The ON/OFF based approach proposed by Zhang and Paxson [39] is the first timing-based
method that can trace stepping stones, even if the traffic were to be encrypted. In their
approach, they calculated the correlation of different flows by using each flow’s OFF
periods. A flow is considered to be in an OFF period when there is no data traffic on it
for more than a time period threshold. Their approach comes from the observation that
two flows are in the same connection chain if their OFF periods coincide.
Yoda and Etoh [40] presented a deviation-based approach for detecting stepping-stone
connections. The deviation is defined as the difference between the average propagation
delay and the minimum propagation delay of two connections. This scheme comes from
the observation that the deviation for two unrelated connections is large enough to be
distinguished from the deviation of connections in the same connection chain.
Wang et al. [41] proposed a correlation scheme using interpacket delay (IPD) characteristics
to detect stepping stones. They defined their correlation metric over the IPDs in a sliding
window of packets of the connections to be correlated. They showed that the IPD
characteristics may be preserved across many stepping stones.
Wang and Reeves [42] presented an active watermark scheme that is designed to be robust
against certain delay perturbations. The watermark is introduced into a connection by
slightly adjusting the interpacket delays of selected packets in the flow. If the delay
perturbation is not quite large, the watermark information will remain along the
connection chain. This is the only active stepping-stone attribution approach.
Strayer et al. [43] presented a State-Space algorithm that is derived from their work on
wireless topology discovery. When a new packet is received, each node is given a weight
that decreases as the elapsed time from the last packet from that node increases. Then
the connections on the same connection chain will have higher weights than other
connections.
However, none of these previous approaches can effectively detect stepping stones when
delay and chaff perturbations exist simultaneously. Although no experimental data is
available, Donoho et al. [44] indicated that there are theoretical limits on the ability of
attackers to disguise their traffic using evasions for sufficiently long connections. They
assumed that the intruder has a maximum delay tolerance, and they used wavelets and
similar multiscale methods to separate the short-term behavior of the flows (delay or chaff)
from the long-term behavior of the flows (the remaining correlation). However, this
method requires the intrusion connections to remain for long periods, and the authors
never experimented to show the effectiveness against chaff perturbation. These evasions
consist of local jittering of packet arrival times and the addition of superfluous packets.
Blum et al. [45] proposed and analyzed algorithms for stepping-stone detection using ideas
from computational learning theory and the analysis of random walks. They achieved
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