Fast interpolation of multivariate polynomials with sparse exponents

Abstract

Consider a sparse multivariate polynomial f with integer coefficients. Assume that f is represented as a “modular black box polynomial”, e.g. via an algorithm to evaluate f at arbitrary integer points, modulo arbitrary positive integers. The problem of sparse interpolation is to recover f in its usual sparse representation, as a sum of coefficients times monomials. For the first time we present a quasi-optimal algorithm for this task in term of the product of the number of terms of f by the maximum of the bit-size of the terms of f.