4.1 Distance Bounding based on Signal
Strength
Assuming the log-distance path loss model for power
decay over distance, the power P
rx
measured by a re-
ceiver equals
P
rx
= P
tx
·C ·
1
d
γ
(3)
where γ is the path loss exponent, and C is a con-
stant. In realistic indoor environments, the path-loss
exponent is typically 6= 2 and is highly dependent on
the environment due to multipath propagation. With
UWB, however, due to the short pulses, multi-path in-
terference is limited and we can expect a stable path
loss ≈ 2 as shown in (Rubio et al., 2013).
In order to test if P is honest, we initially con-
sider the following strategy: V transmits a sequence
of signals to P at different power levels, which are
chosen from a finite dictionary. P measures the sig-
nals’ strength and sends them back to V . V calculates
a distance d between V and P for each transmitted sig-
nal using Equation 3. V accepts the distance as true
if all distances are consistent. Obviously, an attacker
would manage to control its apparent distance to V
by multiplying P
rx
by a constant. Therefore, the basic
strategy considered does not work.
Nonetheless, if P does not know its distance to V ,
there are still bounds on how much P can increase
or decrease the measured distance by cheating on the
RSS. In this case, P must be careful when choosing
the size of the distance decrease/enlargement factor
(k). If P sends V a received power value P
0
rx
too high,
it may eventually exceed the transmitted power P
tx
,
and V detects the fraud. To be on a safe side, P
should always assume that P
tx
is the smallest power
level from the dictionary greater than P
rx
. Therefore,
k ≤
P
tx
next
P
rx
, where P
tx
next
is the smallest transmission
power from the dictionary greater than P
rx
.
Independent of the previous examined assump-
tion, if P performs a DEF, it is bounded by the min-
imum P
rx
that a honest prover would be capable to
receive. Therefore, k ≥
P
rx
min
P
rx
. Another approach can
be applied against the DEF. V sends a sounding mes-
sage to P to get a first estimation of its distance. Based
on this estimation, V adjusts P
tx
so that P
rx
= P
rx
min
,
i.e., the power level at P is the minimum that a hon-
est prover can successfully demodulate. V transmits
a nonce using P
tx
, which P must acknowledge. The
nonce keeps P from sending acknowledgments before
receiving the message. This approach does not work
in case P has a better hardware than a honest prover,
such as a more sensible low noise amplifier or a di-
rectional antenna. In this case P would still succeed
in the DEF.
Besides this intrinsic security flaw, this approach
should only work if the power level measurements are
reasonably stable within a given distance range, i.e.,
there is a deterministic mathematical model to which
the RSS measurements fit well. If the model does not
represent the actual behavior of the system (poor fit),
it is expected that V ’s estimations will, with a high
probability, differ from P’s distance. As a results, the
distance bounding system should present high false
positives and negatives ratios. We examine this issue
in Section 5.
4.2 Bounding Distance Reduction with
Two Verifiers
Regarding the Distance Reduction Fraud, the pro-
posed protocol can be adapted to be effective as
follows: (at least) two verifiers, each located at a
different position, transmit a signal to P, one at a
time, from the P
tx
dictionary. The sequence dictating
which verifier transmits at a certain time-slot can be
agreed among the verifiers beforehand using a secure
channel. For simplicity, we assume that the system
comprises only two verifiers, and that P intends to
perform a distance reduction attack against only one
of them. We refer to this verifier as V while we refer
to the other as V
aux
. V
aux
is positioned closer to P than
V . In a realistic scenario, V may be attached to an
object to be protected and V
aux
should be placed on
P’s path. In order to perform the DRF, P must claim
a higher P
rx
than it actually measured, which we call
P
0
rx
, in such a way that P
0
rx
= P
rx
∗k. k must be consis-
tent, i.e., in case P changes it, it risks claiming to be
at two different distances from a given verifier, either
V or V
aux
, as P has no means to know which verifiers
sent a given signal (please, refer to Section 3). In
case P chooses a value of k too high, it may, upon
the reception of an incoming signal from V
aux
, claim
a P
0
rx
higher than P
tx
, which will be detected as an
attack. This process is illustrated in Figure 2. In order
to maximize the magnitude of the attack, P must
choose a k which virtually brings it close to V
aux
. It
can do this as it knows the position of all the verifiers
by assumption. k should be chosen in such a way that
when V
aux
transmits with its maximum power level
P
tx
max
, P
0
rx
is still less than P
tx
max
, i.e., k ≤
P
tx
max
P
rx
m
ax
. P
tx
max
is usually limited by standards and federal agencies.
To our knowledge, this is the first bound on a distance
reduction attack not relying on the physical property
of the maximum propagation speed which limits the
speed of an electromagnetic wave: the speed of light.
This bound (B
1
) is depicted in orange in Figure 2 and
represents the minimum distance that P can pretend
PECCS 2020 - 10th International Conference on Pervasive and Parallel Computing, Communication and Sensors
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