Skip to main content
SpringerLink
Log in

Verifiable Homomorphic Secret Sharing

  • Conference paper
  • First Online:
Provable Security (ProvSec 2018)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11192))

Included in the following conference series:

Abstract

In this paper, we explore the multi-server (i.e., multiple servers are employed to perform computations) and multi-client (i.e., multiple clients outsource joint computations on their joint inputs) scenario that avoids single points of failure and provides higher security and privacy guarantees. More precisely, we introduce the notion of verifiable homomorphic secret sharing (VHSS) for multi-input, that allows n clients to outsource joint computations on their joint inputs to m servers without requiring any communication between the clients or the servers; while providing the verifiable capability to any user to confirm that the final output (rather than each share) is correct. Our contributions are two-fold: (i) we provide a detailed example for casting Shamir’s secret sharing scheme over a finite field \(\mathbb {F}\) as an n-client, m-server, t-secure perfectly secure, additive HSS scheme for the function f that sums n field elements, and (ii) we propose an instantiation of an n-client, m-server, t-secure computationally secure, multiplicative VHSS scheme for the function f that multiplies n elements under the hardness assumption of the fixed inversion problem in bilinear maps.

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. Ananth, P., Chandran, N., Goyal, V., Kanukurthi, B., Ostrovsky, R.: Achieving privacy in verifiable computation with multiple servers – without FHE and without pre-processing. In: Krawczyk, H. (ed.) PKC 2014. LNCS, vol. 8383, pp. 149–166. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-54631-0_9

    Chapter  Google Scholar 

  2. Backes, M., Fiore, D., Reischuk, R.M.: Verifiable delegation of computation on outsourced data. In: Proceedings of the 2013 ACM SIGSAC Conference on Computer and Communications Security, pp. 863–874. ACM (2013)

    Google Scholar 

  3. Barkol, O., Ishai, Y., Weinreb, E.: On d-multiplicative secret sharing. J. cryptol. 23(4), 580–593 (2010)

    Article  MathSciNet  Google Scholar 

  4. Benaloh, J.C.: Secret sharing homomorphisms: keeping shares of a secret secret (extended abstract). In: Odlyzko, A.M. (ed.) CRYPTO 1986. LNCS, vol. 263, pp. 251–260. Springer, Heidelberg (1987). https://doi.org/10.1007/3-540-47721-7_19

    Chapter  Google Scholar 

  5. Boyle, E., Gilboa, N., Ishai, Y.: Function secret sharing. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015. LNCS, vol. 9057, pp. 337–367. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46803-6_12

    Chapter  Google Scholar 

  6. Boyle, E., Gilboa, N., Ishai, Y.: Breaking the circuit size barrier for secure computation under DDH. In: Robshaw, M., Katz, J. (eds.) CRYPTO 2016. LNCS, vol. 9814, pp. 509–539. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53018-4_19

    Chapter  Google Scholar 

  7. Boyle, E., Gilboa, N., Ishai, Y.: Function secret sharing: improvements and extensions. In: Proceedings of the 2016 ACM SIGSAC Conference on Computer and Communications Security, pp. 1292–1303. ACM (2016)

    Google Scholar 

  8. Boyle, E., Gilboa, N., Ishai, Y.: Group-based secure computation: optimizing rounds, communication, and computation. In: Coron, J.-S., Nielsen, J.B. (eds.) EUROCRYPT 2017. LNCS, vol. 10211, pp. 163–193. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-56614-6_6

    Chapter  Google Scholar 

  9. Boyle, E., Gilboa, N., Ishai, Y., Lin, H., Tessaro, S.: Foundations of homomorphic secret sharing. In: LIPIcs-Leibniz International Proceedings in Informatics, vol. 94. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik (2018)

    Google Scholar 

  10. Chung, K.-M., Kalai, Y., Vadhan, S.: Improved delegation of computation using fully homomorphic encryption. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 483–501. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-14623-7_26

    Chapter  Google Scholar 

  11. Fiore, D., Gennaro, R., Pastro, V.: Efficiently verifiable computation on encrypted data. In: Proceedings of the 2014 ACM SIGSAC Conference on Computer and Communications Security, pp. 844–855. ACM (2014)

    Google Scholar 

  12. Fiore, D., Mitrokotsa, A., Nizzardo, L., Pagnin, E.: Multi-key homomorphic authenticators. In: Cheon, J.H., Takagi, T. (eds.) ASIACRYPT 2016. LNCS, vol. 10032, pp. 499–530. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53890-6_17

    Chapter  Google Scholar 

  13. 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 

  14. Gentry, C.: A Fully Homomorphic Encryption Scheme. Stanford University, Stanford (2009)

    MATH  Google Scholar 

  15. Gordon, S.D., Katz, J., Liu, F.-H., Shi, E., Zhou, H.-S.: Multi-client verifiable computation with stronger security guarantees. In: Dodis, Y., Nielsen, J.B. (eds.) TCC 2015. LNCS, vol. 9015, pp. 144–168. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46497-7_6

    Chapter  Google Scholar 

  16. Cheon, J.H., Lee, D.H.: A note on self-bilinear maps. Bull. Korean Math. Soc. 46, 303–309 (2009)

    Article  MathSciNet  Google Scholar 

  17. Pagnin, E., Mitrokotsa, A., Tanaka, K.: Anonymous single-round server-aided verification of signatures. In: The 5th International Conference on Cryptology and Information Security (Latincrypt) (2017)

    Google Scholar 

  18. Parno, B., Raykova, M., Vaikuntanathan, V.: How to delegate and verify in public: verifiable computation from attribute-based encryption. In: Cramer, R. (ed.) TCC 2012. LNCS, vol. 7194, pp. 422–439. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-28914-9_24

    Chapter  Google Scholar 

  19. Rivest, R.L., Adleman, L., Dertouzos, M.L.: On data banks and privacy homomorphisms. Found. Secure Comput. 4(11), 169–180 (1978)

    MathSciNet  Google Scholar 

  20. Shamir, A.: How to share a secret. Commun. ACM 22(11), 612–613 (1979)

    Article  MathSciNet  Google Scholar 

  21. Tang, C., Chen, Y.: Efficient non-interactive verifiable outsourced computation for arbitrary functions. IACR Cryptology ePrint Archive, 2014:439 (2014)

    Google Scholar 

  22. Wang, F., Yun, C., Goldwasser, S., Vaikuntanathan, V., Zaharia, M.: Splinter: practical private queries on public data. In: NSDI, pp. 299–313 (2017)

    Google Scholar 

  23. Yoshida, M., Obana, S.: Verifiably multiplicative secret sharing. In: Shikata, J. (ed.) ICITS 2017. LNCS, vol. 10681, pp. 73–82. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-72089-0_5

    Chapter  Google Scholar 

Download references

Acknowledgments

This work was partially supported by the Wallenberg AI, Autonomous Systems and Software Program (WASP) funded by the Knut and Alice Wallenberg Foundation and the VR grant PRECIS.

Author information

Authors and Affiliations

  1. Chalmers University of Technology, Gothenburg, Sweden

    Georgia Tsaloli, Bei Liang & Aikaterini Mitrokotsa

Authors
  1. Georgia Tsaloli
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bei Liang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Aikaterini Mitrokotsa
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Georgia Tsaloli .

Editor information

Editors and Affiliations

  1. University of Wollongong, Wollongong, NSW, Australia

    Joonsang Baek

  2. University of Wollongong, Wollongong, NSW, Australia

    Willy Susilo

  3. University of Wollongong, Wollongong, NSW, Australia

    Jongkil Kim

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Tsaloli, G., Liang, B., Mitrokotsa, A. (2018). Verifiable Homomorphic Secret Sharing. In: Baek, J., Susilo, W., Kim, J. (eds) Provable Security. ProvSec 2018. Lecture Notes in Computer Science(), vol 11192. Springer, Cham. https://doi.org/10.1007/978-3-030-01446-9_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-01446-9_3

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-01445-2

  • Online ISBN: 978-3-030-01446-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation