Skip to main content
SpringerLink
Log in

Secure and Efficient Delegation of Pairings with Online Inputs

  • Conference paper
  • First Online:
Smart Card Research and Advanced Applications (CARDIS 2020)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 12609))

Abstract

Delegation of pairings from a computationally weaker client to a computationally stronger server has been advocated to expand the applicability of pairing-based cryptographic protocols to computation paradigms with resource-constrained devices. Important requirements for such delegation protocols include privacy of the client’s inputs and security of the client’s output, in the sense of detecting, with high probability, any malicious server’s attempt to convince the client of an incorrect pairing result. In this paper we show that pairings with inputs only available in the online phase can be efficiently, privately and securely delegated to a single, possibly malicious, server. We present new protocols in 2 different scenarios: (1) the two pairing inputs are publicly known; (2) privacy of both pairing inputs needs to be maintained (left open in previous papers; e.g., [27]). In both cases, we improve the online-phase client’s runtime with respect to previous work. In the latter case, we show the first protocol where the client’s online-phase runtime is faster than non-delegated computation for all of the most practical known curves. In previous work, the client’s runtime was worse, especially for one of the most practical elliptic curves underlying the pairing function (i.e., BN-12).

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 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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. Al-Riyami, S.S., Paterson, K.G.: Certificateless public key cryptography. In: Laih, C.S. (eds.) Advances in Cryptology - ASIACRYPT (2003)

    Google Scholar 

  2. Barbulescu, R., Duquesne, S.: Updating key size estimations for pairings. J. Cryptol. 32(4), 1298–1336 (2018). https://doi.org/10.1007/s00145-018-9280-5

    Article  MathSciNet  MATH  Google Scholar 

  3. Barreto, P.S.L.M., Costello, C., Misoczki, R., Naehrig, M., Pereira, G.C.C.F., Zanon, G.: Subgroup security in pairing-based cryptography. In: Lauter, K., Rodríguez-Henríquez, F. (eds.) Progress in Cryptology - LATINCRYPT (2015)

    Google Scholar 

  4. Boneh, D., Franklin, M.: Identity-based encryption from the Weil pairing. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 213–229. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-44647-8_13

    Chapter  Google Scholar 

  5. Boneh, D., Di Crescenzo, G., Ostrovsky, R., Persiano, G.: Public key encryption with keyword search. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 506–522. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-24676-3_30

    Chapter  Google Scholar 

  6. Boneh, D., Lynn, B., Shacham, H.: Short signatures from the Weil pairing. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 514–532. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-45682-1_30

    Chapter  Google Scholar 

  7. Bos, J.W., Costello, C., Naehrig, M.: Exponentiating in pairing groups. In: Lange, T., Lauter, K., Lisoněk, P. (eds.) SAC 2013. LNCS, vol. 8282, pp. 438–455. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-43414-7_22

    Chapter  MATH  Google Scholar 

  8. Canard, S., Devigne, J., Sanders, O.: Delegating a pairing can be both secure and efficient. In: Boureanu, I., Owesarski, P., Vaudenay, S. (eds.) ACNS 2014. LNCS, vol. 8479, pp. 549–565. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-07536-5_32

    Chapter  MATH  Google Scholar 

  9. Cavallo, B., Di Crescenzo, G., Kahrobaei, D., Shpilrain, V.: Efficient and secure delegation of group exponentiation to a single server. In: Mangard, S., Schaumont, P. (eds.) RFIDSec 2015. LNCS, vol. 9440, pp. 156–173. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-24837-0_10

    Chapter  Google Scholar 

  10. Chevallier-Mames, B., Coron, J.-S., McCullagh, N., Naccache, D., Scott, M.: Secure delegation of elliptic-curve pairing. In: Gollmann, D., Lanet, J.-L., Iguchi-Cartigny, J. (eds.) CARDIS 2010. LNCS, vol. 6035, pp. 24–35. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-12510-2_3

    Chapter  Google Scholar 

  11. Chevalier, C., Laguillaumie, F., Vergnaud, D.: Privately outsourcing exponentiation to a single server: cryptanalysis and optimal constructions. In: Askoxylakis, I., Ioannidis, S., Katsikas, S., Meadows, C. (eds.) ESORICS 2016. LNCS, vol. 9878, pp. 261–278. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-45744-4_13

    Chapter  Google Scholar 

  12. Di Crescenzo, G., Khodjaeva, M., Kahrobaei, D., Shpilrain, V.: Practical and secure outsourcing of discrete log group exponentiation to a single malicious server. In: Proceedings of 9th ACM CCSW, pp. 17–28 (2017)

    Google Scholar 

  13. Di Crescenzo, G., Khodjaeva, M., Kahrobaei, D., Shpilrain, V.: Secure and Efficient Delegation of Elliptic-Curve Pairing. In: Conti, M., Zhou, J., Casalicchio, E., Spognardi, A. (eds.) ACNS 2020. LNCS, vol. 12146, pp. 45–66. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-57808-4_3

    Chapter  MATH  Google Scholar 

  14. Gennaro, R., Gentry, C., Parno, B.: Non-interactive verifiable computing: outsourcing computation to untrusted workers. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 465–482. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-14623-7_25

    Chapter  Google Scholar 

  15. Girault, M., Lefranc, D.: Server-aided verification: theory and practice. In: Roy, B. (ed.) ASIACRYPT 2005. LNCS, vol. 3788, pp. 605–623. Springer, Heidelberg (2005). https://doi.org/10.1007/11593447_33

    Chapter  Google Scholar 

  16. Guillevic, A., Vergnaud, D.: Algorithms for outsourcing pairing computation. In: Joye, M., Moradi, A. (eds.) CARDIS 2014. LNCS, vol. 8968, pp. 193–211. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-16763-3_12

    Chapter  Google Scholar 

  17. Hess, F.: Efficient identity based signature schemes based on pairings. In: Nyberg, K., Heys, H. (eds.) SAC 2002. LNCS, vol. 2595, pp. 310–324. Springer, Heidelberg (2003). https://doi.org/10.1007/3-540-36492-7_20

    Chapter  Google Scholar 

  18. Hohenberger, S., Lysyanskaya, A.: How to securely outsource cryptographic computations. In: Kilian, J. (ed.) TCC 2005. LNCS, vol. 3378, pp. 264–282. Springer, Heidelberg (2005). https://doi.org/10.1007/978-3-540-30576-7_15

    Chapter  Google Scholar 

  19. Joux, A.: A one round protocol for tripartite Diffie–Hellman. In: Bosma, W. (ed.) ANTS 2000. LNCS, vol. 1838, pp. 385–393. Springer, Heidelberg (2000). https://doi.org/10.1007/10722028_23

    Chapter  Google Scholar 

  20. Kachisa, E.J., Schaefer, E.F., Scott, M.: Constructing Brezing-Weng pairing-friendly elliptic curves using elements in the cyclotomic field. In: Galbraith, S.D., Paterson, K.G. (eds.) Pairing 2008. LNCS, vol. 5209, pp. 126–135. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-85538-5_9

    Chapter  MATH  Google Scholar 

  21. Kang, B.G., Lee, M.S., Park, J.H.: Efficient delegation of pairing computation. In: IACR Cryptology ePrint Archive, vol. 259 (2005)

    Google Scholar 

  22. Kim, T., Barbulescu, R.: Extended tower number field sieve: a new complexity for the medium prime case. In: Robshaw, M., Katz, J. (eds.) CRYPTO 2016. LNCS, vol. 9814, pp. 543–571. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53018-4_20

    Chapter  Google Scholar 

  23. Liu, J.K., Au, M.H., Susilo, W.: Self-generated-certificate public key cryptography and certificateless signature/encryption scheme in the standard model. In: Proceedings ACM Symposium on Information, Computer and Communications Security. ACM Press (2007)

    Google Scholar 

  24. Markantonakis, C.: Is the performance of smart card cryptographic functions the real bottleneck? In: Proceedings of IFIP/SEC, pp. 77–92 (2001)

    Google Scholar 

  25. Scott, M.: Unbalancing pairing-based key exchange protocols. In: IACR Cryptology ePrint Archive, vol. 688 (2013)

    Google Scholar 

  26. Vercauteren, F.: Optimal pairings. IEEE Trans. Inf. Theory 56(1), 455–461 (2010)

    Article  MathSciNet  Google Scholar 

  27. Vergnaud, D.: Secure outsourcing in discrete-logarithm-based and pairing-based cryptography. In: Proceedings of WISTP, pp. 7–11 (2018)

    Google Scholar 

  28. Yao, A.: Protocols for secure computations. In: Proceedings of 23rd IEEE FOCS, pp. 160–168 (1982)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Perspecta Labs Inc., Basking Ridge, NJ, USA

    Giovanni Di Crescenzo

  2. CUNY John Jay College of Criminal Justice, New York, NY, USA

    Matluba Khodjaeva

  3. University of York, Heslington, York, UK

    Delaram Kahrobaei

  4. City University of New York, New York, NY, USA

    Vladimir Shpilrain

Authors
  1. Giovanni Di Crescenzo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Matluba Khodjaeva
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Delaram Kahrobaei
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Vladimir Shpilrain
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Giovanni Di Crescenzo .

Editor information

Editors and Affiliations

  1. eShard, Pessac, France

    Pierre-Yvan Liardet

  2. Leiden University and KU Leuven, Leiden, The Netherlands

    Nele Mentens

Rights and permissions

Reprints and permissions

Copyright information

© 2021 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Di Crescenzo, G., Khodjaeva, M., Kahrobaei, D., Shpilrain, V. (2021). Secure and Efficient Delegation of Pairings with Online Inputs. In: Liardet, PY., Mentens, N. (eds) Smart Card Research and Advanced Applications. CARDIS 2020. Lecture Notes in Computer Science(), vol 12609. Springer, Cham. https://doi.org/10.1007/978-3-030-68487-7_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-68487-7_6

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-68486-0

  • Online ISBN: 978-3-030-68487-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation