Skip to main content
SpringerLink
Log in

Universally Composable Oblivious Transfer from Lossy Encryption and the McEliece Assumptions

  • Conference paper
Information Theoretic Security (ICITS 2012)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 7412))

Included in the following conference series:

Abstract

Oblivious transfer (OT) is a primitive of great importance in two-party and multi-party computation. We introduce a general construction of universally composable (UC) oblivious transfer protocols based on lossy cryptosystems in the common reference string (CRS) model, yielding protocols under several assumptions. In order to achieve this, we show that for most known lossy encryption constructions it is possible to distinguish between lossy and injective public keys given the corresponding secret key, similarly to dual-mode encryption in messy mode.

Furthermore, we adapt the techniques of our general construction to obtain the first UC secure OT protocol based on the McEliece assumptions, which are coding theory based assumptions that until now have resisted quantum attacks, thus introducing the first UC secure OT protocol based on coding assumptions.

However, differently from previous results based on dual-mode encryption, our scheme does not require a trapdoor for opening lossy ciphertexts, relying instead on CRS manipulation and cut-and-choose techniques to construct the simulators. In both constructions we circumvent the need for universally composable string commitment schemes, which are required by previous black-box compilers.

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 54.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 72.00
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. Dinh, H., Moore, C., Russell, A.: McEliece and Niederreiter Cryptosystems that Resist Quantum Fourier Sampling Attacks. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 761–779. Springer, Heidelberg (2011)

    Google Scholar 

  2. 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 

  3. Bellare, M., Hofheinz, D., Yilek, S.: Possibility and Impossibility Results for Encryption and Commitment Secure under Selective Opening. In: Joux, A. (ed.) EUROCRYPT 2009. LNCS, vol. 5479, pp. 1–35. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  4. Bellare, M., Micali, S.: Non-interactive Oblivious Transfer and Applications. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 547–557. Springer, Heidelberg (1990)

    Google Scholar 

  5. Berlekamp, E.R., McEliece, R., van Tilborg, H.C.A.: On the inherent intractability of certain coding problems (corresp). IEEE Transactions on Information Theory (24) (1978)

    Google Scholar 

  6. Canetti, R.: Universally composable security: A new paradigm for cryptographic protocols. In: Proceedings of the 42nd IEEE symposium on Foundations of Computer Science, FOCS 2001, pp. 136–145. IEEE Computer Society, Washington, DC (2001)

    Google Scholar 

  7. 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 

  8. Canetti, R., Lindell, Y., Ostrovsky, R., Sahai, A.: Universally composable two-party and multi-party secure computation. In: Proceedings of the Thiry-Fourth Annual ACM Symposium on Theory of Computing, STOC 2002, pp. 494–503. ACM, New York (2002)

    Chapter  Google Scholar 

  9. Canetti, R., Rabin, T.: Universal Composition with Joint State. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 265–281. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  10. Choi, S.G., Dachman-Soled, D., Malkin, T., Wee, H.: Simple, Black-Box Constructions of Adaptively Secure Protocols. In: Reingold, O. (ed.) TCC 2009. LNCS, vol. 5444, pp. 387–402. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  11. Cramer, R., Shoup, V.: Universal Hash Proofs and a Paradigm for Adaptive Chosen Ciphertext Secure Public-Key Encryption. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol. 2332, pp. 45–64. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  12. Crépeau, C., van de Graaf, J., Tapp, A.: Committed Oblivious Transfer and Private Multi-Party Computation. In: Coppersmith, D. (ed.) CRYPTO 1995. LNCS, vol. 963, pp. 110–123. Springer, Heidelberg (1995)

    Google Scholar 

  13. Damgård, I., Kilian, J., Salvail, L.: On the (im)possibility of Basing Oblivious Transfer and Bit Commitment on Weakened Security Assumptions. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 56–73. Springer, Heidelberg (1999)

    Google Scholar 

  14. Damgård, I., Nielsen, J.B., Orlandi, C.: Essentially Optimal Universally Composable Oblivious Transfer. In: Lee, P.J., Cheon, J.H. (eds.) ICISC 2008. LNCS, vol. 5461, pp. 318–335. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  15. David, B.M., Nascimento, A.C.A.: Efficient fully simulatable oblivious transfer from the mceliece assumptions. In: Information Theory Workshop (ITW), pp. 638–642. IEEE (October 2011)

    Google Scholar 

  16. Dowsley, R., van de Graaf, J., Müller-Quade, J., Nascimento, A.C.A.: Oblivious Transfer Based on the Mceliece Assumptions. In: Safavi-Naini, R. (ed.) ICITS 2008. LNCS, vol. 5155, pp. 107–117. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  17. Even, S., Goldreich, O., Lempel, A.: A randomized protocol for signing contracts. In: CRYPTO 1982, pp. 205–210 (1982)

