Experimental Study of Performance and Security Constraints on
Wireless Key Distribution Using Random Phase of
Multipath Radio Signal
Amir I. Sulimov, Alexey D. Smolyakov, Arkadij V. Karpov and Oleg N. Sherstyukov
Department of Radio Physics, Institute of Physics, Kazan Federal University,
18
th
Kremlyovskaya St., Kazan, Russia
Keywords: Encryption Keys Distribution, Common Randomness, Multipath Radio Propagation, Channel Reciprocity,
Randomness of Carrier Phase, Rate of Encryption Key Distribution, Spatial Correlation, Key Interception.
Abstract: The paper presents the results of experimental distribution of encryption keys based on random carrier phase
of fading radio signal measured in a multipath environment. The random bits extraction scheme was
proposed and tested in practice. The proposed scheme is universal and applicable to measurements
digitizing of any observable random variable. Experimental study of spatial correlation of multipath signal
phase in the case of transverse spatial diversity is carried out. Experimental estimation of the key generation
rate and the probability of its passive interception at different distances between the legal user and potential
eavesdropper are also performed. It is shown that the parameters of bit extraction procedure significantly
affect on the performance and security of the key distribution process.
1 INTRODUCTION
The problem of secure distribution of encryption
keys is one of the most important in cryptography.
Amongst the others, the wireless key distribution
methods firstly proposed in (Hershey, 1995; Hassan,
1996) have been actively investigated in the recent
decade. Under this method, a multipath radio
channel is considered as a shared source of
randomness used for the creation of secret key. The
key is generated by observing random variations in
the parameters of fading radio signal received in a
multipath environment. To do this, two nodes (say,
Alice and Bob) transmit to each other a series of
radio signals and measure their parameters when
receiving. The channel reciprocity ensures the
measured signal parameters will be identical at both
sides. Due to a rapid spatial decorrelation of signal
characteristics in a multipath environment the key
interception is very unlikely at practice.
Several methods of the key generation using
different parameters of multipath signal have been
considered in prior publications. An experimental
verification of the amplitude method based on
measurements of random values of received signal
strength has been carried out in (Mathur, 2008;
Wilhelm, 2010; Liu & Trappe, 2010; Wei, 2011;
Croft, 2011; Zan, 2012). An experimental
verification of the channel impulse response (CIR)
method based on measurements of random values of
signal quadrature components has been performed in
(Li, 2006; Wilson, 2007; Hamida, 2009; Madiseh,
2009). However, the phase method seems to be the
most appropriate for the key generation. Unlike the
amplitude and signal quadrature components, the
signal phase often shows uniform probability
distribution, which is desirable for the key
generation. Unfortunately, the prior publications
(Hassan, 1996; Korzhik, 2012; Shehadeh, 2011) on
the phase method are mostly limited to theoretical
analysis and simulation. The only paper
(Smolyakov, 2013) we know, where an attempt of
its experimental verification was made, does not
concern any key interception issues.
The purpose of this paper is to clarify
experimental evaluations of the performance and
security of key distribution based on observation of
the signal phase in a multipath environment.
411
Sulimov A., D. Smolyakov A., V. Karpov A. and N. Sherstyukov O..
Experimental Study of Performance and Security Constraints on Wireless Key Distribution Using Random Phase of Multipath Radio Signal.
DOI: 10.5220/0005101004110416
In Proceedings of the 11th International Conference on Security and Cryptography (SECRYPT-2014), pages 411-416
ISBN: 978-989-758-045-1
Copyright
c
 2014 SCITEPRESS (Science and Technology Publications, Lda.)

2 SCENARIO OF THE
EXPERIMENTS
To perform all the experiments, we designed three
identical test devices (or simply nodes). The two of
them (nodes A = Alice and B = Bob) worked as
legitimate users, and the third one (node E = Eve)
served as a passive eavesdropper, who tried to
intercept the measurements of signal phase on the
side of node B (or simply Bob). Alice and Bob
transmitted to each other a series of probing signals
at carrier frequency f = 962 MHz in a half-duplex
mode with the time frame of activity of 50 ms. The
transmitted power was set at 10 dBm. When
receiving a signal, each node measured the carrier-
phase and stored the data into a built-in SD-memory
card. Thus, each node was performing twenty
measurements of the carrier-phase in one second.
