Skip to main content

A Code-Based 1-out-of-N Oblivious Transfer Based on McEliece Assumptions

  • Conference paper
Information Security Practice and Experience (ISPEC 2012)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 7232))

Abstract

In this paper, we propose an efficient code-based 1-out-of-N oblivious transfer, \(OT_1^N\), based on McEliece assumptions without invoking the \(OT_1^2\) several times as in the paradigm proposed in [20,6]. We also show that the protocol is computationally secure against passive and active adversaries. To our knowledge, this is the first practical code-based \(OT_1^N\) protocol. The proposed protocol is compared with some existing number-theoretic \(OT_1^N\) protocols for efficiency.

Also, the passively secure 1-out-of-2 OT protocol proposed by Dowsley et al. [10] is reviewed. A formal argument of the computational security of the protocol against active adversaries is furnished.

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

Access this chapter

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. Bellare, M., Micali, S.: Non-interactive oblivious transfer and applications. In: Brassard [5], pp. 547–557

    Google Scholar 

  2. Berlekamp, E.R., Mceliece, R.J., Vantilborg, H.C.: On the inherent intractability of certain coding problems. IEEE Transactions on Information Theory (1978)

    Google Scholar 

  3. Bernstein, D.J.: List decoding for binary goppa codes (2008)

    Google Scholar 

  4. Bernstein, D.J., Buchmann, J., Dahmen, E.: Post Quantum Cryptography, 1st edn. Springer, Heidelberg (2008) (incorporated)

    Google Scholar 

  5. Brassard, G. (ed.): CRYPTO 1989. LNCS, vol. 435. Springer, Heidelberg (1990)

    MATH  Google Scholar 

  6. Brassard, G., Crépeau, C., Robert, J.-M.: Information theoretic reductions among disclosure problems. In: FOCS, pp. 168–173. IEEE (1986)

    Google Scholar 

  7. Faugère, J.C., Otmani, A., Perret, L., Tillich, J.P.: A distinguisher for high rate mceliece cryptosystems

    Google Scholar 

  8. Courtois, N.T., Finiasz, M., Sendrier, N.: How to Achieve a McEliece-Based Digital Signature Scheme. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 157–174. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  9. Crépeau, C.: Equivalence between Two Flavours of Oblivious Transfers. In: Pomerance, C. (ed.) CRYPTO 1987. LNCS, vol. 293, pp. 350–354. Springer, Heidelberg (1988)

    Google Scholar 

  10. 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 

  11. Even, S., Goldreich, O., Lempel, A.: A randomized protocol for signing contracts. Commun. ACM 28(6), 637–647 (1985)

    Article  MathSciNet  Google Scholar 

  12. Finiasz, M., Sendrier, N.: Security Bounds for the Design of Code-Based Cryptosystems. In: Matsui, M. (ed.) ASIACRYPT 2009. LNCS, vol. 5912, pp. 88–105. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  13. Goldreich, O., Levin, L.A.: A hard-core predicate for all one-way functions. In: Johnson, D.S. (ed.) STOC, pp. 25–32. ACM (1989)

    Google Scholar 

  14. 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 (1987)

    Google Scholar 

  15. 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 

  16. 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 

  17. Kilian, J.: Founding cryptography on oblivious transfer. In: STOC, pp. 20–31. ACM (1988)

    Google Scholar 

  18. Kobara, K., Morozov, K., Overbeck, R.: Coding-Based Oblivious Transfer. In: Calmet, J., Geiselmann, W., Müller-Quade, J. (eds.) MMICS 2008. LNCS, vol. 5393, pp. 142–156. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  19. Morozov, K., Savvides, G.: Efficient computational oblivious transfer using interactive hashing. In: Proceedings of the 6th ACM Symposium on Information, Computer and Communications Security, ASIACCS 2011, pp. 448–452. ACM, New York (2011)

    Google Scholar 

  20. Naor, M., Pinkas, B.: Oblivious transfer and polynomial evaluation. In: STOC, pp. 245–254 (1999)

    Google Scholar 

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

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  23. Ostrovsky, R., Venkatesan, R., Yung, M.: Fair games against an all-powerful adversary. In: AMS DIMACS Series in Discrete Mathematics and Theoretical Computer Science, pp. 155–169 (1991)

    Google Scholar 

  24. 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 

  25. Peikert, C., Waters, B.: Lossy trapdoor functions and their applications. In: Dwork, C. (ed.) STOC, pp. 187–196. ACM (2008)

    Google Scholar 

  26. Rabin, M.O.: How to exchange secrets with oblivious transfer. Cryptology ePrint Archive, Report 2005/187 (2005), http://eprint.iacr.org/

  27. McEliece, R.J.: A public-key cryptosystem based on algebraic coding theory. JPL DSN Progress Report, 114–116 (1978)

    Google Scholar 

  28. Salomaa, A., Santean, L.: Secret selling of secrets with several buyers. Bulletin of the EATCS 42, 178–186 (1990)

    MATH  Google Scholar 

  29. De Santis, A., Di Crescenzo, G., Persiano, G.: Zero-knowledge arguments and public-key cryptography. Inf. Comput. 121(1), 23–40 (1995)

    Article  MATH  Google Scholar 

  30. Sendrier, N.: The tightness of security reductions in code-based cryptography. In: 2011 IEEE Information Theory Workshop (ITW), pp. 415–419 (October 2011)

    Google Scholar 

  31. Sendrier, N.: Decoding One Out of Many. In: Yang, B.-Y. (ed.) PQCrypto 2011. LNCS, vol. 7071, pp. 51–67. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  32. Shamir, A.: An efficient identification scheme based on permuted kernels (extended abstract). In: Brassard [5], pp. 606–609

    Google Scholar 

  33. Shor, P.W.: Polynominal Time Algorithms for Discrete Logarithms and Factoring on a Quantum Computer. In: Adleman, L.M., Huang, M.-D.A. (eds.) ANTS 1994. LNCS, vol. 877, p. 289. Springer, Heidelberg (1994)

    Chapter  Google Scholar 

  34. Stern, J.: A New Identification Scheme Based on Syndrome Decoding. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 13–21. Springer, Heidelberg (1994)

    Google Scholar 

  35. Tzeng, W.-G.: Efficient 1-out-of-n oblivious transfer schemes with universally usable parameters. IEEE Trans. Computers 53(2), 232–240 (2004)

    Article  MathSciNet  Google Scholar 

  36. Wang, H., Pieprzyk, J.: Efficient One-Time Proxy Signatures. In: Laih, C.-S. (ed.) ASIACRYPT 2003. LNCS, vol. 2894, pp. 507–522. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

K., P.M., Vasant, S., Venkatesan, S., Pandu Rangan, C. (2012). A Code-Based 1-out-of-N Oblivious Transfer Based on McEliece Assumptions. In: Ryan, M.D., Smyth, B., Wang, G. (eds) Information Security Practice and Experience. ISPEC 2012. Lecture Notes in Computer Science, vol 7232. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29101-2_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-29101-2_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-29100-5

  • Online ISBN: 978-3-642-29101-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics