A new deterministic algorithm for sparse multivariate polynomial interpolation

We present a deterministic algorithm to interpolate an m-sparse n-variate polynomial which uses poly(n, m, log H, log d) bit operations. Our algorithm works over the integers. Here H is a bound on the magnitude of the coefficient values of the given polynomial. The degree of given polynomial is bounded by d and m is upper bound on number of monomials. This running time is polynomial in the output size. Our algorithm only requires modular black box access to the given polynomial, as introduced in [12]. As an easy consequence, we obtain an algorithm to interpolate polynomials represented by arithmetic circuits.