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Outsourcing Verifiable Distributed Oblivious Polynomial Evaluation from Threshold Cryptography

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Information and Communications Security (ICICS 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14252))

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Abstract

Distributed oblivious polynomial evaluation (DOPE) is a variant of two-party computation where a sender party \(P_1\) has a polynomial f(x) of degree k and the receiver party \(P_2\) holds an input \(\alpha \). They conduct a secure computation with a number of t distributed cloud servers such that \(P_2\) obtains the correct output \(f(\alpha )\) while the privacy of the inputs is preserved. This system is the building block of many cryptographic models and machine learning algorithms.

We propose a lightweight DOPE scheme with two separate phases: setup and computation, which means that the setup phase can be executed at any time before the actual computation phase. The number of the servers (t) does not depend on the polynomial degree (k), and the main expensive computation is securely outsourced to the cloud servers using the idea of threshold cryptography. As a result, any normal user with low computational power devices (e.g., mobile, laptop, etc.) would be able to evaluate and verify the output over a large field while the security conditions are preserved. Our protocol maintains the security against a static active adversary corrupting a coalition of up to \(t-1\) servers and the opposed party. The main two parties commit to their inputs using non-interactive zero-knowledge proof techniques. The communication complexity is linear and bounded to O(t) field elements which means that, unlike the previous studies in this field, it does not depend on the polynomial degree k.

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Authors and Affiliations

  1. James Cook University, Townsville, QLD, Australia

    Amirreza Hamidi & Hossein Ghodosi

Authors
  1. Amirreza Hamidi
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  2. Hossein Ghodosi
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Correspondence to Amirreza Hamidi .

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Editors and Affiliations

  1. Nankai University, Tianjin, China

    Ding Wang

  2. Columbia University, New York, NY, USA

    Moti Yung

  3. Nankai University, Tianjin, China

    Zheli Liu

  4. Xidian University, Xi’an, China

    Xiaofeng Chen

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Hamidi, A., Ghodosi, H. (2023). Outsourcing Verifiable Distributed Oblivious Polynomial Evaluation from Threshold Cryptography. In: Wang, D., Yung, M., Liu, Z., Chen, X. (eds) Information and Communications Security. ICICS 2023. Lecture Notes in Computer Science, vol 14252. Springer, Singapore. https://doi.org/10.1007/978-981-99-7356-9_14

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  • DOI: https://doi.org/10.1007/978-981-99-7356-9_14

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