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International Workshop on Computer Algebra in Scientific Computing

CASC 2019: Computer Algebra in Scientific Computing pp 215–235Cite as

Revisit Sparse Polynomial Interpolation Based on Randomized Kronecker Substitution

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11661))

Abstract

In this paper, a new reduction based interpolation algorithm for general black-box multivariate polynomials over finite fields is given. The method is based on two main ingredients. A new Monte Carlo method is given to reduce the black-box multivariate polynomial interpolation problem to the black-box univariate polynomial interpolation problem over any ring. The reduction algorithm leads to multivariate interpolation algorithms with better or the same complexities in most cases when combining with various univariate interpolation algorithms. A modified univariate Ben-Or and Tiwari algorithm over the finite field is proposed, which has better total complexity than the Lagrange interpolation algorithm. Combining our reduction method and the modified univariate Ben-Or and Tiwari algorithm, we give a Monte Carlo multivariate interpolation algorithm, which has better total complexity in most cases for sparse interpolation of black-box polynomial over finite fields.

Partially supported by an NSFC grant No.11688101.

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Author information

Authors and Affiliations

  1. KLMM, UCAS, Academy of Mathematics and Systems Science Chinese Academy of Sciences, Beijing, China

    Qiao-Long Huang & Xiao-Shan Gao

  2. Cheriton School of Computer Science, University of Waterloo, Waterloo, ON, Canada

    Qiao-Long Huang

Authors
  1. Qiao-Long Huang
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  2. Xiao-Shan Gao
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Corresponding author

Correspondence to Xiao-Shan Gao .

Editor information

Editors and Affiliations

  1. Coventry University, Coventry, UK

    Matthew England

  2. University of Kassel, Kassel, Germany

    Wolfram Koepf

  3. Plekhanov Russian University of Economics, Moscow, Russia

    Timur M. Sadykov

  4. University of Kassel, Kassel, Germany

    Werner M. Seiler

  5. Russian Academy of Sciences, Novosibirsk, Russia

    Evgenii V. Vorozhtsov

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Huang, QL., Gao, XS. (2019). Revisit Sparse Polynomial Interpolation Based on Randomized Kronecker Substitution. In: England, M., Koepf, W., Sadykov, T., Seiler, W., Vorozhtsov, E. (eds) Computer Algebra in Scientific Computing. CASC 2019. Lecture Notes in Computer Science(), vol 11661. Springer, Cham. https://doi.org/10.1007/978-3-030-26831-2_15

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  • DOI: https://doi.org/10.1007/978-3-030-26831-2_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-26830-5

  • Online ISBN: 978-3-030-26831-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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