    Google Scholar 

  18. Faugère, J.C., Gauthier, V., Otmani, A., Perret, L., Tillich, J.P.: A distinguisher for high rate mceliece cryptosystems. Cryptology ePrint Archive. Report 2010/331 (2010)

    Google Scholar 

  19. Garay, J.A., Mackenzie, P., Yang, K.: 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 

  20. Goldreich, O., Micali, S., Wigderson, A.: How to play any mental game. In: STOC 1987: Proceedings of the Nineteenth Annual ACM Symposium on Theory of Computing, pp. 218–229. ACM, New York (1987)

    Chapter  Google Scholar 

  21. Green, M., Hohenberger, S.: Universally Composable Adaptive Oblivious Transfer. In: Pieprzyk, J. (ed.) ASIACRYPT 2008. LNCS, vol. 5350, pp. 179–197. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  22. Haitner, I.: Semi-Honest to Malicious Oblivious Transfer—the Black-Box Way. In: Canetti, R. (ed.) TCC 2008. LNCS, vol. 4948, pp. 412–426. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  23. Hemenway, B., Libert, B., Ostrovsky, R., Vergnaud, D.: Lossy Encryption: Constructions from General Assumptions and Efficient Selective Opening Chosen Ciphertext Security. In: Lee, D.H. (ed.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 70–88. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  24. Ishai, Y., Kushilevitz, E., Lindell, Y., Petrank, E.: Black-box constructions for secure computation. In: Proceedings of the Thirty-Eighth Annual ACM Symposium on Theory of Computing, STOC 2006, pp. 99–108. ACM, New York (2006), http://doi.acm.org/10.1145/1132516.1132531

    Chapter  Google Scholar 

  25. Jarecki, S., Shmatikov, V.: Efficient Two-Party Secure Computation on Committed Inputs. In: Naor, M. (ed.) EUROCRYPT 2007. LNCS, vol. 4515, pp. 97–114. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  26. 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 

  27. Kilian, J.: Founding crytpography on oblivious transfer. In: STOC 1988: Proceedings of the Twentieth Annual ACM Symposium on Theory of Computing, pp. 20–31. ACM, New York (1988)

    Chapter  Google Scholar 

  28. Lindell, A.Y.: Efficient Fully-Simulatable Oblivious Transfer. In: Malkin, T. (ed.) CT-RSA 2008. LNCS, vol. 4964, pp. 52–70. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  29. McEliece, R.J.: A public-key cryptosystem based on algebraic coding theory. dsn progress report. In: Jet Propulsion Laboratories, CALTECH, pp. 42–44 (1978)

    Google Scholar 

  30. Naor, M., Pinkas, B.: Efficient oblivious transfer protocols. In: Proceedings of the Twelfth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2001, Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, pp. 448–457 (2001)

    Google Scholar 

  31. Nojima, R., Imai, H., Kobara, K., Morozov, K.: Semantic security for the mceliece cryptosystem without random oracles. Des. Codes Cryptography 49(1-3), 289–305 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  32. Peikert, C., Vaikuntanathan, V., Waters, B.: A Framework for Efficient and Composable Oblivious Transfer. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 554–571. Springer, Heidelberg (2008)

    Google Scholar 

  33. Peikert, C., Waters, B.: Lossy trapdoor functions and their applications. In: Proceedings of the 40th Annual ACM Symposium on Theory of Computing, STOC 2008, pp. 187–196. ACM, New York (2008)

    Chapter  Google Scholar 

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

    Google Scholar 

  35. Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. In: STOC 2005: Proceedings of the Thirty-Seventh Annual ACM Symposium on Theory of Computing, pp. 84–93. ACM, New York (2005)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electrical Engineering, University of Brasilia, Brazil

    Bernardo Machado David & Anderson C. A. Nascimento

  2. Institute of Cryptography and Security, Faculty of Informatics, Karlsruhe Institute of Technology, Germany

    Jörn Müller-Quade

Authors
  1. Bernardo Machado David
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Anderson C. A. Nascimento
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jörn Müller-Quade
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, Pennsylvania State University, 16802, University Park, PA, USA

    Adam Smith

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

David, B.M., Nascimento, A.C.A., Müller-Quade, J. (2012). Universally Composable Oblivious Transfer from Lossy Encryption and the McEliece Assumptions. In: Smith, A. (eds) Information Theoretic Security. ICITS 2012. Lecture Notes in Computer Science, vol 7412. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32284-6_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-32284-6_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-32283-9

  • Online ISBN: 978-3-642-32284-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation