Skip to main content
Springer Nature Link
Log in

Verifiable DOPE from Somewhat Homomorphic Encryption, and the Extension to DOT

  • Conference paper
  • First Online:
Science of Cyber Security (SciSec 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13580))

Included in the following conference series:

  • 1210 Accesses

Abstract

Distributed oblivious polynomial evaluation (DOPE) is a special case of two-party computation where a sender party holds a polynomial f(x) of degree t and a receiver party has an input \(x_2\). They communicate with a set of distributed cloud servers to implement a secure computation such that the receiver party obtains \(f(x_2)\), while the privacy of their inputs is preserved.

We present a verifiable and private DOPE protocol using additive homomorphic encryption in the presence of k distributed servers where k does not depend on the degree t. The sender is involved in the offline phase which can be implemented at any time well in advance of the actual online computation phase. Our protocol holds the unconditional security against a malicious sender in the offline phase and a static active adversary corrupting a coalition of at most \(k-1\) dishonest servers in the online computation phase with negligible probability of error. In addition, it preserves strong privacy conditions for a DOPE system. The communication complexity is determined by the term kt which improves the DOPE approaches of [18] and [5]. Also, the proposed protocol can be extended to a protocol of secure \(\left( {\begin{array}{c}1\\ 2\end{array}}\right) \) distributed oblivious transfer with the linear communication complexity O(k) where the same setting of security is achieved.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Similar content being viewed by others

References

  1. Bendlin, R., Damgård, I., Orlandi, C., Zakarias, S.: Semi-homomorphic encryption and multiparty computation. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 169–188. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-20465-4_11

    Chapter  Google Scholar 

  2. Blundo, C., D’Arco, P., De Santis, A., Stinson, D.: On unconditionally secure distributed oblivious transfer. J. Cryptol. 20(3), 323–373 (2007)

    Article  MathSciNet  Google Scholar 

  3. Blundo, C., D’Arco, P., De Santis, A., Stinson, D.R.: New results on unconditionally secure distributed oblivious transfer. In: Nyberg, K., Heys, H. (eds.) SAC 2002. LNCS, vol. 2595, pp. 291–309. Springer, Heidelberg (2003). https://doi.org/10.1007/3-540-36492-7_19

    Chapter  MATH  Google Scholar 

  4. Chang, Y.-C., Lu, C.-J.: Oblivious polynomial evaluation and oblivious neural learning. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 369–384. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-45682-1_22

    Chapter  Google Scholar 

  5. Cianciullo, L., Ghodosi, H.: Unconditionally secure distributed oblivious polynomial evaluation. In: Lee, K. (ed.) ICISC 2018. LNCS, vol. 11396, pp. 132–142. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-12146-4_9

    Chapter  Google Scholar 

  6. Corniaux, C.L., Ghodosi, H.: A verifiable 1-out-of-n distributed oblivious transfer protocol. IACR Cryptol. ePrint Arch. 2013, 63 (2013)

    Google Scholar 

  7. Damgård, I., Jurik, M.: A generalisation, a simplification and some applications of paillier’s probabilistic public-key system. In: Kim, K. (ed.) PKC 2001. LNCS, vol. 1992, pp. 119–136. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-44586-2_9

    Chapter  MATH  Google Scholar 

  8. Damgård, I., Keller, M., Larraia, E., Pastro, V., Scholl, P., Smart, N.P.: Practical covertly secure MPC for dishonest majority – or: breaking the SPDZ limits. In: Crampton, J., Jajodia, S., Mayes, K. (eds.) ESORICS 2013. LNCS, vol. 8134, pp. 1–18. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40203-6_1

    Chapter  Google Scholar 

  9. Damgård, I., Pastro, V., Smart, N., Zakarias, S.: Multiparty computation from somewhat homomorphic encryption. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 643–662. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-32009-5_38

    Chapter  Google Scholar 

  10. Freedman, M.J., Ishai, Y., Pinkas, B., Reingold, O.: Keyword Search and Oblivious Pseudorandom Functions. In: Kilian, J. (ed.) TCC 2005. LNCS, vol. 3378, pp. 303–324. Springer, Heidelberg (2005). https://doi.org/10.1007/978-3-540-30576-7_17

    Chapter  Google Scholar 

  11. Freedman, M.J., Nissim, K., Pinkas, B.: Efficient private matching and set intersection. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 1–19. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-24676-3_1

