Deterministic Interpolation of Sparse Black-box Multivariate Polynomials using Kronecker Type Substitutions

10/03/2017

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by   Qiao-Long Huang, et al.

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In this paper, we propose two new deterministic interpolation algorithms for a sparse multivariate polynomial given as a standard black-box by introducing new Kronecker type substitutions. Let f∈[x_1,...,x_n] be a sparse black-box polynomial with a degree bound D. When = or a finite field, our algorithms either have better bit complexity or better bit complexity in D than existing deterministic algorithms. In particular, in the case of deterministic algorithms for standard black-box models, our second algorithm has the current best complexity in D which is the dominant factor in the complexity.