Sparse Interpolation of Black-box Multivariate Polynomials using Kronecker Type Substitutions
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In this paper, we give two new deterministic interpolation algorithms for black-box multivariate polynomials. For a t-sparse and n-variate polynomial f with a degree bound D and a term bound T, we show that at least half of the terms of f can be recovered from the univariate polynomials obtained from f by three types of Kronecker substitutions. We then give a criterion to check whether these terms really belong to f. Repeat the above procedure for at most log(t) times, f can be recovered. The algorithm has better complexity in D than existing deterministic algorithms when the coefficients are from Q, and has better complexities in T and D and the same complexity in n when the coefficients are from a finite field.
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