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Statistically Sender-Private OT from LPN and Derandomization

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Advances in Cryptology – CRYPTO 2022 (CRYPTO 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13509))

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Abstract

We construct a two-message oblivious transfer protocol with statistical sender privacy (SSP OT) based on the Learning Parity with Noise (LPN) Assumption and a standard Nisan-Wigderson style derandomization assumption. Beyond being of interest on their own, SSP OT protocols have proven to be a powerful tool toward minimizing the round complexity in a wide array of cryptographic applications from proofs systems, through secure computation protocols, to hard problems in statistical zero knowledge (SZK).

The protocol is plausibly post-quantum secure. The only other constructions with plausible post quantum security are based on the Learning with Errors (LWE) Assumption. Lacking the geometric structure of LWE, our construction and analysis rely on a different set of techniques.

Technically, we first construct an SSP OT protocol in the common random string model from LPN alone, and then derandomize the common random string. Most of the technical difficulty lies in the first step. Here we prove a robustness property of the inner product randomness extractor to a certain type of linear splitting attacks. A caveat of our construction is that it relies on the so called low noise regime of LPN. This aligns with our current complexity-theoretic understanding of LPN, which only in the low noise regime is known to imply hardness in SZK.

A full version of this work is available [12].

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Acknowledgements

Nir Bitansky is a member of the checkpoint institute of information security. This work was supported by the Israel Science Foundation (Grants No. 484/18 and 2137/19, by Len Blavatnik and the Blavatnik Family Foundation, by the Blavatnik Interdisciplinary Cyber Research Center at Tel Aviv University, and by the European Union Horizon 2020 Research and Innovation Program via ERC Project REACT (Grant 756482).

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  1. Tel Aviv University, Tel Aviv, Israel

    Nir Bitansky & Sapir Freizeit

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  1. Nir Bitansky
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Correspondence to Sapir Freizeit .

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  1. New York University, New York, NY, USA

    Yevgeniy Dodis

  2. University of Florida, Gainesville, FL, USA

    Thomas Shrimpton

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Bitansky, N., Freizeit, S. (2022). Statistically Sender-Private OT from LPN and Derandomization. In: Dodis, Y., Shrimpton, T. (eds) Advances in Cryptology – CRYPTO 2022. CRYPTO 2022. Lecture Notes in Computer Science, vol 13509. Springer, Cham. https://doi.org/10.1007/978-3-031-15982-4_21

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