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Unconditionally Secure Oblivious Polynomial Evaluation: A Survey and New Results

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Abstract

Oblivious polynomial evaluation (OPE) is a two-party protocol that allows a receiver, ℛ to learn an evaluation f(α), of a sender, 𝒮’s polynomial (f(x)), whilst keeping both α and f(x) private. This protocol has attracted a lot of attention recently, as it has wide ranging applications in the field of cryptography. In this article we review some of these applications and, additionally, take an in-depth look at the special case of information theoretic OPE. Specifically, we provide a current and critical review of the existing information theoretic OPE protocols in the literature. We divide these protocols into two distinct cases (three-party and distributed OPE) allowing for the easy distinction and classification of future information theoretic OPE protocols. In addition to this work, we also develop several modifications and extensions to existing schemes, resulting in increased security, flexibility and efficiency. Lastly, we also identify a security aw in a previously published OPE scheme.

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Authors and Affiliations

  1. College of Science and Engineering, James Cook University, Townsville, QLD, 4811, Australia

    Louis Cianciullo & Hossein Ghodosi

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  1. Louis Cianciullo
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  2. Hossein Ghodosi
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Correspondence to Louis Cianciullo.

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Cianciullo, L., Ghodosi, H. Unconditionally Secure Oblivious Polynomial Evaluation: A Survey and New Results. J. Comput. Sci. Technol. 37, 443–458 (2022). https://doi.org/10.1007/s11390-022-0878-6

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