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Polynomial Multiplication over Finite Fields in Time O(n logn).
- Source :
- Journal of the ACM; Mar2022, Vol. 69 Issue 2, p1-40, 40p
- Publication Year :
- 2022
-
Abstract
- Assuming a widely believed hypothesis concerning the least prime in an arithmetic progression, we show that polynomials of degree less than n over a finite field F<subscript>q</subscript> with q elements can be multiplied in time O(n logq log(n logq)), uniformly in q. Under the same hypothesis, we show how to multiply two n-bit integers in time O(n logn); this algorithm is somewhat simpler than the unconditional algorithm from the companion paper [22]. Our results hold in the Turing machine model with a finite number of tapes. [ABSTRACT FROM AUTHOR]
- Subjects :
- TURING machines
ARITHMETIC series
MULTIPLICATION
POLYNOMIALS
INTEGERS
FINITE fields
Subjects
Details
- Language :
- English
- ISSN :
- 00045411
- Volume :
- 69
- Issue :
- 2
- Database :
- Complementary Index
- Journal :
- Journal of the ACM
- Publication Type :
- Academic Journal
- Accession number :
- 156015352
- Full Text :
- https://doi.org/10.1145/3505584