ВЕРОЯТНОСТНЫЕ ХАРАКТЕРИСТИКИ АЛГОРИТМА ОБНАРУЖЕНИЯ СИНХРОСИГНАЛОВ НА ОСНОВЕ ВЫБОРА СМЕЖНОЙ ПАРЫ СЕГМЕНТОВ С МАКСИМАЛЬНЫМ СУММАРНЫМ ОТСЧЁТОМ
Ключевые слова:
Квантовое распределение ключа, синхронизация, максимальный суммарный отсчёт, вероятностные характеристики
Аннотация
Предложен алгоритм обнаружения синхросигналов на основе выбора смежной пары
сегментов с максимальным суммарным отсчётом. Указанный алгоритм учитывает не-
достатки альтернативного алгоритма обнаружения синхросигнала на основе сравнения
суммы отсчётов со смежной пары сегментов с пороговым уровнем, состоящие в необхо-
димости знания уровня фонового и шумового воздействия, который определяет пороговый
уровень и вероятность ошибочного обнаружения сигнальной пары сегментов. Исследована
зависимость вероятности ошибки обнаружения синхроимпульса от среднего числа сиг-
нальных фотонов в синхроимпульсе при различных значениях числа сегментов во временном
кадре. Так, вероятность ошибочного обнаружения синхроимпульса в течение кадра значи-
тельно уменьшается по мере роста среднего числа фотонов в синхроимпульсе. Например,
при увеличении среднего числа сигнальных фотонов в синхроимпульсе с до 5 вероятность
ошибки обнаружения синхроимпульса снижается в 37 раз. Необходимо отметить слабое
влияние числа пар сегментов на вероятность ошибочного обнаружения, что указывает на
слабое влияние импульсов темнового тока на вероятностные характеристики предложен-
ного алгоритма обнаружения синхросигналов. Получены аналитические выражения для
точного и экспресс-расчёта вероятностных характеристик обнаружения, учитывающие
вероятность нахождения синхроимпульса на границе двух смежных сегментов в связи с
равенством длительностей синхроимпульса и временного сегмента. Результаты расчёта
по точным выражениям вероятности обнаружения синхроимпульса показали, что при
отношении сигнал/шум равном 0 и выше влиянием шумовых импульсов на вероятность
обнаружения синхроимпульса можно пренебречь. Отмечено, вероятность обнаружения
будет тем больше, чем больше число регистрируемых событий, или, другими словами, чем
больше сумма средних чисел сигнальных фотонов и импульсов темнового тока. Расчёт
вероятности обнаружения синхроимпульса по упрощённым выражениям показывает не-
значительное отклонение от расчётов по точным формулам, которое не превышает
5,3 %, причём расчёт по приближённым выражениям даёт заниженный результат. Полу-
ченные приближённые аналитические выражения могут применяться для экспресс-
расчёта вероятности обнаружения синхроимпульса в паре сегментов.
Литература
1. Lindsey W.С. Synchronization Systems in Communication and Control. Prentice-Hall, Englewood
Cliffs, New Jersey, 1972.
2. Stiffler Dzh. Teoriya sinkhronnoy svyazi [Synchronous communication theory]: transl. from
engl., ed. by E.M. Gabidulina. Moscow: Svyaz', 1975.
3. Gal'yardi R.M., Karp Sh. Opticheskaya svyaz' [Optical communication]: transl. from engl., ed.
by A.G. Sheremet'eva. Moscow: Svyaz', 1978, 424 p.
4. Viterbi A.D., Omura Dzh.K. Printsipy tsifrovoy svyazi i kodirovaniya [Principles of digital
communication and coding]: transl. from engl., ed. by K.Sh. Zigangirova. Moscow: Radio i
svyaz', 1982, 536 p.
5. Yilong Geng, Shiyu Liu, and Zi Yin. Exploiting a Natural Network Effect for Scalable, Finegrained
Clock Synchronization, NSDI'18: Proceedings of the 15th USENIX Conference on
Networked Systems Design and Implementation, 2018, pp. 81-94.
6. Govindan Kannan Pravein., Joshi Raj., Chan Mun Choon. Precise Time-synchronization in
the Data-Plane Using Programmable Switching ASICs, Proceedings of the 2019 ACM Symposium
on SDN Research, ACM, 2019, pp. 8-20. DOI: 10.1145/3314148.3314353.
7. Rumyantsev K.E. Sistemy kvantovogo raspredeleniya klyucha: monografiya [Systems of quantum
key distribution: monograph]. Taganrog: Izd-vo TTI YuFU, 2011, 264 p.
8. Rumyantsev K.E. Sinkhronizatsiya v sisteme kvantovogo raspredeleniya klyucha s
avtomaticheskoy kompensatsiey polyarizatsionnykh iskazheniy [Synchronization in a quantum
key distribution system with automatic compensation of polarization distortions],
Telekommunikatsii [Telecommunications], 2017, No. 2, pp. 32-40.
9. Rumyantsev K.E., Plenkin A.P. Sinkhronizatsiya sistemy kvantovogo raspredeleniya klyucha pri
ispol'zovanii fotonnykh impul'sov dlya povysheniya zashchishchennosti [Synchronization of the
system of quantum key distribution when using photon pulses to increase security], Izvestiya
YuFU. Tekhnicheskie nauki [Izvestiya SFedU. Engineering Sciences], 2014, No. 8, pp. 81-96.
10. Plenkin A., Rumyantsev K., Rudinsky E. Comparative analysis of single-photon synchronization
algorithms in the quantum key distribution system, Proceedings of IEEE East-West Design
& Test Symposium (EWDTS), 2017, pp. 1-5. DOI: 10.1109/EWDTS.2017.8110047.
11. Rumyantsev K.E., Rudinsky E.A. Time synchronization method in quantum key distribution
system with automatic compensation of polarization distortions, Proceedings of the 2nd International
Conference on Multimedia and Image Processing (ICMIP), 2017, pp. 346-349. DOI:
10.1109/ICMIP.2017.68.
12. Mironov Y.K., Mironova P.D., Rumyantsev K.E. Study of the characteristics of the synchronization
algorithm for a quantum key distribution system based on comparing the number of
samples from an adjacent pair of time windows with a threshold level, IOP Conf. Series: Materials
Science and Engineering, 1069, 2021, Paper 012011, pp. 1-8. DOI: 10.1088/1757-
899X/1069/1/012011.
13. Mironov Y., Mironova P., Rumyantsev K. Characteristics of a two-stage synchronization algorithm
in the system of quantum key distribution with dividing a fiber-optic line into sections
with decreasing length, ACM International Conference Proceeding Series, 2020, Paper
No. 3433596, pp. 1-5. DOI: 10.1145/3433174.3433595.
14. Mironov Y.K., Mironova P.D., Rumyantsev K.E. Methodology for calculating the average time
of entry into synchronism of stations of the system of quantum key distribution with sequential
polling of fiber-optic line sections with decreasing length by the graphic-analytical method,
E3S Web of Conferences, 2020, Vol. 224, pp. 1-9. DOI: 10.1051/e3sconf/202022401032.
15. Mironov Y.K., Rumyantsev K.E. Single-Photon Algorithm for Synchronizing the System of
Quantum Key Distribution with Polling Sections of a Fiber-Optic Line, Futuristic Trends in
Networks and Computing Technologies, 2020, pp. 87-97. DOI: https://doi.org/10.1007/978-
981-15-4451-4_8.
16. Rumyantsev K.Y., Bamatgireeva K.B., Mironov Y.K. Single Photon Algorithm of Search of a
Pulse Radiation Source, Communications in Computer and Information Science, 2019, 958,
pp. 95-108. DOI: 10.1007/978-981-13-3804-5_8.
17. Kurochkin V.L. i dr. Eksperimental'nye issledovaniya v oblasti kvantovoy kriptografii [Experimental
research in the field of quantum cryptography], Fotonika [Photonics], 2012, Vol. 5, pp. 54-66.
18. Rumyantsev K.E., Plenkin A.P. Bezopasnost' rezhima sinkhronizatsii sistemy kvantovogo
raspredeleniya klyuchey // Izvestiya YuFU. Tekhnicheskie nauki [Izvestiya SFedU. Engineering
Sciences], 2015, No. 5 (166), pp. 135-153.
19. Mironov Ya.K. Modelirovanie etapa testirovaniya dvukhetapnogo vremennogo algoritma
sinkhronizatsii pri nakhozhdenii odnofotonnogo istochnika izlucheniya v signal'nom uchastke
VOLS [Simulation of the testing stage of a two-stage time synchronization algorithm when a
single-photon radiation source is in the signal section of the FOCL], Fundamental'nye i
prikladnye aspekty komp'yuternykh tekhnologiy i informatsionnoy bezopasnosti: materialy VIII
Vserossiyskoy nauchno-tekhnicheskoy konferentsii [Fundamental and Applied Aspects of
Computer Technologies and Information Security: Proceedings of the VIII All-Russian Scientific
and Technical Conference], 2022, pp. 19-21.
20. Mironov Y.K., Rumyantsev K.E. Providing the Required Probability of Synchronization Error When
Splitting a Fiber-Optic Line into Sections with Decreasing Length in a Quantum Key Distribution
System, Proceedings - 2021 3rd International Conference on System Reliability and Safety Engineering,
SRSE 2021, 2021, pp. 145-149. DOI: 10.1109/SRSE54209.2021.00032.
21. Mironov Ya.K. Sinkhronizatsiya stantsiy sistemy kvantovogo raspredeleniya klyucha s
posledovatel'nym oprosom uchastkov volokonno-opticheskoy linii s ubyvayushchey dlinoy
[Synchronization of stations of the quantum key distribution system with sequential polling of
sections of a fiber-optic line with decreasing length], Fundamental'nye i prikladnye aspekty
komp'yuternykh tekhnologiy i informatsionnoy bezopasnosti: Mater. VII Vserossiyskoy
nauchno-tekhnicheskoy konferentsii [Fundamental and applied aspects of computer technology
and information security: materials of the VII All-Russian Scientific and Technical Conference],
2021, pp. 109-112.
22. Mironov Ya.K., Mironova P.D., Rumyantsev K.E. Veroyatnostnye kharakteristiki porogovogo
algoritma obnaruzheniya sinkhroimpul'sov v sisteme kvantovogo raspredeleniya klyucha na
osnove informatsii so smezhnoy pary vremennykh segmentov [Probabilistic Characteristics of
a Threshold Sync Detection Algorithm in a Quantum Key Distribution System Based on Information
from an Adjacent Pair of Time Segments], Izvestiya YuFU. Tekhnicheskie nauki
[Izvestiya SFedU. Engineering Sciences], 2020, No. 4 (207), pp. 221-229.
23. Mironov Ya.K., Mironova P.D., Rumyantsev K.E. Issledovanie kharakteristik algoritma
sinkhronizatsii sistemy kvantovogo raspredeleniya klyucha na osnove sravneniya chisla
otschetov so smezhnoy pary vremennykh okon s porogovym urovnem [Investigation of the
characteristics of the synchronization algorithm of the quantum key distribution system based
on the comparison of the number of samples from an adjacent pair of time windows with a
threshold level], Sb. dokladov II Vse-rossiyskoy nauchnoy konferentsii (s priglasheniem
zarubezhnykh uchenykh) [Collection of reports of the II All-Russian scientific conference
(with the invitation of foreign scientists)], 2020, pp. 219-226.
24. Mironova P.D. Sinkhronizatsiya stantsiy sistemy kvantovogo raspredeleniya klyucha na
osnove porogovogo testa dlya otschetov so smezhnoy pary vremennykh segmentov [Synchronization
of stations of the quantum key distribution system based on a threshold test for readings
from an adjacent pair of time segments], Fundamental'nye i prikladnye aspekty
komp'yuternykh tekhnologiy i informatsionnoy bezopasnosti: Mater. VII Vserossiyskoy
nauchno-tekhnicheskoy konferentsii [Fundamental and applied aspects of computer technology
and information security: materials of the VII All-Russian Scientific and Technical Conference],
2021, pp. 107-109.
