Fast polynomial factorization over high algebraic extensions of finite fields

Erich Kaltofen, Victor Shoup

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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)
Title of host publicationProceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC
PublisherACM
Pages184-188
Number of pages5
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

Fingerprint

Factorization
Polynomials
Costs

ASJC Scopus subject areas

  • Computer Science(all)

Cite this

Kaltofen, E., & Shoup, V. (1997). Fast polynomial factorization over high algebraic extensions of finite fields. In Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC (pp. 184-188). ACM.

Fast polynomial factorization over high algebraic extensions of finite fields. / Kaltofen, Erich; Shoup, Victor.

Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC. ACM, 1997. p. 184-188.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Kaltofen, E & Shoup, V 1997, Fast polynomial factorization over high algebraic extensions of finite fields. in Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC. ACM, pp. 184-188, Proceedings of the 1997 22nd International Symposium on Symbolic and Algebraic Computation, ISSAC, Maui, HI, USA, 7/21/97.
Kaltofen E, Shoup V. Fast polynomial factorization over high algebraic extensions of finite fields. In Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC. ACM. 1997. p. 184-188
Kaltofen, Erich ; Shoup, Victor. / Fast polynomial factorization over high algebraic extensions of finite fields. Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC. ACM, 1997. pp. 184-188
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