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Conference Papers Year : 2020

Essentially optimal sparse polynomial multiplication

Pascal Giorgi
Bruno Grenet
Armelle Perret Du Cray
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We present a probabilistic algorithm to compute the product of two univariate sparse polynomials over a field with a number of bit operations that is quasi-linear in the size of the input and the output. Our algorithm works for any field of characteristic zero or larger than the degree. We mainly rely on sparse interpolation and on a new algorithm for verifying a sparse product that has also a quasi-linear time complexity. Using Kronecker substitution techniques we extend our result to the multivariate case.
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Dates and versions

hal-02476609 , version 1 (13-05-2020)
hal-02476609 , version 2 (31-08-2020)



Pascal Giorgi, Bruno Grenet, Armelle Perret Du Cray. Essentially optimal sparse polynomial multiplication. ISSAC 2020 - 45th International Symposium on Symbolic and Algebraic Computation, Jul 2020, Kalamata, Greece. pp.202-209, ⟨10.1145/3373207.3404026⟩. ⟨hal-02476609v2⟩
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