25. Mironova P.D. Algoritm sinkhronizatsii stantsiy sistemy kvantovogo raspredeleniya klyucha
na osnove porogovogo testa dlya otschetov so smezhnoy pary vremennykh segmentov s
uchetom dispersionnykh i polyarizatsionnykh svoystv VOLS [Synchronization algorithm for
stations of a quantum key distribution system based on a threshold test for readings from an
adjacent pair of time segments, taking into account the dispersion and polarization properties
of FOCL], Fundamental'nye i prikladnye aspekty komp'yuternykh tekhnologiy i
informatsionnoy bezopasnosti: Mater. VIII Vserossiyskoy nauchno-tekhnicheskoy konferentsii
[Fundamental and applied aspects of computer technology and information security: materials
of the VIII All-Russian Scientific and Technical Conference], 2022, pp. 22-25.
26. Rumyantsev K.E., Linenko P.D., Shakir H.H.-Sh. Evaluation of the Influence of the Dispersion
Properties of a Fiber-Optic Line on the Efficiency of an Algorithm for Single-Photon Synchronization
of Quantum Key Distribution System, Conference Proceedings - 2019 Radiation
and Scattering of Electromagnetic Waves, RSEMW 2019, 2019, pp. 392-395. DOI:
10.1109/RSEMW.2019.8792769.
Cliffs, New Jersey, 1972.
2. Stiffler Dzh. Teoriya sinkhronnoy svyazi [Synchronous communication theory]: transl. from
engl., ed. by E.M. Gabidulina. Moscow: Svyaz', 1975.
3. Gal'yardi R.M., Karp Sh. Opticheskaya svyaz' [Optical communication]: transl. from engl., ed.
by A.G. Sheremet'eva. Moscow: Svyaz', 1978, 424 p.
4. Viterbi A.D., Omura Dzh.K. Printsipy tsifrovoy svyazi i kodirovaniya [Principles of digital
communication and coding]: transl. from engl., ed. by K.Sh. Zigangirova. Moscow: Radio i
svyaz', 1982, 536 p.
5. Yilong Geng, Shiyu Liu, and Zi Yin. Exploiting a Natural Network Effect for Scalable, Finegrained
Clock Synchronization, NSDI'18: Proceedings of the 15th USENIX Conference on
Networked Systems Design and Implementation, 2018, pp. 81-94.
6. Govindan Kannan Pravein., Joshi Raj., Chan Mun Choon. Precise Time-synchronization in
the Data-Plane Using Programmable Switching ASICs, Proceedings of the 2019 ACM Symposium
on SDN Research, ACM, 2019, pp. 8-20. DOI: 10.1145/3314148.3314353.
7. Rumyantsev K.E. Sistemy kvantovogo raspredeleniya klyucha: monografiya [Systems of quantum
key distribution: monograph]. Taganrog: Izd-vo TTI YuFU, 2011, 264 p.
8. Rumyantsev K.E. Sinkhronizatsiya v sisteme kvantovogo raspredeleniya klyucha s
avtomaticheskoy kompensatsiey polyarizatsionnykh iskazheniy [Synchronization in a quantum
key distribution system with automatic compensation of polarization distortions],
Telekommunikatsii [Telecommunications], 2017, No. 2, pp. 32-40.
9. Rumyantsev K.E., Plenkin A.P. Sinkhronizatsiya sistemy kvantovogo raspredeleniya klyucha pri
ispol'zovanii fotonnykh impul'sov dlya povysheniya zashchishchennosti [Synchronization of the
system of quantum key distribution when using photon pulses to increase security], Izvestiya
YuFU. Tekhnicheskie nauki [Izvestiya SFedU. Engineering Sciences], 2014, No. 8, pp. 81-96.
