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Brief Announcement: Efficient Probabilistic Approximations for Sign and Compare

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Stabilization, Safety, and Security of Distributed Systems (SSS 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14310))

Abstract

Fully Homomorphic Encryption (FHE) is a prime candidate for designing privacy-preserving schemes due to its cryptographic security guarantees. For word-wise FHE schemes, often, the complex functions need to be approximated as low-order polynomials. Meanwhile, Artificial Neural Networks (ANN) are known for their ability to approximate arbitrary functions. This paper presents an ANN-based probabilistic polynomial approximation approach using a Perceptron with linear activation in our publicly available Python library. Our approach can be used to generate approximation polynomials with desired degree terms. We further provide third and seventh-degree approximations for univariate \(Sign(x) \in \{-1,0,1\}\) and \(Compare(a-b) \in \{0,\frac{1}{2},1\}\) functions in the intervals \([-1,1]\) and \([-5,-5]\). Finally, we empirically show that our polynomials improve up to 15% accuracy over Chebyshev’s.

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Authors and Affiliations

  1. Stevens Institute of Technology, Hoboken, NJ, 07030, USA

    Devharsh Trivedi

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  1. Devharsh Trivedi
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Correspondence to Devharsh Trivedi .

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Editors and Affiliations

  1. Ben-Gurion University of the Negev, Be'er-Sheva, Israel

    Shlomi Dolev

  2. New Jersey Institute of Technology, Newark, NJ, USA

    Baruch Schieber

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Trivedi, D. (2023). Brief Announcement: Efficient Probabilistic Approximations for Sign and Compare. In: Dolev, S., Schieber, B. (eds) Stabilization, Safety, and Security of Distributed Systems. SSS 2023. Lecture Notes in Computer Science, vol 14310. Springer, Cham. https://doi.org/10.1007/978-3-031-44274-2_21

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  • DOI: https://doi.org/10.1007/978-3-031-44274-2_21

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  • Online ISBN: 978-3-031-44274-2

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