=Paper=
{{Paper
|id=Vol-3094/paper_6
|storemode=property
|title=
Development of Algorithms for Increasing the Information Secrecy of the Satellite Communication System Based on the Use of Authentication Technology
|pdfUrl=https://ceur-ws.org/Vol-3094/paper_6.pdf
|volume=Vol-3094
|authors=Nikita Chistousov,Igor Kalmykov,Aleksandr Olenev,Natalya Kalmykova
}}
==
Development of Algorithms for Increasing the Information Secrecy of the Satellite Communication System Based on the Use of Authentication Technology ==
https://ceur-ws.org/Vol-3094/paper_6.pdf
Development of Algorithms for Increasing the Information
Secrecy of the Satellite Communication System Based on the Use
of Authentication Technology
Nikita Chistousov 1, Igor Kalmykov 1, Aleksandr Olenev 2 and Natalya Kalmykova 1
1
North-Caucasus Federal University, Pushkina, 1, Stavropol, 355009, Russia.
2
Stavropol State Pedagogical Institute, Lenina St., 417 "A" , Stavropol, 355028, Russia
Abstract
One of the most promising applications of low-earth orbit satellite systems is remote
monitoring and control systems for unattended objects located in the Far North. Therewith,
there is a tendency to increase the groupings of such satellites. Therefore, ensuring the
information secrecy of the low-earth orbit satellite becomes an important task. To prevent the
intruder satellite from imposing a previously captured and delayed control command, it is
proposed to use the "friend-foe" system for satellites, which uses a zero-knowledge
authentication algorithm. It is necessary to increase the speed of the satellite authentication
process to reduce the probability of a response signal being picked up. To do this, it is proposed
to use modular codes (MC), which can simultaneously perform the operations of addition,
subtraction, and multiplication. As a result, the probability of picking up the signal of the
responder located onboard the satellite is reduced. In addition, the MC can correct multi-bit
errors within a single remainder in the presence of two redundant bases. Therefore, the
development of an algorithm for correcting errors arising in the process of satellite
authentication caused by failures, and interference in the communication channel is an urgent
task. The work aims to increase the information secrecy of the low-earth orbit satellite by using
the developed authentication algorithm, which has a minimum time for determining the
satellite status, as well as an algorithm for correcting errors that occur during the operation of
the satellite identification system and data transmission, implemented using a single algebraic
system – parallel modular codes.
Keywords 1
satellite authentication algorithm, modular code, error detection, and correction algorithm
1. Introduction
In recent years, there has been a tendency to an increase in the number of low-orbit satellite
constellations, which are used in remote monitoring, control, and management systems for unattended
objects of environmentally hazardous technologies used in the production and transportation of
hydrocarbons in the Far North. Herewith, an increase in the number of countries involved in the
development of the Arctic's natural resources contributes to the intensification of destructive impacts
on the low-earth orbit satellite (LEOS) to disrupt their work. One of the promising areas to counteract
these actions is to ensure the information secrecy of the LEOS [1-3].
To increase the information secrecy of the LEOS, it is proposed to use a satellite authentication
system that will not allow the intruder satellite to impose on the receiver an intercepted and delayed
signal that can disable the control object and cause an environmental disaster. To reduce the probability
AISMA-2021: International Workshop on Advanced in Information Security Management and Applications, October 1, 2021, Stavropol,
Krasnoyarsk, Russia
EMAIL: chistousov.nik@yandex.ru (Nikita Chistousov); kia762@yandex.ru (Igor Kalmykov); olenevalexandr@gmail.com (Aleksandr
Olenev); kmi545@yandex.ru (Natalya Kalmykova)
ORCID: 0000-0002-0286-7391 (Nikita Chistousov); 0000-0002-9854-5310 (Igor Kalmykov); 0000-0003-2719-6624 (Aleksandr Olenev);
0000-0003-2498-8765 (Natalya Kalmykova)
© 2022 Copyright for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR Workshop Proceedings (CEUR-WS.org)
59
of picking up a response signal by an intruder satellite, it is proposed to use modular codes (MC), which
will increase the speed of satellite identification. Therewith, the MC can also correct errors that occur
in the calculation process due to failures [4, 5]. The article presents the developed algorithm for
detecting and correcting MC errors that occur during the satellite authentication process and are caused
by both failures, and interference in the communication channel, the use of which will ensure the
information secrecy of the LEOS even during destructive impacts of natural and artificial nature on the
identification system.
