Skip to main content
SpringerLink
Log in

Isogeny-Based Group Key Establishment Scheme

  • Conference paper
  • First Online:
Intelligent Sustainable Systems

Part of the book series: Lecture Notes in Networks and Systems ((LNNS,volume 579))

  • 551 Accesses

Abstract

In providing secure group-oriented communication and data access control, one important task is to establish a shared key between group members. To build such protocols, various mathematical apparatus can be used. Most modern group key establishment schemes are a generalization of the Diffie–Hellman key agreement protocol. This paper presents a group key agreement protocol based on assumptions relating to isogeny of supersingular elliptic curves. The properties of isogeny graphs, as well as the abundance of hard assumptions, make it possible to build flexible protocols. The proposed scheme is decentralized and implies the presence of a trusted party (group manager). Establishing a shared key is carried out in 2 rounds, one of which is aimed at confirming the identity of the group users. Analysis of the proposed protocol security is given. In addition, performance characteristics show that there are restrictions on the size of groups due to the need to calculate the isogenies of elliptic curves.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 259.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Xu, S.: On the security of group communication schemes. J. Comput. Secur. 15, 129–169 (2007). https://doi.org/10.3233/JCS-2007-15106

    Article  Google Scholar 

  2. Fatin, A.D., Pavlenko, E.Y., Poltavtseva, M.A.: A survey of mathematical methods for security analysis of cyberphysical systems. Autom. Control Comput. Sci. 54, 983–987 (2021). https://doi.org/10.3103/S014641162008012X

  3. Kalinin, M., Krundyshev, V., Rezedinova, E., Zegzhda, P.: Role-based access control for vehicular adhoc networks. In: 2018 IEEE Int. Black Sea Conf. Commun. Networking, BlackSeaCom (2018). https://doi.org/10.1109/BlackSeaCom.2018.8433628

  4. Aleksandrova, E.B., Poltavtseva, M.A., Shmatov, V.S.: Ensuring the big data integrity through verifiable zero-knowledge operations. Commun. Comput. Inf. Sci. 1544 CCIS, 211–221 (2022). https://doi.org/10.1007/978-981-16-9576-6_15

  5. Karuturi, N.N., Gopalakrishnan, R., Srinivasan, R., Chandrasekaran, P.R.: Foundations of group key management-framework, security model and a generic construction. IACR Cryptology ePrint Archive (2008)

    Google Scholar 

  6. Azarderakhsh, R., et al.: Practical supersingular isogeny group key agreement. Cryp-tology ePrint Archive (2019)

    Google Scholar 

  7. De Feo, L., Jao, D., Plût, J.: Towards quantum-resistant cryptosystems from supersingular elliptic curve isogenies. J. Math. Cryptol. 8, 209–247 (2014). https://doi.org/10.1007/978-3-642-25405-5_2

    Article  MATH  Google Scholar 

  8. Hougaard, H.B., Miyaji, A.: SIT: supersingular isogeny tree-based group key ex-change. In: Proc. 15th Asia Jt. Conf. Inf. Secur. AsiaJCIS pp 46–53 (2020). 0.1109/AsiaJCIS50894.2020.00019

    Google Scholar 

  9. Furukawa, S., Kunihiro, N., Takashima, K.: Multi-party key exchange protocols from supersingular isogenies. In: Proc. 2018 Int. Symp. Inf. Theory Its Appl. ISITA 2018 pp 208–212 (2019). https://doi.org/10.23919/ISITA.2018.8664316

  10. Okada, H., Kiyomoto, S., Cid, C.: A comparison of GKE protocols based on SIDH. In: Proc. 18th Int. Conf. Secur. Cryptogr. SECRYPT 2021 pp. 507–514 (2021). https://doi.org/10.5220/0010547305070514

  11. Rostovtsev, A., Stolbunov A.: Public-key cryptosystem based on isogenies. Cryptology ePrint Archive (2006)

    Google Scholar 

  12. Silverman, J.H.: The arithmetic of elliptic curves 106 (2009)

    Google Scholar 

  13. Xiao, G., Luo, L., Deng, Y.: Constructing cycles in isogeny graphs of supersingular elliptic curves. J. Math. Cryptol. 15, 454–464 (2021). https://doi.org/10.1515/jmc-2020-0029

    Article  MATH  Google Scholar 

  14. Couveignes, J.-M.: Hard homogeneous spaces (2006)

    Google Scholar 

  15. Srinath, M.S., Chandrasekaran, V.: Isogeny-based quantum-resistant Undeniable blind signature scheme. Int. J. Netw. Secur. 20, 9–18 (2018). https://doi.org/10.6633/IJNS.201801.20(1).02

    Article  Google Scholar 

  16. Urbanik, D., Jao, D.: New techniques for SIDH-based NIKE. J. Math. Cryptol. 14, 120–128 (2020). https://doi.org/10.1515/jmc-2015-0056

    Article  MATH  Google Scholar 

  17. Castryck, W., Lange, T., Martindale, C., Panny, L., Renes, J.: CSIDH: an efficient post-quantum commutative group action. Lect. Notes Comput. Sci. (including Subser. Lect. Notes Artif. Intell. Lect. Notes Bioinform.). 11274 LNCS, 395–427 (2018). https://doi.org/10.1007/978-3-030-03332-3_15

  18. Heo, D., Kim, S., Park, Y.H., Hong, S.: On the performance analysis for CSIDH-based cryptosystems. Appl. Sci. 10, 6927 (2020). https://doi.org/10.3390/APP10196927

  19. Jaiswal, P., Kumar, A., Tripathi, S.: Design of secure group key agreement protocol using elliptic curve cryptography. In: 2014 Int. Conf. High Perform. Comput. Appl. ICHPCA 2014 (2015). https://doi.org/10.1109/ICHPCA.2014.7045305

  20. Broker, R.: Constructing supersingular elliptic curves. J. Comb. Number Theory 1, 269–273 (2009)

    MATH  Google Scholar 

  21. Ti, Y.B.: Fault attack on supersingular isogeny cryptosystems. Lect. Notes Comput. Sci. (including Subser. Lect. Notes Artif. Intell. Lect. Notes Bioinform.). 10346 LNCS, 107–122 (2017). https://doi.org/10.1007/978-3-319-59879-6_7

Download references

Acknowledgements

The reported study was funded by Ministry of Digital Development, Communications and Mass Media of the Russian Federation, project number 12/21-k (grant «Information Security»).

Author information

Authors and Affiliations

  1. Peter the Great St.Petersburg Polytechnic University, St.Petersburg, Russia

    Yarmak Anastasia

Authors
  1. Yarmak Anastasia
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yarmak Anastasia .

Editor information

Editors and Affiliations

  1. School of Mathematics, Computer Science and Engineering, Liverpool Hope University, Liverpool, UK

    Atulya K. Nagar

  2. Namibia University of Science and Technology, Windhoek, Namibia

    Dharm Singh Jat

  3. Department of Computer Science and Engineering, Sri Aurobindo Institute of Technology, Indore, Madhya Pradesh, India

    Durgesh Kumar Mishra

  4. Global Knowledge Research Foundation, Ahmedabad, Gujarat, India

    Amit Joshi

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Anastasia, Y. (2023). Isogeny-Based Group Key Establishment Scheme. In: Nagar, A.K., Singh Jat, D., Mishra, D.K., Joshi, A. (eds) Intelligent Sustainable Systems. Lecture Notes in Networks and Systems, vol 579. Springer, Singapore. https://doi.org/10.1007/978-981-19-7663-6_11

Download citation

Publish with us

Policies and ethics

Search

Navigation