    Chapter  Google Scholar 

  12. Gajera, H., Giraud, M., Gérault, D., Das, M.L., Lafourcade, P.: Verifiable and private oblivious polynomial evaluation. In: Laurent, M., Giannetsos, T. (eds.) WISTP 2019. LNCS, vol. 12024, pp. 49–65. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-41702-4_4

    Chapter  Google Scholar 

  13. Gilboa, N.: Two party RSA key generation. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 116–129. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-48405-1_8

    Chapter  Google Scholar 

  14. Hanaoka, G., Imai, H., Mueller-Quade, J., Nascimento, A.C.A., Otsuka, A., Winter, A.: Information theoretically secure oblivious polynomial evaluation: model, bounds, and constructions. In: Wang, H., Pieprzyk, J., Varadharajan, V. (eds.) ACISP 2004. LNCS, vol. 3108, pp. 62–73. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-27800-9_6

    Chapter  MATH  Google Scholar 

  15. Hazay, C., Lindell, Y.: Efficient oblivious polynomial evaluation with simulation-based security. IACR Cryptol. ePrint Arch. 2009, 459 (2009)

    Google Scholar 

  16. Kamara, S., Raykova, M.: Parallel homomorphic encryption. In: Adams, A.A., Brenner, M., Smith, M. (eds.) FC 2013. LNCS, vol. 7862, pp. 213–225. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-41320-9_15

    Chapter  Google Scholar 

  17. Kiayias, A., Leonardos, N., Lipmaa, H., Pavlyk, K., Tang, Q.: Optimal rate private information retrieval from homomorphic encryption. Proc. Priv. Enhancing Technol. 2015(2), 222–243 (2015)

    Article  Google Scholar 

  18. Li, H.-D., Yang, X., Feng, D.-G., Li, B.: Distributed oblivious function evaluation and its applications. J. Comput. Sci. Technol. 19(6), 942–947 (2004). https://doi.org/10.1007/BF02973458

    Article  MathSciNet  Google Scholar 

  19. Lindell, Y.: How to simulate it-a tutorial on the simulation proof technique. Tutorials on the Foundations of Cryptography pp. 277–346 (2017)

    Google Scholar 

  20. Lindell, Y., Pinkas, B.: Privacy preserving data mining. Journal of cryptology 15(3) (2002)

    Google Scholar 

  21. Naor, M., Pinkas, B.: Oblivious transfer and polynomial evaluation. In: Proceedings of the thirty-first annual ACM symposium on Theory of computing, pp. 245–254 (1999)

    Google Scholar 

  22. Naor, M., Pinkas, B.: Distributed oblivious transfer. In: Okamoto, T. (ed.) ASIACRYPT 2000. LNCS, vol. 1976, pp. 205–219. Springer, Heidelberg (2000). https://doi.org/10.1007/3-540-44448-3_16

    Chapter  Google Scholar 

  23. Naor, M., Pinkas, B.: Efficient oblivious transfer protocols. In: SODA. 1, 448–457 (2001)

    Google Scholar 

  24. Paillier, P.: Public-key cryptosystems based on composite degree residuosity classes. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 223–238. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-48910-X_16

    Chapter  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  26. Tassa, T., Jarrous, A., Ben-Ya’akov, Y.: Oblivious evaluation of multivariate polynomials. J. Math. Cryptology 7(1), 1–29 (2013)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. James Cook University, Townsville, Australia

    Amirreza Hamidi & Hossein Ghodosi

Authors
  1. Amirreza Hamidi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hossein Ghodosi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Amirreza Hamidi .

Editor information

Editors and Affiliations

  1. University of Aizu, Aizuwakamatsu, Fukushima, Japan

    Chunhua Su

  2. Kyushu University, Fukuoka, Japan

    Kouichi Sakurai

  3. Institute of Information Engineering, Chinese Academy of Sciences, Beijing, China

    Feng Liu

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Hamidi, A., Ghodosi, H. (2022). Verifiable DOPE from Somewhat Homomorphic Encryption, and the Extension to DOT. In: Su, C., Sakurai, K., Liu, F. (eds) Science of Cyber Security. SciSec 2022. Lecture Notes in Computer Science, vol 13580. Springer, Cham. https://doi.org/10.1007/978-3-031-17551-0_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-17551-0_7

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-17550-3

  • Online ISBN: 978-3-031-17551-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics