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Revisit Sparse Polynomial Interpolation Based on Randomized Kronecker Substitution

  • Qiao-Long Huang
  • Xiao-Shan GaoEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, 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.

Keywords

Randomized Kronecker substitution Sparse polynomial interpolation Black-box Finite field Monte Carlo algorithm 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.KLMM, UCAS, Academy of Mathematics and Systems Science Chinese Academy of SciencesBeijingChina
  2. 2.Cheriton School of Computer ScienceUniversity of WaterlooWaterlooCanada

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