2. Materials and methods
2.1. Modular codes
Modular codes are arithmetic non-positional codes [4, 5]. In these codes, the integer X is uniquely
given by a tuple of the remainder
Х ( х1 , х2 ,..., хk ) , (1)
where хi Х mod mi , mi –bases of the modular code; ( mi , m j ) 1 ; i 1,..., k .
Since the bases of MC are pairwise prime numbers mi, where i 1,..., k , their product sets the size
of the working range
k
M k mi X . (2)
i 1
Since modular codes perform summation, diminution, and multiplication operations in parallel
Х С (( х1 с1 ) mod m1 , ( х2 с2 ) mod m2 ,..., ( хk сk ) mod mk ) , (3)
Х С (( х1 с1 ) mod m1 , ( х2 с2 ) mod m2 ,..., ( хk сk ) mod mk ) , (4)
Х С (( х1 с1 ) mod m1 , ( х2 с2 ) mod m2 ,..., ( хk сk ) mod mk ) , (5)
then it is advisable to use them to increase the speed of calculations. Since authentication algorithms
use such operations, they can be implemented in the MC. Therefore, modular codes have found wide
application in real-time systems.
In works [6-9] it is offered to use modular code for construction of special processors of digital
signal processing. Modular codes allow to increase the efficiency of digital filters [10-13]. Work [14]
presents the protocol "Electronic Cash" with inspection correction rules of the electronic e-cash number
for e-Commerce systems, which uses SOC. This allows to increase the authentication speed of the
applicant. In [15] it is shown that the codes of a polynomial residue number system, aimed at reducing
the effects of failures in the AES cipher. Error correction of digital signal processing devices using non-
positional modular codes is shown in [16-19]. The use of redundant modular codes for improving the
fault tolerance of special processors for digital signal processing is shown in [20]. A method of
increasing the reliability of telemetric well information transmitted by the wireless communication
channel is shown in [21]. Consider the use of modular codes in authentication protocols. Let's use the
protocol given in the [22].
2.2. Development of an authentication algorithm in MC
In this algorithm, the following parameters are used:
m1, …, mk –bases of the modular code;
the satellite secret key X ( X1 , ..., X k ) M k ;
the session key Y ( j ) ( Y1 ( j ), ..., Yk ( j )) M k ;
60
and the parameter L( j ) ( L1 ( j ), ..., Lk ( j )) M k used to verify the repeated use of the
session key, where X X i mod mi ; Y ( j ) Yi ( j ) mod mi ; L( j ) Li ( j ) mod mi ;
i =1,2,..., k; j is the number of the communication session.
The preliminary stage of the satellite authentication algorithm:
1. The responder calculates the true status of the satellite
W1 b X1 bY1 ( j )b L1 ( j ) ;
m1
W2 b X 2 bY2 ( j )b L2 ( j ) ;
m2 (6)
Wk b X k bYk ( j )b Lk ( j ) ;
mk
where b is the generating multiplicative group to modulo mi.
2. The responder chooses random numbers
k
X , Y ( j ), L( j ) M k mi , (7)
i 1
and makes a noise of the secret parameters of the algorithm
X i* X i X i
pi
,
Yi* ( j ) Yi ( j ) Yi ( j )
pi
, (8)
L*i ( j ) Li ( j ) Li ( j )
pi
,
where pi ( mi ) is the Euler function of the number mi; X , Y ( j ), L( j ) – random numbers;
X i X m Y ( j ) Yi ( j ) mod mi ; L( j ) Li ( j ) mod mi .
i
3. The responder calculates the noisy status of the satellite
W1* b X1 bY1 ( j )b L1 ( j )
* * *
;
m1
W2* b X 2 bY2 ( j )b L2 ( j )
* * *
;
m2 (9)
* * *
Wk* b X k bYk ( j )b Lk ( j ) ;
mk
The authentication algorithm consists of the following steps.
1. The requester passes the responder a random number g = (g1, g2 ,…, gk).
2. The responder, having received number g, calculates the answers
vi ( 1 ) X i* g i X i ,
pi
vi ( 2 ) Yi* ( j ) g i Yi ( j ) , (10)
pi
vi ( 3 ) L*i ( j ) g i Li ( j ) .
pi
The responder transmits the following data to the requester
( W , ..., W ), ( W , ..., W ), ( v (1 ), ..., v (1 )), ( v ( 2 ), ..., v ( 2 )), ( v ( 3 ), ..., v ( 3 )).
