New algorithms for finding irreducible polynomials over finite fields

  • Authors:

  • V. Shoup

  • Affiliations:

  • Dept. of Comput. Sci., Wisconsin Univ., Madison, WI, USA

  • Venue:
  • SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
  • Year:
  • 1988

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Abstract

An algorithm is presented for finding an irreducible polynomial of specified degree over a finite field. It is deterministic and runs in polynomial time for fields of small characteristics. A proof is given of the stronger result, that the problem of finding irreducible polynomials of specified degree over a finite field K is deterministic-polynomial-time reducible to the problem of factoring polynomials over the prime field of K.