10. Plenkin A., Rumyantsev K., Rudinsky E. Comparative analysis of single-photon synchronization
algorithms in the quantum key distribution system, Proceedings of IEEE East-West Design
& Test Symposium (EWDTS), 2017, pp. 1-5. DOI: 10.1109/EWDTS.2017.8110047.
11. Rumyantsev K.E., Rudinsky E.A. Time synchronization method in quantum key distribution
system with automatic compensation of polarization distortions, Proceedings of the 2nd International
Conference on Multimedia and Image Processing (ICMIP), 2017, pp. 346-349. DOI:
10.1109/ICMIP.2017.68.
12. Mironov Y.K., Mironova P.D., Rumyantsev K.E. Study of the characteristics of the synchronization
algorithm for a quantum key distribution system based on comparing the number of
samples from an adjacent pair of time windows with a threshold level, IOP Conf. Series: Materials
Science and Engineering, 1069, 2021, Paper 012011, pp. 1-8. DOI: 10.1088/1757-
899X/1069/1/012011.
13. Mironov Y., Mironova P., Rumyantsev K. Characteristics of a two-stage synchronization algorithm
in the system of quantum key distribution with dividing a fiber-optic line into sections
with decreasing length, ACM International Conference Proceeding Series, 2020, Paper
No. 3433596, pp. 1-5. DOI: 10.1145/3433174.3433595.
14. Mironov Y.K., Mironova P.D., Rumyantsev K.E. Methodology for calculating the average time
of entry into synchronism of stations of the system of quantum key distribution with sequential
polling of fiber-optic line sections with decreasing length by the graphic-analytical method,
E3S Web of Conferences, 2020, Vol. 224, pp. 1-9. DOI: 10.1051/e3sconf/202022401032.
15. Mironov Y.K., Rumyantsev K.E. Single-Photon Algorithm for Synchronizing the System of
Quantum Key Distribution with Polling Sections of a Fiber-Optic Line, Futuristic Trends in
Networks and Computing Technologies, 2020, pp. 87-97. DOI: https://doi.org/10.1007/978-
981-15-4451-4_8.
16. Rumyantsev K.Y., Bamatgireeva K.B., Mironov Y.K. Single Photon Algorithm of Search of a
Pulse Radiation Source, Communications in Computer and Information Science, 2019, 958,
pp. 95-108. DOI: 10.1007/978-981-13-3804-5_8.
17. Kurochkin V.L. i dr. Eksperimental'nye issledovaniya v oblasti kvantovoy kriptografii [Experimental
research in the field of quantum cryptography], Fotonika [Photonics], 2012, Vol. 5, pp. 54-66.
18. Rumyantsev K.E., Plenkin A.P. Bezopasnost' rezhima sinkhronizatsii sistemy kvantovogo
raspredeleniya klyuchey // Izvestiya YuFU. Tekhnicheskie nauki [Izvestiya SFedU. Engineering
Sciences], 2015, No. 5 (166), pp. 135-153.
19. Mironov Ya.K. Modelirovanie etapa testirovaniya dvukhetapnogo vremennogo algoritma
sinkhronizatsii pri nakhozhdenii odnofotonnogo istochnika izlucheniya v signal'nom uchastke
VOLS [Simulation of the testing stage of a two-stage time synchronization algorithm when a
single-photon radiation source is in the signal section of the FOCL], Fundamental'nye i
prikladnye aspekty komp'yuternykh tekhnologiy i informatsionnoy bezopasnosti: materialy VIII
Vserossiyskoy nauchno-tekhnicheskoy konferentsii [Fundamental and Applied Aspects of
Computer Technologies and Information Security: Proceedings of the VIII All-Russian Scientific
and Technical Conference], 2022, pp. 19-21.
20. Mironov Y.K., Rumyantsev K.E. Providing the Required Probability of Synchronization Error When
Splitting a Fiber-Optic Line into Sections with Decreasing Length in a Quantum Key Distribution
System, Proceedings - 2021 3rd International Conference on System Reliability and Safety Engineering,
SRSE 2021, 2021, pp. 145-149. DOI: 10.1109/SRSE54209.2021.00032.