1 k 1
*
k
*
1 k 1 k 1 k
3. The requester checks the received responses
61
Z1 W1g1 b v1 ( 1 )b v1 ( 2 )b v1 ( 3 ) ,
m1
Z 2 W2g2 b v2 ( 1 )b v2 ( 2 )b v2 ( 3 ) ,
m2 . (11)
Z k Wkgk b vk ( 1 )b vk ( 2 )b vk ( 3 ) .
mk
Applicant A has the "own" status if the equality is met Z1 W1* ,..., Z k Wk* .
The originality of this solution is based on a new idea – the use of MC, which effectively provides
parallelization of calculations at the level of arithmetic operations when authenticating the satellite. The
novelty of the obtained result is that an authentication algorithm has been developed for the first time,
implemented in MCs, the use of which makes it possible to increase the information secrecy of the
LEOS by reducing the probability of selecting a response signal "Own", caused by a reduction in the
time spent on satellite identification due to parallelization of the calculation at the level of arithmetic
operations.
When implementing the hardware design of the system, the Vivado HLS 2019.2 development tool
was used. The clock frequency of the FPGA was 250 MHz. Comparative analysis showed that it takes
3.1 ms to complete one round of the authentication stage using Shnor protocol and 1.2 ms for the
developed protocol when using a 32-bit base.
2.3. Error correction algorithm in modular codes
To correct a batch of errors within a single remainder xi* xi xi , where
mi
xi 1, ..., mi 1 is the error depth, two control bases are introduced [4, 5]
pk 1 pk 2 pk pk 1 . (12)
The result is the full range of the code
k 2
M k 2 mi . (13)
i 1
Redundant MC does not contain an error during execution
k
X ( x1 ,..., xk , xk 1 , xk 2 ) M k mi . (14)
i 1
Therefore, the MC use the positional characteristic (PC) interval number, which shows the location
of the code relative to Mk
X
S , (15)
Mk
where is the integer part when dividing.
If the positional characteristic:
S = 0 – there is no error;
S > 0 – there is an error.
Let us use the Chinese remainder theorem to translate from modular code to positional code,
X x1B1 x2 B2 ... xk 2 Bk 2 mod M k 2
k 2
(16)
xi Bi mod M k 2 ,
i 1
where Bi – orthogonal basis of the redundant MC.
The orthogonal bases are calculated according to [4]
62
M k 2
Bi M k12 . (17)
mi mi
Let us substitute expression (15) into expression (14). The result is the algorithm for calculating this
positional characteristic in the MC without translating it into a positional code
k 2 k 1
S k 1 xi К i j B*j M k mod mk 1 ,
i1 j 1
(18)
S x К B* M 1 mod m ,
k 2 k
k 2
i1 i i j j k k 2
j 1
where Bi K i M k Bi* ; Bi* is the orthogonal basis of the redundant MC.
The originality of the developed algorithm is based on a new idea – to use redundant MC to correct
errors caused not only by failures of the satellite identification system but also by interference in the
channel. In addition, the MC can correct multi-bit errors within a single remainder in the presence of
two redundant bases. This allowed assuming that the redundant MC are close to the Reed-Solomon
codes in their correcting abilities. This means that the use of redundant MC will allow abandoning the
cascade codes, in which the external code is designed to detect and correct errors caused by failures,
and the internal code – to search for and correct errors caused by interference in the communication
channel. The novelty of the obtained result lies in the fact that for the first time an algorithm was
developed for correcting errors by redundant MC arising in the process of satellite authentication caused
by both failures, and interference in the communication channel, which will ensure information secrecy
of the LEOS even during the destructive effects on the system. To evaluate the effectiveness of the
algorithm for constructing a modular turbo code, a software package was created that allows simulating
a communication channel with impulse noise. The analysis of the research results shows that the
application of the developed algorithm for constructing a modular turbo code makes it possible to
increase the noise immunity of the identification system. So, with the signal-to-noise ratio Eb/N0 = 13
dB, the probability of a system error using the developed algorithm is P 3 105 , while for the
classical МС - P 8,6 105 .
3. Acknowledgements
This work was supported by the Russian Foundation for Basic Research, project No. 20-37-90009
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