A Fully Simulatable Oblivious Transfer Scheme Using Vector Decomposition

Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 309)

Abstract

Oblivious transfer is one of the most basic and widely used protocol primitives in cryptography. It can be described as a two-party protocol used for interaction between a sender and a receiver. A 1-out-of-2 oblivious transfer is the interaction between a sender and a receiver in which a sender has two strings m 0 and m 1. At the end of the interaction, receiver learns exactly one of the strings m 0 and m 1, while the sender learns nothing. Lindell showed how to achieve efficient and fully simulatable non-adaptive oblivious transfer under decisional Diffie–Hellman (DDH) problem, Nth residuosity and quadratic residuosity assumptions, as well as the assumption that homomorphic encryption exists. We propose a scheme based on this protocol under the assumption namely vector decomposition problem. Our scheme is non-adaptive and fully simulatable.

Keywords

Vector decomposition problem Oblivious transfer 

References

  1. 1.
    Balasubramanian, R., Koblitz, N.: The improbability that an elliptic curve has sub exponential discrete log problem under the Menezes-Okamoto-Vanstone algorithm. J. Cryptology. 11(2), 141–145 (1998)CrossRefMATHMathSciNetGoogle Scholar
  2. 2.
    Duursma, I., Kiyavash, N.: The vector decomposition problem for elliptic and hyperelliptic curves. J. Ramanujan Math. Soc. 20(1), 5976 (2005)MathSciNetGoogle Scholar
  3. 3.
    Even, S., Goldreich, O., Lempel, A.: A randomized protocol for signing contracts. In: CRYPTO 1982, pp. 205210 (1982)Google Scholar
  4. 4.
    Galbraith, S.D., Verheul, E.: An analysis of the vector decomposition problem. In: Cramer, R. (ed.) PKC 2008. LNCS, vol. 4939, pp. 308327. Springer, Heidelberg (2008)Google Scholar
  5. 5.
    Green, M., Hohenberger, S: Blind identity-based encryption and simulatable oblivious transfer. In ASIACRYPT ‘07, vol. 4833 of LNCS, pp. 265–282 (2007)Google Scholar
  6. 6.
    Green, M., Hohenberger, S: Universally composable adaptive oblivious transfer. In ASIACRYPT, pp. 179–197 (2008)Google Scholar
  7. 7.
    Lindell, Y.: Efficient fully-simulatable oblivious transfer. In: Malkin, T.G. (ed.) CT-RSA 2008. LNCS, vol. 4964, pp. 5270. Springer, Heidelberg (2008)Google Scholar
  8. 8.
    Okamoto, T., Takashima, K.: Homomorphic encryption and signatures from vector decomposition. In Pairing, pp. 57–74 (2008)Google Scholar
  9. 9.
    Praveen, I., Sethumadhavan, M.: An efficient pairing computation, 1st international conference on security of internet of things (SecurIT 2012), pp. 145–149, 2012. ISBN: 978–1–4503–1822–88Google Scholar
  10. 10.
    Praveen, I., Sethumadhavan, M.: An application of vector decomposition problem in public key cryptography using homomorphic encryption, international conference on emerging research in computing, information, communication and applications-ERCICA (2013)Google Scholar
  11. 11.
    Rabin, M.O.: How to exchange secrets by oblivious transfer, technical report TR-81, Aiken Computation Laboratory, Harvard University (1981)Google Scholar
  12. 12.
    Yoshida, M.: Inseparable multiplex transmission using the pairing on elliptic curves and its application to watermarking. In: Fifth conference on algebraic geometry, number theory, coding theory and cryptography, University of Tokyo (2003)Google Scholar

Copyright information

© Springer India 2015

Authors and Affiliations

  1. 1.TIFAC Core in Cyber SecurityAmrita Vishwa Vidyapeetham (University)CoimbatoreIndia
  2. 2.Department of MathematicsAmrita Vishwa Vidyapeetham (University)CoimbatoreIndia

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