Skip to main content

2022 | OriginalPaper | Buchkapitel

Efficient Application of the Residue Number System in Elliptic Cryptography

verfasst von : M. Babenko, A. Redvanov, A. Djurabaev

Erschienen in: Advances in Automation III

Verlag: Springer International Publishing

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

The article is devoted to the study of the efficiency of arithmetic operations with points of an elliptic curve using the residue number system. Based on the obtained data, it was found that the use of the residue number system with moduli of a special type from the operations with an elliptic curve from NIST FIPS 186 allows gaining 7.72% for the operation of addition and 7.50% for the operation of doubling points of an elliptic curve on average.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literatur
1.
Zurück zum Zitat Washington, L.C.: Elliptic Curves: Number Theory and Cryptography. Discrete Mathematics and Its Applications. Chapman & Hall/CRC, New York (2003)CrossRef Washington, L.C.: Elliptic Curves: Number Theory and Cryptography. Discrete Mathematics and Its Applications. Chapman & Hall/CRC, New York (2003)CrossRef
3.
Zurück zum Zitat Avanzi, R., et al.: Handbook of Elliptic and Hyperelliptic Curve Cryptography. CRC Press, New York (2005) Avanzi, R., et al.: Handbook of Elliptic and Hyperelliptic Curve Cryptography. CRC Press, New York (2005)
4.
Zurück zum Zitat Verneuil, V.: Elliptic curve cryptography and security of embedded devices. Cryptography and Security, Université de Bordeaux (2012) Verneuil, V.: Elliptic curve cryptography and security of embedded devices. Cryptography and Security, Université de Bordeaux (2012)
7.
Zurück zum Zitat Garner, H.L.: The residue number system. Papers presented at the March 3–5 Western Joint Computer Conference, pp. 146–153 (1959) Garner, H.L.: The residue number system. Papers presented at the March 3–5 Western Joint Computer Conference, pp. 146–153 (1959)
8.
Zurück zum Zitat Schinianakis, D.M., Kakarountas, A.P., Stouraitis, T.: A new approach to elliptic curve cryptography: an RNS architecture. In: IEEE Mediterranean Electrotechnical Conference, pp. 1241–1245 (2006) Schinianakis, D.M., Kakarountas, A.P., Stouraitis, T.: A new approach to elliptic curve cryptography: an RNS architecture. In: IEEE Mediterranean Electrotechnical Conference, pp. 1241–1245 (2006)
9.
Zurück zum Zitat Chervyakov, N., Babenko, M., Tchernykh, A., Kucherov, N., Miranda-López, V., Cortés-Mendoza, J.M.: AR-RRNS: configurable reliable distributed data storage systems for Internet of Things to ensure security. Future Gener. Comput. Syst. 92, 1080–1092 (2019)CrossRef Chervyakov, N., Babenko, M., Tchernykh, A., Kucherov, N., Miranda-López, V., Cortés-Mendoza, J.M.: AR-RRNS: configurable reliable distributed data storage systems for Internet of Things to ensure security. Future Gener. Comput. Syst. 92, 1080–1092 (2019)CrossRef
10.
Zurück zum Zitat Chervyakov, N.I., et al.: An approximate method for comparing modular numbers and its application to the division of numbers in residue number systems. Cybern. Syst. Anal. 50(6), 977–984 (2014)MathSciNetCrossRef Chervyakov, N.I., et al.: An approximate method for comparing modular numbers and its application to the division of numbers in residue number systems. Cybern. Syst. Anal. 50(6), 977–984 (2014)MathSciNetCrossRef
11.
Zurück zum Zitat Chervyakov, N.I., Molahosseini, A.S., Lyakhov, P.A., Babenko, M.G., Deryabin, M.A.: Residue-to-binary conversion for general moduli sets based on approximate Chinese remainder theorem. Int. J. Comput. Math. 94(9), 1833–1849 (2017)CrossRef Chervyakov, N.I., Molahosseini, A.S., Lyakhov, P.A., Babenko, M.G., Deryabin, M.A.: Residue-to-binary conversion for general moduli sets based on approximate Chinese remainder theorem. Int. J. Comput. Math. 94(9), 1833–1849 (2017)CrossRef
12.
Zurück zum Zitat Esmaeildoust, M., Schinianakis, D., Javashi, H., Stouraitis, T., Navi, K.: Efficient RNS implementation of elliptic curve point multiplication over GF(p). IEEE Trans. Very Large Scale Integr. (VLSI) Syst. 21(8), 1545–1549 (2013) Esmaeildoust, M., Schinianakis, D., Javashi, H., Stouraitis, T., Navi, K.: Efficient RNS implementation of elliptic curve point multiplication over GF(p). IEEE Trans. Very Large Scale Integr. (VLSI) Syst. 21(8), 1545–1549 (2013)
13.
Zurück zum Zitat Asif, S., Kong, Y.: Highly parallel modular multiplier for elliptic curve cryptography in residue number system. Circuits Syst. Signal Process. 36(3), 1027–1051 (2017)MathSciNetCrossRef Asif, S., Kong, Y.: Highly parallel modular multiplier for elliptic curve cryptography in residue number system. Circuits Syst. Signal Process. 36(3), 1027–1051 (2017)MathSciNetCrossRef
14.
Zurück zum Zitat Babenko, M., et al.: RNS number comparator based on a modified diagonal function. Electronics 9, 1784 (2020)CrossRef Babenko, M., et al.: RNS number comparator based on a modified diagonal function. Electronics 9, 1784 (2020)CrossRef
15.
Zurück zum Zitat Vershkov, N., Babenko, M., Kuchukov, V., Kuchukova, N.: Search for the global extremum using the correlation indicator for neural networks supervised learning. Program. Comput. Softw. 46, 609–618 (2020)MathSciNetCrossRef Vershkov, N., Babenko, M., Kuchukov, V., Kuchukova, N.: Search for the global extremum using the correlation indicator for neural networks supervised learning. Program. Comput. Softw. 46, 609–618 (2020)MathSciNetCrossRef
16.
Zurück zum Zitat Tchernykh, A., et al.: Scalable data storage design for nonstationary IoT environment with adaptive security and reliability. IEEE Internet Things J. 7, 10171–10188 (2020)CrossRef Tchernykh, A., et al.: Scalable data storage design for nonstationary IoT environment with adaptive security and reliability. IEEE Internet Things J. 7, 10171–10188 (2020)CrossRef
18.
Zurück zum Zitat Chervyakov, N., Babenko, M., Tchernykh, A., Kucherov, N., Miranda-López, V., Cortés-Mendoza, J.M.: AR-RRNS: configurable reliable distributed data storage systems for Internet of Things to ensure security. Future Gener. Comput. Syst. 92, 1080–1092 (2019)CrossRef Chervyakov, N., Babenko, M., Tchernykh, A., Kucherov, N., Miranda-López, V., Cortés-Mendoza, J.M.: AR-RRNS: configurable reliable distributed data storage systems for Internet of Things to ensure security. Future Gener. Comput. Syst. 92, 1080–1092 (2019)CrossRef
19.
Zurück zum Zitat Tchernykh, A., Schwiegelsohn, U., Talbi, E., Babenko, M.: Towards understanding uncertainty in cloud computing with risks of confidentiality, integrity, and availability. J. Comput. Sci. 36, 100581 (2019)CrossRef Tchernykh, A., Schwiegelsohn, U., Talbi, E., Babenko, M.: Towards understanding uncertainty in cloud computing with risks of confidentiality, integrity, and availability. J. Comput. Sci. 36, 100581 (2019)CrossRef
20.
Zurück zum Zitat Tchernykh, A., et al.: AC-RRNS: anti-collusion secured data sharing scheme for cloud storage. Int. J. Approx. Reason. 102, 60–73 (2018)MathSciNetCrossRef Tchernykh, A., et al.: AC-RRNS: anti-collusion secured data sharing scheme for cloud storage. Int. J. Approx. Reason. 102, 60–73 (2018)MathSciNetCrossRef
Metadaten
Titel
Efficient Application of the Residue Number System in Elliptic Cryptography
verfasst von
M. Babenko
A. Redvanov
A. Djurabaev
Copyright-Jahr
2022
DOI
https://doi.org/10.1007/978-3-030-94202-1_44