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Faster polynomial multiplication over finite fields

Abstract : Let p be a prime, and let M_p(n) denote the bit complexity of multiplying two polynomials in F_p[X] of degree less than n. For n large compared to p, we establish the bound M_p(n)=O(n log n 8^(log^∗ n) log p), where log^∗ is the iterated logarithm. This is the first known Fürer-type complexity bound for F_p[X], and improves on the previously best known bound M_p(n)=O(n log n log log n log p).
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https://hal.archives-ouvertes.fr/hal-01022757
Contributor : Joris van der Hoeven <>
Submitted on : Wednesday, February 11, 2015 - 5:09:19 PM
Last modification on : Wednesday, November 18, 2020 - 10:32:03 PM
Long-term archiving on: : Saturday, September 12, 2015 - 11:02:02 AM

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  • HAL Id : hal-01022757, version 2

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David Harvey, Joris van der Hoeven, Grégoire Lecerf. Faster polynomial multiplication over finite fields. 2014. ⟨hal-01022757v2⟩

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