to the definition of covertness in [1], [2], [16]- [18], [67], [68], and invisibility in [69], [70], we define covertness: We present results under the assumption that P(H 0 ) = P(H 1 ) = 1/2. However, this results in covertness for the general case [71, Appendix A].…”