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Extending Oblivious Transfer Efficiently

or - How to Get Active Security with Constant Cryptographic Overhead

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Book cover Progress in Cryptology - LATINCRYPT 2014 (LATINCRYPT 2014)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 8895))

Abstract

On top of the passively secure extension protocol of [IKNP03] we build a new construction secure against active adversaries. We can replace the invocation of the hash function that is used to check the receiver is well-behaved with the XOR of bit strings. This is possible by applying a cut-and-choose technique on the length of the bit strings that the receiver sends in the reversed OT. We also improve on the number of seeds required for the extension, both asymptotically and practically. Moreover, the protocol used to test receiver’s behaviour enjoys unconditional security.

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Notes

  1. 1.

    The hidden constant is quite big.

  2. 2.

    \(\mathsf {Bob}\) would learn e.g. the distance of two non-transmitted secrets. It is trivial to check that if two correlated pairs are used by \(\mathsf {Alice}\), then \(\mathbf {x}_i^{(1+b_i)} \oplus \mathbf {x}_j^{(1+b_j)} = \mathbf {y}_i^{(1+b_i)} \oplus \mathbf {y}_j^{(1+b_j)} \oplus \mathbf {l}_i \oplus \mathbf {l}_j\).

  3. 3.

    The purpose of the otherwise seemingly artificial functionality is to give a neat security analysis, both inwardly and outwardly.

  4. 4.

    The cost to pay is increasing the length of the input bit strings to the \(\mathcal {OT}^{}_{}\), using a PRG one would only need to obliviously transfer the PRG seed.

  5. 5.

    The reader can check the relation is reflexive, symmetric and transitive.

  6. 6.

    Parameter \(\ell \) lies in \([\frac{1}{n},1]\).

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Acknowledgments

This work has been supported in part by EPSRC via grant EP/I03126X.

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Authors and Affiliations

  1. Department of Computer Science, University of Bristol, Bristol, UK

    Enrique Larraia

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  1. Enrique Larraia
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Correspondence to Enrique Larraia .

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Editors and Affiliations

  1. University of Campinas, Campinas, Brazil

    Diego F. Aranha

  2. University of Waterloo, Waterloo, Ontario, Canada

    Alfred Menezes

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Larraia, E. (2015). Extending Oblivious Transfer Efficiently. In: Aranha, D., Menezes, A. (eds) Progress in Cryptology - LATINCRYPT 2014. LATINCRYPT 2014. Lecture Notes in Computer Science(), vol 8895. Springer, Cham. https://doi.org/10.1007/978-3-319-16295-9_20

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  • DOI: https://doi.org/10.1007/978-3-319-16295-9_20

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  • Print ISBN: 978-3-319-16294-2

  • Online ISBN: 978-3-319-16295-9

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