Rotations and Translations of Number Field Sieve Polynomials

  • Jason E. Gower
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2894)

Abstract

We present an algorithm that finds polynomials with many roots modulo many primes by rotating candidate Number Field Sieve polynomials using the Chinese Remainder Theorem. We also present an algorithm that finds a polynomial with small coefficients among all integral translations of X of a given polynomial in ℤ[X]. These algorithms can be used to produce promising candidate Number Field Sieve polynomials.

Keywords

Minimal Size Error Message Chinese Remainder Theorem Distinct Root Root Property 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Lenstra, A.K., Lenstra Jr., H.W. (eds.): The Development of the Number Field Sieve. Lecture Notes in Mathematics, vol. 1554. Springer, Berlin (1993)MATHGoogle Scholar
  2. 2.
    Murphy, B.: Polynomial Selection for the Number Field Sieve Integer Factorisation Algorithm. PhD thesis, Australian National University (July 1999)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Jason E. Gower
    • 1
  1. 1.CERIAS and Department of MathematicsPurdue UniversityWest LafayetteUSA

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