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The Simplest Protocol for Oblivious Transfer

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Progress in Cryptology -- LATINCRYPT 2015 (LATINCRYPT 2015)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 9230))

Abstract

Oblivious Transfer (OT) is the fundamental building block of cryptographic protocols. In this paper we describe the simplest and most efficient protocol for 1-out-of-n OT to date, which is obtained by tweaking the Diffie-Hellman key-exchange protocol. The protocol achieves UC-security against active and adaptive corruptions in the random oracle model. Due to its simplicity, the protocol is extremely efficient and it allows to perform m 1-out-of-n OTs using only:

  • Computation: \((n+1)m+2\) exponentiations (mn for the receiver, \(mn+2\) for the sender) and

  • Communication: \(32(m+1)\) bytes (for the group elements), and 2mn ciphertexts.

We also report on an implementation of the protocol using elliptic curves, and on a number of mechanisms we employ to ensure that our software is secure against active attacks too. Experimental results show that our protocol (thanks to both algorithmic and implementation optimizations) is at least one order of magnitude faster than previous work.

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Notes

  1. 1.

    I.e., UC security [Can01], which is impossible to achieve without some kind of trusted setup assumptions [CF01].

  2. 2.

    Standard hash functions do not take group elements as inputs, and in later sections we will give explicit encodings of group elements into bitstrings.

  3. 3.

    This subsection assumes that the reader is familiar with standard security definitions and proofs for two-party computation protocols such as those presented in [HL10].

  4. 4.

    The main goal of this argument is to show that a corrupted sender knows the message vectors.

  5. 5.

    The main goal of this argument is to show that a corrupted receiver knows the choice value.

  6. 6.

    We stress that non-deterministic in this context does not mean that the encoding involves any randomness.

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Acknowledgments

We are very grateful to: Daniel J. Bernstein and Tanja Lange for invaluable comments and suggestions regarding elliptic curve cryptography and for editorial feedback on earlier versions of this paper; Yehuda Lindell for useful comments on our proof of security; Peter Schwabe for various helps on implementation, including providing low-level code for field arithmetic; the anonymous LATINCRYPT reviewer and in particular Gregory Neven.

Tung Chou is supported by Netherlands Organisation for Scientific Research (NWO) under grant 639.073.005. Claudio Orlandi is supported by: the Danish National Research Foundation and The National Science Foundation of China (grant 61361136003) for the Sino-Danish Center for the Theory of Interactive Computation; the Center for Research in Foundations of Electronic Markets (CFEM); the European Union Seventh Framework Programme ([FP7/2007-2013]) under grant agreement number ICT-609611 (PRACTICE).

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Authors and Affiliations

  1. Technische Universieit Eindhoven, Eindhoven, The Netherlands

    Tung Chou

  2. Aarhus University, Aarhus, Denmark

    Claudio Orlandi

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  1. Tung Chou
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Correspondence to Claudio Orlandi .

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Editors and Affiliations

  1. Microsoft Research, Redmond, Washington, USA

    Kristin Lauter

  2. CINVESTAV-IPN, Mexico City, Distrito Federal, Mexico

    Francisco Rodríguez-Henríquez

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Chou, T., Orlandi, C. (2015). The Simplest Protocol for Oblivious Transfer. In: Lauter, K., Rodríguez-Henríquez, F. (eds) Progress in Cryptology -- LATINCRYPT 2015. LATINCRYPT 2015. Lecture Notes in Computer Science(), vol 9230. Springer, Cham. https://doi.org/10.1007/978-3-319-22174-8_3

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  • DOI: https://doi.org/10.1007/978-3-319-22174-8_3

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