Skip to main content
SpringerLink
Log in

Essentially Optimal Universally Composable Oblivious Transfer

  • Conference paper
Book cover Information Security and Cryptology – ICISC 2008 (ICISC 2008)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 5461))

Included in the following conference series:

Abstract

Oblivious transfer is one of the most important cryptographic primitives, both for theoretical and practical reasons and several protocols were proposed during the years. We propose a protocol which is simultaneously optimal on the following list of parameters: Security: it has universal composition. Trust in setup assumptions: only one of the parties needs to trust the setup (and some setup is needed for UC security). Trust in computational assumptions: only one of the parties needs to trust a computational assumption. Round complexity: it uses only two rounds. Communication complexity: it communicates \(\mathcal{O}(1)\) group elements to transfer one out of two group elements. The Big-O notation hides 32, meaning that the communication is probably not optimal, but is essentially optimal in that the overhead is at least constant. Our construction is based on pairings, and we assume the presence of a key registration authority.

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 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aiello, W., Ishai, Y., Reingold, O.: Priced oblivious transfer: How to sell digital goods. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 119–135. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  2. Boneh, D., Boyen, X., Shacham, H.: Short Group Signatures. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 41–55. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  3. Barak, B., Canetti, R., Nielsen, J.B., Pass, R.: Universally composable protocols with relaxed set-up assumptions. In: FOCS, pp. 186–195. IEEE Computer Society, Los Alamitos (2004)

    Google Scholar 

  4. Boneh, D., Franklin, M.K.: Identity-based encryption from the weil pairing. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 213–229. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  5. Canetti, R.: Universally composable security: A new paradigm for cryptographic protocols. In: FOCS, pp. 136–145 (2001)

    Google Scholar 

  6. Canetti, R., Fischlin, M.: Universally composable commitments. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 19–40. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  7. Canetti, R., Krawczyk, H.: Universally composable notions of key exchange and secure channels. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol. 2332, pp. 337–351. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  8. Camenisch, J., Neven, G., Shelat, A.: Simulatable adaptive oblivious transfer. In: Naor [Nao07], pp. 573–590

    Google Scholar 

  9. Damgård, I., Nielsen, J.B.: Perfect hiding and perfect binding universally composable commitment schemes with constant expansion factor. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 581–596. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  10. Damgård, I., Nielsen, J.B., Wichs, D.: Isolated proofs of knowledge and isolated zero knowledge. In: Smart, N.P. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 509–526. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  11. Fischlin, M.: Universally composable oblivious transfer in the multi-party setting. In: Pointcheval, D. (ed.) CT-RSA 2006. LNCS, vol. 3860, pp. 332–349. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  12. Garay, J.A.: Efficient and universally composable committed oblivious transfer and applications. In: Naor, M. (ed.) TCC 2004. LNCS, vol. 2951, pp. 297–316. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  13. Green, M., Hohenberger, S.: Blind identity-based encryption and simulatable oblivious transfer. In: Kurosawa, K. (ed.) ASIACRYPT 2007. LNCS, vol. 4833, pp. 265–282. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  14. Green, M., Hohenberger, S.: Universally composable adaptive oblivious transfer (2008)

    Google Scholar 

  15. Goldreich, O., Micali, S., Wigderson, A.: How to play any mental game or a completeness theorem for protocols with honest majority. In: STOC, pp. 218–229. ACM, New York (1987)

    Google Scholar 

  16. Groth, J., Ostrovsky, R., Sahai, A.: Perfect non-interactive zero knowledge for np. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 339–358. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  17. Groth, J., Sahai, A.: Efficient non-interactive proof systems for bilinear groups. In: Smart, N.P. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 415–432. Springer, Heidelberg (2008), http://eprint.iacr.org/2007/155

    Chapter  Google Scholar 

  18. Joux, A.: A one round protocol for tripartite diffie-hellman. In: Bosma, W. (ed.) ANTS 2000. LNCS, vol. 1838, pp. 385–394. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  19. Jarecki, S., Shmatikov, V.: Efficient two-party secure computation on committed inputs. In: Naor [Nao07], pp. 97–114

    Google Scholar 

  20. Kalai, Y.T.: Smooth projective hashing and two-message oblivious transfer. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 78–95. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  21. Lindell, A.Y.: Efficient fully-simulatable oblivious transfer. In: Malkin, T.G. (ed.) CT-RSA 2008. LNCS, vol. 4964, pp. 52–70. Springer, Heidelberg (2008), http://eprint.iacr.org/2008/035

    Chapter  Google Scholar 

  22. Menezes, A., Okamoto, T., Vanstone, S.A.: Reducing elliptic curve logarithms to logarithms in a finite field. IEEE Transactions on Information Theory 39(5), 1639–1646 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  23. Naor, M. (ed.): EUROCRYPT 2007. LNCS, vol. 4515. Springer, Heidelberg (2007)

    MATH  Google Scholar 

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

    Google Scholar 

  25. Naor, M., Pinkas, B.: Computationally secure oblivious transfer. J. Cryptology 18(1), 1–35 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  26. Peikert, C., Vaikuntanathan, V., Waters, B.: A framework for efficient and composable oblivious transfer. Cryptology ePrint Archive, Report 2007/348 (2007), http://eprint.iacr.org/

  27. Rabin, M.O.: How to exchange secrets by oblivious transfer. Technical Report TR-81, Harvard Aiken Computation Laboratory (1981)

    Google Scholar 

  28. Wiesner, S.: Conjugate coding. SIGACT News 15(1), 78–88 (1983)

    Article  MATH  Google Scholar 

  29. Yao, A.C.-C.: How to generate and exchange secrets (extended abstract). In: FOCS, pp. 162–167. IEEE, Los Alamitos (1986)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. BRICS, Department of Computer Science, Aarhus University, Åbogade 34, 8200, Århus, Denmark

    Ivan Damgård, Jesper Buus Nielsen & Claudio Orlandi

Authors
  1. Ivan Damgård
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jesper Buus Nielsen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Claudio Orlandi
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Electronic and Electrical Engineering, Pohang University of Science and Technology (POSTECH), San 31 Hyoja-dong, Nam-gu,, 790-784, Pohang, Kyungbuk, Korea

    Pil Joong Lee

  2. Department of Mathematical Sciences, Seoul National University, 599 Gwanakno, Gwanak-gu, 151-742, Seoul, Korea

    Jung Hee Cheon

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Damgård, I., Nielsen, J.B., Orlandi, C. (2009). Essentially Optimal Universally Composable Oblivious Transfer. In: Lee, P.J., Cheon, J.H. (eds) Information Security and Cryptology – ICISC 2008. ICISC 2008. Lecture Notes in Computer Science, vol 5461. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00730-9_20

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-00730-9_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00729-3

  • Online ISBN: 978-3-642-00730-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation