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Two-Round Maliciously-Secure Oblivious Transfer with Optimal Rate

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Advances in Cryptology – EUROCRYPT 2024 (EUROCRYPT 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14656))

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Abstract

We give a construction of a two-round batch oblivious transfer (OT) protocol in the CRS model that is UC-secure against malicious adversaries and has (near) optimal communication cost. Specifically, to perform a batch of k oblivious transfers where the sender’s inputs are bits, the sender and the receiver need to communicate a total of \(3k + o(k) \cdot \textsf{poly}(\lambda )\) bits. We argue that 3k bits are required by any protocol with a black-box and straight-line simulator. The security of our construction is proven assuming the hardness of Quadratic Residuosity (QR) and the Learning Parity with Noise (LPN).

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Notes

  1. 1.

    Straight-line simulation is required to show UC-security.

  2. 2.

    Correlated OTs are generated by sampling a fixed offset \(\varDelta \leftarrow \{0,1\}^\lambda \) and generating several instances of the form \((b,v + b\cdot \varDelta )\) where \(b \leftarrow \{0,1\}\) and \(v \leftarrow \{0,1\}^\lambda \). The receiver gets \((b,v + b\cdot \varDelta )\) and the sender gets \((v,\varDelta )\).

  3. 3.

    The QR-based construction in [34] is based on Cocks’ cryptosystem, but we will describe a version here based on the Brakerski Goldwasser encryption scheme [15].

  4. 4.

    For this to happen, we just have to set \(o(\nu )=n,L,t_1,t_2\) accordingly.

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Acknowledgement

Pedro Branco is funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - Project number 537717419 and partially funded by the German Federal Ministry of Education and Research (BMBF) in the course of the 6GEM research hub under grant number 16KISK038. Nico Döttling: Funded by the European Union (ERC, LACONIC, 101041207). Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council. Neither the European Union nor the granting authority can be held responsible for them.

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Authors and Affiliations

  1. Max Planck Institute for Security and Privacy, Bochum, Germany

    Pedro Branco

  2. Helmholtz Center for Information Security (CISPA), Saarbrücken, Germany

    Nico Döttling

  3. University of Toronto, Toronto, Canada

    Akshayaram Srinivasan

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  1. Pedro Branco
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  2. Nico Döttling
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Correspondence to Pedro Branco .

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Editors and Affiliations

  1. Zama, Paris, France

    Marc Joye

  2. Ruhr University Bochum, Bochum, Germany

    Gregor Leander

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Branco, P., Döttling, N., Srinivasan, A. (2024). Two-Round Maliciously-Secure Oblivious Transfer with Optimal Rate. In: Joye, M., Leander, G. (eds) Advances in Cryptology – EUROCRYPT 2024. EUROCRYPT 2024. Lecture Notes in Computer Science, vol 14656. Springer, Cham. https://doi.org/10.1007/978-3-031-58751-1_10

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