Secure Key Distribution based on Meteor Burst Communications
Amir I. Sulimov and Arkadij V. Karpov
Department of Radio Physics, Institute of Physics, Kazan Federal University,
18
th
Kremlyovskaya St., Kazan, Russia
Keywords: Encryption Keys Distribution, Common Randomness, Meteor Burst Radio Propagation, Channel
Reciprocity, Randomness of Carrier Phase, Randomness of Propagation Time, Randomizing Factor.
Abstract: The paper discusses possibility of secure encryption keys distribution based on stochastic properties of
meteor burst radio propagation. Unlike wireless key distribution, this method provides much greater channel
length and key distribution distances, which is up to 2000 km. Another important advantage is an ability of
meteor burst communications to operate in severe climate, under conditions of polar and other remote areas.
The paper also considers various physical factors ensuring stochastic variations in characteristics of received
radio signal, which are applicable for the secret key generation. The simulation results revealing the most
important randomizing factors within meteor burst channel are presented.
1 INTRODUCTION
Over the last 25-30 years there is an active
discussion in the publications of a large number of
researchers about the possibility of secure key
distribution based on stochastic properties of
physical layer of data channels. Historically, the first
method to realize this idea was the quantum key
distribution proposed in the mid-1980s (Bennett,
1984). Ten years after, the idea of encryption keys
distribution based on physical properties of
reciprocal radio channels was proposed (Hershey,
1995). In many subsequent works, such as (Mathur,
2008; Madiseh, 2008; Madiseh, 2009), the multipath
fading effect within indoor environment and its
unpredictability have been considered as a common
source of randomness to create a shared secret key at
two parties (say, Alice and Bob). The channel
reciprocity ensured symmetry of the key instances at
Alice and Bob. The secret key was generated based
on random signal characteristics (e.g. phase,
amplitude and quadrature components), whose
measurements were identical at both sides of the
link. A rapid spatial decorrelation of multipath
signal characteristics ensured inability of key
interception even at small spatial diversities.
A short-range radio is the main drawback of
multipath channel, which typically limits key
distribution distances by 1 km only. However, the
years of research and development in the field of
meteor burst communication systems have shown
that, like the multipath channels, the meteor radio
propagation has all properties necessary for the key
distribution.
The purpose of this paper is to show that the
stochastic properties of meteor radio propagation
(MRP) provide encryption keys generation and their
secure distribution over the distances up to 2000 km.
2 METEOR PHENOMENA AND
“METEOR CRYPTOGRAPHY”
Every second a countless number of meteor particles
invade into the Earth's atmosphere at the speed of 12
to 72 km/s. These particles are so small that their
weights range from 0.01 mg to several grams only.
Under the influence of a high atmospheric drag the
meteor particles burn at altitudes of 70-120 km
leaving ionized trails behind them. These trails
scatter incident radio waves acting as natural
retranslators. Thus, emitted by Alice radio signal is
reflected from a meteor trail and will be eventually
received by Bob. So, a meteor burst communication
link is established between Alice and Bob. In fact,
only a small part of all meteor trails is suitable for
the communication between the given locations of
Alice and Bob to arise. To be more specific, the
communication will come only if a trail provides
445
Sulimov A. and Karpov A..
Secure Key Distribution based on Meteor Burst Communications.
DOI: 10.5220/0005113104450450
In Proceedings of the 11th International Conference on Security and Cryptography (SECRYPT-2014), pages 445-450
ISBN: 978-989-758-045-1
Copyright
c
2014 SCITEPRESS (Science and Technology Publications, Lda.)
desired geometry of scattering and sufficient signal
strength.
Typically, only 50-350 suitable meteor trails are
observed within 1 hour. This is a small number,
which naturally leads to a small (a few hundreds
bps) capacity of meteor burst communication
systems. However, the meteor burst channel (MBC)
has a number of particular properties that can be
used for the secure generation and distribution of
encryption keys. According to experimental studies
(Desourdis, 1993) the MBC can be considered as a
reciprocal channel with a satisfactory
approximation. Just like in the case of multipath
fading channels, it allows detection of identical
values of random signal characteristics both by Alice
and Bob.
The scattering by meteor trails can be
approximately regarded as a specular reflection from
a certain point M lying on its surface (McKinley,
1961). This leads to a limited area around the
communication point where the scattered signal can
be received. Obviously, the strongest signal will be
received at the direction of specular reflection and a
rapid spatial decorrelation will be observed with the
rise of diversity. Such decorrelation makes key
interception almost impossible at practice.
Finally, a significant randomness exists within
the MBC. The invasion of meteor particles into the
Earth's atmosphere along with its ablation and
formation of ionized trail, emergence of the
reflecting point M are mostly unpredictable
processes. Specifically, the coordinates of the
reflecting point M are also random. This causes
randomness of the A-M-B path for the signal
transmitted from Alice to Bob. As a result, random
values of the carrier phase φ, time delay τ and
amplitude U will be detected at the signal receiving.
These values should be identical at both sides of the
link due to channel reciprocity:
{U
AB
;φ
AB
;τ
AB
}={U
BA
;φ
BA
;τ
BA
}. Thus, the MBC
channel can be considered as a common source of
randomness for Alice and Bob. This allows them to
create a shared secret key by performing at both
sides a series of measurements of random
characteristics of radio reflections from the meteor
trails. The authors called such an approach to
encryption keys distribution the “meteor
cryptography".
3 PREVIOUS WORKS
The concept of meteor cryptography was proposed
by researchers from Kazan Federal University
(Russia) in 2001. This idea was preceded by almost
50 years of active theoretical and experimental
studies in the field of meteor radio propagation and
system development for the meteor burst
communication and time synchronization. As a
result of this hard work, the prototypes of meteor
burst synchronization systems with sub-nanosecond
accuracy were created (Sidorov, 1993; Korneyev,
2003; Korneyev, 2007). Such accuracy allows
synchronous detection of received signal carrier
phase at both sides of the meteor burst
communication link. It was experimentally shown
(Desourdis, 1993) that the phase values measured at
both sides of the link are very close to each other.
It should be noted, that in typical meteor burst
communication link signal propagates over the
distances of hundreds kilometers. Besides, due to
randomness of coordinates of the reflecting point at
meteor trail the propagation path is also random. As
a result, the carrier phase of received signal is a
random variable which could be used for the
encryption keys generation.
In previous works (Karpov, 2005; Sidorov, 2007)
on meteor cryptography the main efforts were
focused at the discussion of technical aspects of
implementation of encryption key distribution
systems. However, we feel that a very important part
of the research work has been missed. It was not
taken into account that the meteor burst
communications is a very specific technical field
familiar only to a limited number of specialists. The
basic principles of meteor cryptography were not
disclosed properly in the prior works. In particular,
the sources of randomness within the meteor burst
channel have not been indicated.
The following sections of this paper are devoted
to discussion of basic mechanisms of the MBC
randomness. A significance of different randomizing
factors will also be investigated for the values of
carrier phase φ and propagation delay τ of meteor
radio reflections.
4 RESEARCH METHODS
Meteor burst channel is difficult in understanding.
Its performance is influenced by many factors of
different nature: by equipment, astronomical,
atmospheric conditions, etc. All these factors have a
complex impact on the measured signal parameters.
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446
Unfortunately, we can’t separate them in an
experiment, which makes a study of individual
influence of each randomizing factor impossible.
Moreover, the scattering from meteor trails takes its
place at random coordinates at altitudes of 80-110
km. Thus, immediate observation and control of
propagation of radio signals is very difficult to
implement. For this reason, all the experimental
study of meteor burst propagation is based on
indirect measurements only.
That’s why simulation is the only solution. The
simulation makes it easy to enable and disable
various randomizing factors while monitoring
changes in the statistical characteristics of received
signal parameters.
The vast majority of MBC simulation models is
based on simple mathematical models developed in
the 1950-s (McKinley, 1961). These models can’t
simulate complex electrodynamic effects taking
place at the scattering off ionized meteor trails. At
the same time, these effects are vital for the studies
of encryption keys distribution. The KAMET
simulation model (Karpov, 2001) based on rigorous
diffractional theory of radio waves scattering
(Khuzyashev, 1984) includes and adequately
reproduces all necessary effects.
We used the Moscow-Kazan MBC link for the
simulation purposes. The following technical
specifications were used during simulation:
Link length: 720 km;
Carrier frequency: f = 50 MHz;
Transmitted power: P
T
= 2000 W;
Required signal-to-noise ratio: 20 dB;
Threshold level: U
0
= 0,5 μV (which
corresponds to SNR=20 dB);
Standard deviation of turbulent wind velocity:
σ
V
= 25 mps.
