Faster Sparse Multivariate Polynomial Interpolation of Straight-Line Programs

TL;DR

This paper introduces a faster algorithm for sparse multivariate polynomial interpolation of straight-line programs, especially effective with many variables and large degrees, improving upon previous methods.

Contribution

The authors develop a new algorithm that enhances the efficiency of sparse polynomial interpolation over finite fields, particularly in high-variable scenarios.

Findings

Algorithm is competitive with existing methods.

Significant speedup for polynomials with many variables.

Effective for polynomials with large degrees and few nonzero terms.

Abstract

Given a straight-line program whose output is a polynomial function of the inputs, we present a new algorithm to compute a concise representation of that unknown function. Our algorithm can handle any case where the unknown function is a multivariate polynomial, with coefficients in an arbitrary finite field, and with a reasonable number of nonzero terms but possibly very large degree. It is competitive with previously known sparse interpolation algorithms that work over an arbitrary finite field, and provides an improvement when there are a large number of variables.