Fast polynomial factorization over high algebraic extensions of finite fields

Erich Kaltofen, Victor Shoup

Research output: Contribution to conferencePaper

Abstract

New algorithms are presented for factoring polynomials of degree n over the finite field of q elements, where q is a power of 2. When log q = n1+a, where a>0 is constant, these algorithms are asymptotically faster than previous known algorithms, the fastest of which required time Ω(n(log q)2), or Ω(n3+2a) in this case, which corresponds to the cost of computing xq modulo an n degree polynomial. The new algorithms factor an arbitrary polynomial in time O(n3+a+1+o(1)+n2.69+1.69a). All measures are in fixed precision operations, that is in bit complexity. Moreover, in the special case where all the irreducible factors have the same degree, the new algorithms run in time O(n2.69+1.69a). In particular, one may test a polynomial for irreducibility in O(n2.69+1.69a) bit operations. These results generalize to the case where q = pk, where p is a small, fixed prime.

Original languageEnglish (US)
Pages184-188
Number of pages5
DOIs
StatePublished - 1997
EventProceedings of the 1997 22nd International Symposium on Symbolic and Algebraic Computation, ISSAC - Maui, HI, USA
Duration: Jul 21 1997Jul 23 1997

Other

OtherProceedings of the 1997 22nd International Symposium on Symbolic and Algebraic Computation, ISSAC
CityMaui, HI, USA
Period7/21/977/23/97

ASJC Scopus subject areas

  • Mathematics(all)

Fingerprint Dive into the research topics of 'Fast polynomial factorization over high algebraic extensions of finite fields'. Together they form a unique fingerprint.

  • Cite this

    Kaltofen, E., & Shoup, V. (1997). Fast polynomial factorization over high algebraic extensions of finite fields. 184-188. Paper presented at Proceedings of the 1997 22nd International Symposium on Symbolic and Algebraic Computation, ISSAC, Maui, HI, USA, . https://doi.org/10.1145/258726.258777