5 BASIC RANDOMIZING
FACTORS OF METEOR BURST
CHANNEL
An analysis of meteor radio propagation reveals
following basic randomizing factors in the meteor
burst channel:
1. Random spatial orientation of each meteor trail;
2. Random coordinates M(x,y,z) of the reflecting
point on the meteor trail;
3. Random mass m of meteor particle which
produces the ionized trail;
4. Random moment of occurrence of signal fading
(Weitzen, 1987);
5. Random direction and magnitude of the
turbulent wind velocity blowing in the vicinity
of the reflecting points of meteor trail
(Weitzen, 1987);
6. Channel noise and measurement errors.
We used the Pearson correlation coefficient R
1
between the adjacent measurements of observable
signal parameter as a measure of randomness. Since
it characterizes statistical relationship between the
parameters of two successively detected meteor
radio reflections, the value of R
1
can be considered
as an indicator of predictability of generated keys.
We consider the carrier phase φ and propagation
delay τ of received signal as observed random
parameters implied for the key generation.
The τ variable is mainly determined by the
geometric path of received signal:
c
MBAM )(
(1)
In formula (1) c means speed of light, AM and BM
are the distances between the reflecting point of
meteor trail and communication points of the link.
Therefore, randomness of the τ variable is almost
completely determined only by the second
randomizing factor (random coordinates of the
reflecting point). Factor no.5 also gives a small
contribution. However, the total shift of the
reflecting point made by turbulent winds during
signal detection rarely exceeds 100 m (or several λ).
This is much lesser than the contribution of
geometric path (1), which typically is of hundreds
kilometers or more.
The variable φ consists of two components: the
path length shift (2π·τ) and polarization phase shift
added by the scattering of radio wave from a meteor
trail. For this reason, the phase value φ is affected by
greater number of randomizing factors. For example,
factor no. 5 is very significant for the carrier phase
and we should not neglect it. This is due to wind
shift of the reflecting point at several λ leads to large
changes in the carrier phase.
6 SELECTION OF
MEASUREMENTS
During the detection of meteor radio reflection its
amplitude and phase are changing in time. These
SecureKeyDistributionbasedonMeteorBurstCommunications
447
changes are recorded as the Amplitude-Time
Response (ATR) and the Phase-Time Response of
radio reflection, respectively. In fact, only
approximate channel reciprocity is observed for the
meteor burst propagation. Calculations and
experiments show that the Phase-Time Response
φ
AB
(t) recorded in point B is slightly different with
the Phase-Time Response φ
BA
(t) recorded in A. Such
difference occurs due to non-absolute reciprocity of
MBC. Figure 1 shows an example of simulated
Phase-Time Responses observed synchronously in
communication points A and B. We should outline
that no noise effect was enabled for these curves.
Figure 2 shows differential PTR for the above
example, which indicates presence of some channel
non-reciprocity. This reciprocity is a consequence of
non-identical scattering of radio waves transmitted
by the opposite communication points. It occurs
every time the reflecting point is located non-
symmetrically relative to the communication points
A and B.
Figure 1: Examples of Phase-Time Responses of the same
meteor radio reflection observed at both sides of the link
The profiles of PTR and differential PTR are
unpredictable and individual for every specific
meteor radio reflection. For the keys generated in
points A and B to be identical, the moment of
minimum absolute value of channel non-reciprocity
should be used to make phase measurements. Such
point (t* = 0.13s) is marked in Figure 2 with a circle.
In this approach, only a single value of the carrier
phase φ and propagation delay τ should be extracted
from each meteor radio reflection.
Figure 2: Example of MBC non-reciprocity.
7 SIMULATION RESULTS
To evaluate significance of various randomizing
factors, a simulation of the test Moscow-Kazan radio
link has been carried out. Step by step, we reduced
the number of randomizing factors at each stage of
the simulation. For each set of randomizing factors a
sample of N = 5000 meteor radio reflections was
simulated. This allowed the points A and B to collect
5000 measurements of the carrier phase φ and
propagation delay τ implied for the key generation
purposes. For each simulated radio reflection a PTR
consisting of M = 2000 points with sampling interval
Δt = t
j+1
t
j
= 5ms has been calculated.
The simulation results are summarized in the Table
1. The second column of the table contains short
symbolic notation of enabled ("+") and disabled ("–
") randomizing factors. The symbol ("x") denotes
that this factor is not significant, i.e. its activation
and disabling did not affect at the simulation results.
It was found at the stage no.5 that the factor no. 4
should be classified as non-significant. At the
subsequent stages of simulation this factor was
ignored.
Table 1: Simulation results.
Stage
No.