21. Mironov Ya.K. Sinkhronizatsiya stantsiy sistemy kvantovogo raspredeleniya klyucha s
posledovatel'nym oprosom uchastkov volokonno-opticheskoy linii s ubyvayushchey dlinoy
[Synchronization of stations of the quantum key distribution system with sequential polling of
sections of a fiber-optic line with decreasing length], Fundamental'nye i prikladnye aspekty
komp'yuternykh tekhnologiy i informatsionnoy bezopasnosti: Mater. VII Vserossiyskoy
nauchno-tekhnicheskoy konferentsii [Fundamental and applied aspects of computer technology
and information security: materials of the VII All-Russian Scientific and Technical Conference],
2021, pp. 109-112.
22. Mironov Ya.K., Mironova P.D., Rumyantsev K.E. Veroyatnostnye kharakteristiki porogovogo
algoritma obnaruzheniya sinkhroimpul'sov v sisteme kvantovogo raspredeleniya klyucha na
osnove informatsii so smezhnoy pary vremennykh segmentov [Probabilistic Characteristics of
a Threshold Sync Detection Algorithm in a Quantum Key Distribution System Based on Information
from an Adjacent Pair of Time Segments], Izvestiya YuFU. Tekhnicheskie nauki
[Izvestiya SFedU. Engineering Sciences], 2020, No. 4 (207), pp. 221-229.
23. Mironov Ya.K., Mironova P.D., Rumyantsev K.E. Issledovanie kharakteristik algoritma
sinkhronizatsii sistemy kvantovogo raspredeleniya klyucha na osnove sravneniya chisla
otschetov so smezhnoy pary vremennykh okon s porogovym urovnem [Investigation of the
characteristics of the synchronization algorithm of the quantum key distribution system based
on the comparison of the number of samples from an adjacent pair of time windows with a
threshold level], Sb. dokladov II Vse-rossiyskoy nauchnoy konferentsii (s priglasheniem
zarubezhnykh uchenykh) [Collection of reports of the II All-Russian scientific conference
(with the invitation of foreign scientists)], 2020, pp. 219-226.
24. Mironova P.D. Sinkhronizatsiya stantsiy sistemy kvantovogo raspredeleniya klyucha na
osnove porogovogo testa dlya otschetov so smezhnoy pary vremennykh segmentov [Synchronization
of stations of the quantum key distribution system based on a threshold test for readings
from an adjacent pair of time segments], Fundamental'nye i prikladnye aspekty
komp'yuternykh tekhnologiy i informatsionnoy bezopasnosti: Mater. VII Vserossiyskoy
nauchno-tekhnicheskoy konferentsii [Fundamental and applied aspects of computer technology
and information security: materials of the VII All-Russian Scientific and Technical Conference],
2021, pp. 107-109.
25. Mironova P.D. Algoritm sinkhronizatsii stantsiy sistemy kvantovogo raspredeleniya klyucha
na osnove porogovogo testa dlya otschetov so smezhnoy pary vremennykh segmentov s
uchetom dispersionnykh i polyarizatsionnykh svoystv VOLS [Synchronization algorithm for
stations of a quantum key distribution system based on a threshold test for readings from an
adjacent pair of time segments, taking into account the dispersion and polarization properties
of FOCL], Fundamental'nye i prikladnye aspekty komp'yuternykh tekhnologiy i
informatsionnoy bezopasnosti: Mater. VIII Vserossiyskoy nauchno-tekhnicheskoy konferentsii
[Fundamental and applied aspects of computer technology and information security: materials
of the VIII All-Russian Scientific and Technical Conference], 2022, pp. 22-25.
26. Rumyantsev K.E., Linenko P.D., Shakir H.H.-Sh. Evaluation of the Influence of the Dispersion
Properties of a Fiber-Optic Line on the Efficiency of an Algorithm for Single-Photon Synchronization
of Quantum Key Distribution System, Conference Proceedings - 2019 Radiation
and Scattering of Electromagnetic Waves, RSEMW 2019, 2019, pp. 392-395. DOI:
10.1109/RSEMW.2019.8792769.
