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Point-Counting Method for Embarrassingly Parallel Evaluation in Secure Computation

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Foundations and Practice of Security (FPS 2015)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 9482))

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Abstract

In this paper we propose an embarrassingly parallel method for use in secure computation. The method can be used for a special class of functions over real numbers - namely, for functions f for which there exist functions g and h such that \(g(f(x),x)=h(x)\) and \(g(\cdot ,x)\) is monotonous. These functions include \(f(x)=\frac{1}{x}\) and \(f(x)=\sqrt{x}\), but also the logarithm function or any function that can be represented as finding a root of a polynomial with secret coefficients and a sufficiently low rank. The method relies on counting techniques rather than evaluation of series, allowing the result to be obtained using less rounds of computations with the price of more communication in one round. Since the complexity of oblivious computing methods (like secret-shared multi-party computations (SMC)) is largely determined by the round complexity, this approach has a potential to give better performance/precision ratio compared to series-based approaches. We have implemented the method for several functions and benchmarked them using Sharemind SMC engine.

This research was supported by the European Regional Development Fund through Centre of Excellence in Computer Science (EXCS) and the Estonian Research Council under Institutional Research Grant IUT27-1 and Estonian Doctoral School in Information and Communication Technologies.

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Notes

  1. 1.

    http://sharemind.cyber.ee/.

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Author information

Authors and Affiliations

  1. Cybernetica, Ãœlikooli 2, Tartu, Estonia

    Jan Willemson

  2. Institute of Computer Science, University of Tartu, Liivi 2, Tartu, Estonia

    Toomas Krips

  3. STACC, Ãœlikooli 2, Tartu, Estonia

    Toomas Krips & Jan Willemson

Authors
  1. Toomas Krips
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  2. Jan Willemson
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Correspondence to Toomas Krips .

Editor information

Editors and Affiliations

  1. Télécom SudParis, Evry, France

    Joaquin Garcia-Alfaro

  2. School of Computer Science, Carleton University, Ottawa, Ontario, Canada

    Evangelos Kranakis

  3. École des Mines de Nancy, Université de Lorraine, Nancy Cedex, France

    Guillaume Bonfante

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Krips, T., Willemson, J. (2016). Point-Counting Method for Embarrassingly Parallel Evaluation in Secure Computation . In: Garcia-Alfaro, J., Kranakis, E., Bonfante, G. (eds) Foundations and Practice of Security. FPS 2015. Lecture Notes in Computer Science(), vol 9482. Springer, Cham. https://doi.org/10.1007/978-3-319-30303-1_5

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  • DOI: https://doi.org/10.1007/978-3-319-30303-1_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-30302-4

  • Online ISBN: 978-3-319-30303-1

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