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arXiv · 2402.10139

Fast interpolation and multiplication of unbalanced polynomials

Pascal Giorgi·Bruno Grenet·Armelle Perret du Cray·Daniel S. Roche
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Abstract

We consider the classical problems of interpolating a polynomial given a black box for evaluation, and of multiplying two polynomials, in the setting where the bit-lengths of the coefficients may vary widely, so-called unbalanced polynomials. Writing s for the total bit-length and D for the degree, our new algorithms have expected running time $\tilde{O}(s \log D)$, whereas previous methods for (resp.) dense or sparse arithmetic have at least $\tilde{O}(sD)$ or $\tilde{O}(s^2)$ bit complexity.

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Pascal Giorgi, Bruno Grenet, Armelle Perret du Cray, Daniel S. Roche. 2024-02-15. Fast interpolation and multiplication of unbalanced polynomials. https://doi.org/10.1145/3666000.3669717

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