Enabled randomizing factors
)(
1
R
)(
1
R )(
1
PTRR
1 1+| 2+| 3+| 4+| 5+| 6x 0.015 0.008 0.401
2 1–| 2+| 3+| 4+| 5+| 6x 0.002 0.022 0.407
3 1–| 2+| 3–| 4+| 5+| 6x 0.001 0.004 0.580
4 1–| 2+| 3–| 4+| 5–| 6x 0.013 0.010 0.698
5 1–| 2+| 3–| 4–| 5–| 6x 0.003 0.012 0.690
6 1–| 2–| 3+| 4x| 5+| 6x 0.007 0.011 0.826
7 1–| 2–| 3–| 4x| 5+| 6x 0.010 0.015 0.915
8 1–| 2–| 3–| 4x| 5–| 6x 1.000 1.000 1.000
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448
N
k
k
N
i
i
N
i
ii
R
2
1
1
1
1
1
1
)(
(2)
The third and fourth columns of the Table 1
show values of the Pearson correlation coefficient R
1
between the adjacent measurements of the phase φ
and propagation delay τ. Each of the 5000 simulated
measurements has been selected according to the
selection criterion discussed in the section 6. The
simulation results show that the samples of phase
and propagation delay measurements remain to be
random up to exclusion of all the MBC randomizing
factors. Therefore, the values in the third and fourth
columns do not allow indication of the significance
of individual randomizing factors.
To get more indicative measure of statistical
relationship between the successively detected
meteor radio reflections, we should consider a
correlation between the whole Phase-Time
Responses but not the correlation between their
single counts, as we did before. The R
1
(PTR) values
calculated according to the formula (3) are presented
in the last column of the Table 1.
1
1
2
1
1
1
1
1
1
)()(
)()(
1
1
)(
N
i
M
k
ki
M
j
ji
M
j
jiji
tt
tt
N
PTRR
(3)
At the first and the second simulation stages the
mass m of meteor particles was a random variable
with the inverse-power probability distribution. At
the third stage masses of all the simulated meteor
particles were fixed at value m = 5·10
-4
g. The same
value was also used at the simulation stages no. 4, 5,
7 and 8.
The simulation showed that the factor no. 2
“random coordinates M(x,y,z) of the reflecting
point” is the most significant randomizing factor in
meteor burst channel. Even if all the simulated
meteor trails have the same spatial orientation (i.e.
factor no. 1 is disabled) there is still a great
randomness in the characteristics of received signal
due to presence of the factor no. 2. This allows
considering the factor no. 2 as the most basic
randomizing factor. As it can be traced out from the
last column of the Table 1, the shapes of Phase-Time
Responses for the successively detected meteor
radio reflections are becoming mostly identical as
we reduce the number of enabled randomizing
factors.
The simulation also showed that the Phase-Time
Response of radio reflection produced by an
underdensed meteor trail typically has a smooth
shape with no sharp phase discontinuities.
Conversely, the Phase-Time Response of radio
reflection produced by an overdensed meteor trail
typically reveals much more intensive variation of
the carrier phase in time. In other words, the phase
measurements produced by the overdensed meteor
trails are more stochastic.
8 CONCLUSIONS
Based on the simulation results, we can rank the
randomizing factors of meteor burst channel in order
of their significance as follows:
1) Random coordinates M(x,y,z) of the reflecting
point on the meteor trail (factor 2);
2) Random spatial orientation of each meteor trail
(factor no. 1);
3) Random direction and magnitude of the
turbulent wind velocity blowing in the vicinity
of the reflecting points of meteor trail (factor
no. 5);
4) Random mass m of meteor particle which
produces the ionized trail (factor no. 3);
5) Random moment of occurrence of signal fading
(factor no. 4);
6) Other randomizing factors.
Enabling the factors no.1, 2 and 5 ensures
unpredictability of the carrier phase φ and
propagation delay τ of received signal. No any
immediate influence of the number of enabled
randomizing factors on the statistical and
probabilistic properties of observed random
variables have been identified during the simulation.
The only exception is the factor no. 2, which is the
most basic in randomizing the observed parameters
of received signal. It was also found that the factor
no. 4 barely affects on the probabilistic and
statistical properties of observed variables.
Radio reflections produced by the overdensed
meteor trails have less predictable variations of the
signal amplitude and phase. However, a serious
drawback of the overdensed trails is a higher value
of the channel non-reciprocity. Rise of the channel
non-reciprocity results in a higher probability of bit
mismatch between the keys generated by Alice and
Bob. Thus, the use of radio reflections produced by
the overdensed trails provides higher entropy of
SecureKeyDistributionbasedonMeteorBurstCommunications
449
encryption key but reduces a key generation rate due
to increased channel non-reciprocity.
The future research work should be aligned at the
performance evaluation and security analysis of the
meteor cryptography systems. Non-reciprocity
effects of meteor radio propagation and spatial
correlation features of meteor burst channel should
be considered to address the above problems.
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