Polynomial multiplication over finite fields in time O(n log n)

Abstract : Assuming a widely-believed hypothesis concerning the least prime in an arithmetic progression, we show that two n-bit integers can be multiplied in time O(n log n) on a Turing machine with a finite number of tapes; we also show that polynomials of degree less than n over a finite field F_q with q elements can be multiplied in time O(n log q log(n log q)), uniformly in q.
Complete list of metadatas

https://hal.archives-ouvertes.fr/hal-02070816
Contributor : Joris van der Hoeven <>
Submitted on : Monday, March 18, 2019 - 11:38:16 AM
Last modification on : Friday, April 12, 2019 - 1:31:47 AM
Long-term archiving on : Wednesday, June 19, 2019 - 1:55:37 PM

File

ffnlogn.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-02070816, version 1

Collections

Citation

David Harvey, Joris van der Hoeven. Polynomial multiplication over finite fields in time O(n log n). 2019. ⟨hal-02070816⟩

Share

Metrics

Record views

1054

Files downloads

1091