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## Faster polynomial multiplication over finite fields

David Harvey
• Function : Author
• PersonId : 958313
Joris van Der Hoeven
Grégoire Lecerf

#### 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).

### Dates and versions

hal-01022757 , version 1 (15-07-2014)
hal-01022757 , version 2 (11-02-2015)

### Identifiers

• HAL Id : hal-01022757 , version 2

### Cite

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

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