Oblivious Transfer Based on the McEliece Assumptions

  • Conference paper
Information Theoretic Security (ICITS 2008)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 5155))

Included in the following conference series:

Abstract

We implement one-out-of-two bit oblivious transfer (OT) based on the assumptions used in the McEliece cryptosystem: the hardness of decoding random binary linear codes, and the difficulty of distinguishing a permuted generating matrix of Goppa codes from a random matrix. To our knowledge this is the first OT reduction to these problems only.

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

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /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
EUR 29.95
Price includes VAT (France)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
EUR 42.79
Price includes VAT (France)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
EUR 52.74
Price includes VAT (France)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free ship** 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.

Similar content being viewed by others

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. Beaver, D.: Precomputing Oblivious Transfer. In: Coppersmith, D. (ed.) CRYPTO 1995. LNCS, vol. 963, pp. 97–109. Springer, Heidelberg (1995)

    Google Scholar 

  3. 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 

  4. Berlekamp, E.R., McEliece, R.J., Avan Tilborg, H.C.: On the Inherent Intractability of Certain Coding Problems. IEEE Trans. Inf. Theory 24, 384–386 (1978)

    Article  MATH  Google Scholar 

  5. Blum, A., Furst, M., Kearns, M., Lipton, R.J.: Cryptographic primitives based on hard learning problems. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 278–291. Springer, Heidelberg (1994)

    Google Scholar 

  6. Canteaut, A., Chabaud, F.: A new algorithm for finding minimum-weight words in a linear code: application to primitive narrow-sense BCH codes of length 511. IEEE Trans. Inf. Theory 44(1), 367–378 (1998)

    Article  MATH  MathSciNet  Google Scholar 

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

    Chapter  Google Scholar 

  8. Crépeau, C.: Equivalence between two flavors of oblivious transfers. In: Pomerance, C. (ed.) CRYPTO 1987. LNCS, vol. 293, pp. 350–354. Springer, Heidelberg (1988)

    Google Scholar 

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

    Google Scholar 

  10. 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 

  11. Even, S., Goldreich, O., Lempel, A.: A randomized protocol for signing contracts. In: Proceedings CRYPTO 1982, pp. 205–210. Plenum Press (1983)

    Google Scholar 

  12. Fischer, J., Stern, J.: An Efficient Pseudo-Random Generator Provably as Secure as Syndrome Decoding. In: Maurer, U.M. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 245–255. Springer, Heidelberg (1996)

    Google Scholar 

  13. Gertner, Y., Kannan, S., Malkin, T., Reingold, O., Viswanathan, M.: The Relationship between Public Key Encryption and Oblivious Transfer. In: FOCS 2000, pp. 325–335 (2000)

    Google Scholar 

  14. Goldreich, O.: Foundations of Cryptography (Basic Applications), vol. 2. Cambridge University Press, Cambridge (2004)

    MATH  Google Scholar 

  15. Goldreich, O., Levin, L.A.: Hard-Core Predicates for Any One-Way Function. In: 21st ACM Symposium on the Theory of Computing, pp. 25–32 (1989)

    Google Scholar 

  16. Goldreich, O., Micali, S., Wigderson, A.: How to Play Any Mental Game, or: A completeness theorem for protocols with honest majority. In: Proc. 19th ACM STOC, pp. 218–229. ACM Press, New York (1987)

    Google Scholar 

  17. Haitner, I.: implementing Oblivious Transfer Using Collection of Dense Trapdoor Permutations. In: Naor, M. (ed.) TCC 2004. LNCS, vol. 2951, pp. 394–409. Springer, Heidelberg (2004)

    Google Scholar 

  18. Kalai, Y.: Smooth Projective Hashing and Two-Message Oblivious Transfer. In: Cramer, R.J.F. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 78–95. Springer, Heidelberg (2005)

    Google Scholar 

  19. Kobara, K., Morozov, K., Overbeck, R.: Oblivious Transfer via McEliece’s PKC and Permuted Kernels, Cryptology ePrint Archive 2007/382 (2007)

    Google Scholar 

  20. Kilian, J.: Founding Cryptography on Oblivious Transfer. In: 20th ACM STOC, pp. 20–31. ACM Press, New York (1988)

    Google Scholar 

  21. Kobara, K., Imai, H.: Semantically Secure McEliece Cryptosystems – Conversions for McEliece PKC. In: Kim, K.-c. (ed.) PKC 2001. LNCS, vol. 1992, pp. 19–35. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  22. McEliece, R.J.: The Theory of Information and Coding. The Encyclopedia of Mathematics and Its Applications, vol. 3. Addison-Wesley, Reading (1977)

    MATH  Google Scholar 

  23. McEliece, R.J.: A Public-Key Cryptosystem Based on Algebraic Coding Theory. In: Deep Space Network progress Report (1978)

    Google Scholar 

  24. Naor, M.: Bit Commitment using Pseudo-Randomness. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 128–136. Springer, Heidelberg (1990)

    Google Scholar 

  25. Naor, M., Pinkas, B.: Efficient Oblivious Transfer Protocols. In: SODA 2001 (SIAM Symposium on Discrete Algorithms) (2001)

    Google Scholar 

  26. Nojima, R., Imai, H., Kobara, K., Morozov, K.: Semantic Security for the McEliece Cryptosystem without Random Oracles. WCC 2007, Versailles, France (April 2007)

    Google Scholar 

  27. Rabin, M.O.: How to Exchange Secrets by Oblivious Transfer. Technical Memo TR-81, Aiken Computation Laboratory, Harvard University (1981)

    Google Scholar 

  28. Regev, O.: On Lattices, Learning with Errors, Random Linear Codes, and Cryptography. In: Proc. 37th STOC, pp. 84–93 (2005)

    Google Scholar 

  29. Sendrier, N.: Finding the Permutation Between Equivalent Linear Codes: The Support Splitting Algorithm. IEEE Trans. Inf. Theory 46(4), 1193–1203 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  30. Shamir, A.: An efficient identification scheme based on permuted kernels. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 606–609. Springer, Heidelberg (1990)

    Google Scholar 

  31. Wiesner, S.: Conjugate coding. Sigact News 15(1), 78–88 (1983) (original manuscript written circa 1970)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Reihaneh Safavi-Naini

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Dowsley, R., van de Graaf, J., Müller-Quade, J., Nascimento, A.C.A. (2008). Oblivious Transfer Based on the McEliece Assumptions. In: Safavi-Naini, R. (eds) Information Theoretic Security. ICITS 2008. Lecture Notes in Computer Science, vol 5155. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85093-9_11

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-85093-9_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-85092-2

  • Online ISBN: 978-3-540-85093-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Navigation