The reference oscillators of all the three nodes have
been synchronized via coaxial cables. To provide the
most intense random variations of the signal phase,
an omni-directional antenna has been used in each
node for the signal reception.
The experiments have been carried out in a
typical academic environment, which is a good
example of multipath propagation medium (see
Figure 1). The placements of nodes A and B were
fixed, and the distance between them (length of the
test link) was 4.5 m. The E node has been placed at
various spatial diversities d from Bob in a transverse
relative to the link direction. The value of d has been
varied in the range from 0 cm to 100cm with 5 cm
increment. The zero spacing (d = 0 cm) has been
implemented by using a common receiving antenna
for both B and E nodes.
Figure 1: Experimental setup.
A sample of 9000 measurements has been
collected at each node for every fixed placement of
the nodes A, B and E. In a typical multipath
environment, such a small sample is insufficient to
create a long enough key. The reason is the low
channel variability (Madiseh, 2009). To ensure a
high channel variability (or high Doppler frequency
f
D
) the researchers were actively walking within the
test room in various directions while the sample was
being collected. In addition, antenna of the node A
was being randomly shifted in the range ±50cm in
perpendicular (relative to the link axis) plane. Such
actions provided quite a satisfactory Doppler
frequency f
D
= 10÷30 Hz, which made it possible to
keep up to 50% of a primary sample after
implementing the measurements decorrelation.
The collected measurement data {φ
A
}, {φ
B
} and
{φ
E
} has been copied on a laptop, where with the
help of a special software it has been converted into
the keys K
A
, K
B
and K
E
, respectively. After this, we
have examined a bit disagreement rate of the
generated keys and a cross-correlation between the
phase samples.
3 BIT EXTRACTION
To generate the keys from the collected samples of
signal phase measurements a bit extraction
procedure is necessary to be performed. To extract
random bits, the full range of the signal phase
variation φ[-π;π] is divided into 2
m
quantization
intervals. The variable m denotes the number of bits
we want to extract from a single phase measurement.
We called it a “codeword length” and expressed the
values of m in bits per measure (or simply bpm for
short).
a)
b)
Figure 2: Extraction of bits from the carrier phase
measurements: a) m=2bpm, b) m=3bpm.
In our bit extraction scheme, each quantization
interval is mapped into a binary codeword of length
m. When the phase measurement falls into some
quantization interval, an associated codeword is
SECRYPT2014-InternationalConferenceonSecurityandCryptography
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formed at the output. An encryption key is generated
by combining or hashing all the resultant codewords.
To increase entropy of the key, the measurements
decorrelation procedure (Croft, 2011) is performed
before the bit extraction.
Another important requirement is to ensure
uniformity of the generated key. To fulfil this
requirement, the phase measurements should fill all
the quantization intervals uniformly. This is possible
if the carrier phase will be a uniformly distributed
random variable. However, this is not always true in
practice. For example, the presence of intense line-
of-sight wave violates the signal phase uniformity.
In this case, we should use non-uniform quantization
of measurements with the variable-width intervals.
The choice of optimal codeword length is the
most important step at the bit extraction. It is
obvious, that the rise of m will increase a key
generation rate R
K
, but it will also increase a bit
disagreement rate between the K
A
and K
B
keys. It
should be noted, that due to measurement errors and
impact of the channel noise the perfect cross-
correlation between the {φ
A
} and {φ
B
} samples
collected by Alice and Bob is impossible in practice.
As a result, the φ
A
and φ
B
measurements always
have some deviation Δφ = φ
A
– φ
B
 0. If the width
of quantization intervals is sufficiently large, the
deviation Δφ will not cause any mismatch between
the codewords formed by Alice and Bob (see fig.2a).
However, the rise of m increases probability of
codewords mismatch (see fig.2b). Thus, there must
be an optimal value m*, which maximizes the key
generation rate and minimizes the probability of bit
disagreement between the K
A
and K
B
keys.
4 EXPERIMENTAL RESULTS
Comparison of phase measurements collected by the
nodes A and B showed a high cross-correlation ρ
φ
=
0.95÷0.99 between the samples, which confirmed
reciprocity of the multipath channel. Some mismatch
of the {φ
A
} and {φ
B
} samples is explained by non-
ideal calibration of experimental equipment and by
impact of the channel noise. Despite the high
correlation between measurement data of Alice and
Bob, the K
A
and K
B
keys contained a large fraction
of bits in mismatch. The minimum experimentally
achieved key disagreement rate p
e
was about 3%.
In (Liu & Trappe, 2010; Korzhik, 2012) the key
disagreement rate p
e
has been considered as a
function of cross-correlation coefficient ρ
φ
between
the measurement data of Alice and Bob. This
concept is very useful in practice, since it allows
estimation of the key disagreement rate even before
implementing the bit extraction procedure. Figure 3
shows such dependence observed at the experiments.
Despite the lack of experimental data for the range
ρ
φ
[0.3;0.8], the curve in Figure 3 is in a good
agreement with the results in (Liu & Trappe, 2010),
but shows slightly lower values of probability p
e
. It
should be noted, that the curve in Figure 3 is
applicable not only for estimating the p
e
value of
disagreement rate between the K
A
and K
B
keys, but it
also can be used for evaluating the p
int
value of
disagreement rate between the K
B
and K
E
keys. In
the latter case, we should use a cross-correlation
between the {φ
B
} and {φ
E
} samples as an argument.
Figure 3: Probability of bit disagreement as a function of
cross-correlation between the phase measurements.
To eliminate a mismatch between the K
A
and K
B
keys, their reconciliation with a cyclic redundancy
codes (CRC) of the CRC-16-CCITT standard was
being performed. The use of CRC-codes is
analogous to the well-known method of privacy
amplification (Bennet, 1995) but easier to
implement. Just as in the privacy amplification
method, after successful check of some fragment of
the K
A
and K
B
keys we should remove at least 16
arbitrary bits. In our experiments, the optimal length
of verified fragment of the K
A
and K
B
keys was in
the range from 18 to 41 bits of which we removed
16 arbitrary bits. It is clear, that the keys
reconciliation led to a huge loss. An efficiency of the
key reconciliation process was characterized by the
η = (Ν
+
/Ν) parameter. Here N
+
is the key length after
and N is the key length before the reconciliation,
respectively. Due to high values of the key
disagreement rate p
e
the maximum experimentally
achieved value of η was about 10%.
Figure 4 presents achieved key generation rate
R
K
expressed in bits per second (or simply in bps) as
a function of the codeword length m. The key
generation rate was estimated as R
K
=(N
+
/T), where T
is duration of the samples collecting. In our
ExperimentalStudyofPerformanceandSecurityConstraintsonWirelessKeyDistributionUsingRandomPhaseof
MultipathRadioSignal
413

experiments, it was T = 9000•50 ms = 450 s. The
curves in Figure 4 are presented for three different
values of the cross-correlation coefficient between
the {φ
A
} and {φ
B
} samples. It can be clearly seen,
that small changes in the ρ
φ
value lead to a
significant reduction in the key generation rate.
Relatively high values of the key disagreement rate
p
e
resulted in small values of optimal codeword
length m*, which in the experiments were only 1 or
2 bpm. All attempts to extract more random bits
from each measurement caused a rapid rise in the
key disagreement rate p
e
and to an expected sharp
decrease in the efficiency of key reconciliation η.
The maximum achieved key generation rate slightly
exceeded 2 bps, which is in correspondence with the
results of other verifications of the wireless key
distribution (Madiseh, 2009).
Figure 4: Key generation rate as a function of the
codeword length.
A spatial correlation of the signal phase and its
relationship with the key disagreement rate has also
been investigated during the experiments. To do this,
the cross-correlation coefficient between the {φ
B
}
and {φ
E
} samples along with the key disagreement
rate p
int
of the K
B
and K
E
keys have been determined
for each value of the spatial diversity d. The
observed dependencies are presented at Figures 5
and 6, respectively.
Figure 5: Spatial autocorrelation function of carrier-phase.
The maximum correlation between the {φ
B
} and
{φ
E
} samples has been detected when Bob and Eve
used a common antenna for the probing signals
reception. The highest value was 0.8828. A mutual
influence of input circuits of both nodes prevented
correlation between the {φ
B
} and {φ
E
} samples to be
higher. This mutual influence caused additional
distortions in the signal phase which made deviation
of the φ
B
and φ
E
measurements much greater.
Furthermore, the closer receiving antennas of the B
and E nodes were the stronger antenna array effect
we observed. When the spatial diversity d of nodes
became less λ, we observed strong distortions of
radiation pattern of both the receiving antennas.
The curves in Figure 6 actually reproduce the
profile of autocorrelation function presented at
Figure 5. It should be clarified, that value p
int
= 0
indicates absolute identity of the K
B
and K
E
keys,
which means perfect key interception by Eve.
Conversely, value p
int
= 50% means absolute
independence of the K
B
and K
E
keys and absence of
the key interception threat. Figure 6 shows the two
curves obtained for different values of the codeword
length m. It can be seen, that the reduction of m
increases a key interception probability. This is
Figure 6: Probability of bit disagreement between the K
B
and K
E
keys as a function of spatial diversity of Bob and
Eve.
Figure 7: Probability of bit disagreement between the K
B
and K
E
keys as a function of the codeword length.
reasonable, because with a decrease in the number of
quantization intervals the probability 2
-m
of a simple
guessing the codewords increases.
SECRYPT2014-InternationalConferenceonSecurityandCryptography
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Figure 7 illustrates this effect in more details. It
presents the dependence of key disagreement rate
between the K
B
and K
E
as a function of the codeword
length m for three values of cross-correlation
coefficient between the {φ
B
} and {φ
E
} samples. The
presented curves demonstrate sharp decline in the
probability of key interception with increase in m at
low values of cross-correlation coefficient. This
result is in agreement with the conclusions of
fundamental work (Maurer, 1993), where it has been
shown, that not only the number of successfully
distributed bits N
+
should be considered for the key
generation rate R
K
estimation, but the amount of
mutual information I(K
E
;K
B
) between the K
B
and K
E
keys is also should be taken into account.
5 CONCLUSIONS
The experiments showed feasibility of wireless key
distribution based on measurements of carrier-phase
in a multipath environment. The key generation rate
R
K
~ 2 bps has been achieved at the Doppler
frequency f
D
~ 30Hz and cross-correlation between
the measurement samples of Alice and Bob close to
0.99. Investigation of spatial autocorrelation of the
signal phase showed an existence of the passive key
interception threat even at distances more than 3λ.
Furthermore, it was found that absolute correlation
between the measurement data of two closely spaced
nodes is hardly achievable in practice. The complex
effects of mutual influence of antennas and input
circuits of both nodes restrict the ability to intercept
generated keys. Experimental results have shown
that the behaviour of probability of passive key
interception when varying a spatial diversity of
legitimate user and eavesdropper basically repeats
the profile of the spatial autocorrelation function for
the measurement data. It was also shown an
existence of optimal number of bits, which should be
extracted from a single measurement of observable
random variable to maximize the key generation rate
and to reduce the probability of its interception.
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