Faster polynomial multiplication over finite fields
Computational Complexity
2014-07-15 v1 Symbolic Computation
Number Theory
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 F\"urer-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).
Keywords
Cite
@article{arxiv.1407.3361,
title = {Faster polynomial multiplication over finite fields},
author = {David Harvey and Joris van der Hoeven and Grégoire Lecerf},
journal= {arXiv preprint arXiv:1407.3361},
year = {2014}
}