Straight-line complexity and integer factorization

  • Richard J. Lipton
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 877)


We show that if polynomials with many rational roots have polynomial length straight-line complexity, then integer factorization is “easy”.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    N. Biggs. Algebraic Graph Theory. Cambridge University Press, 1974.Google Scholar
  2. 2.
    A. Borodin, private communication, 1994.Google Scholar
  3. 3.
    A. Borodin and S. Cook. On the Number of Additions to Compute Specific Polynomials. SIAM Journal of Computing, (5):7–15, 1976.Google Scholar
  4. 4.
    Manuel Blum, Paul Feldman, and Silvio Micali. Non-Interactive Zero-Knowledge and Its Applications. In Proceedings of the 20th Annual ACM Symposium on the Theory of Computing, pages 103–112, 1988.Google Scholar
  5. 5.
    D. Bressound. Factorization and Primality Testing. Springer-Verlag, 1989.Google Scholar
  6. 6.
    Joan Feigenbaum and Michael Merritt. Distributed Computing and Cryptography. DIMACS Workshop Series, 1989.Google Scholar
  7. 7.
    Erich Kaltofen. Computing with Polynomials Given by Straight-Line Programs II Sparse Factorization. In Proceedings of the 26th IEEE Symposium on Foundations of Computer Science, pages 451–458, 1985.Google Scholar
  8. 8.
    Erich Kaltofen. Uniform Closure Properties of P-Computable Functions. In Proceedings of the 18th Annual ACM Symposium on the Theory of Computing, pages 330–337, 1986.Google Scholar
  9. 9.
    Erich Kaltofen. Single-Factor Hensel Lifting and Its Application to the Straight-Line Complexity of Certain Polynomials. In Proceedings of the 19th Annual ACM Symposium on the Theory of Computing, pages 443–452, 1987.Google Scholar
  10. 10.
    Serge Lang. Algebra. Addison-Wesley, 1984.Google Scholar
  11. 11.
    Richard J. Lipton. Polynomials with 0–1 Coefficients that are Hard to Evaluate. SIAM Journal of Computing, 7(1):61–69, 1978.Google Scholar
  12. 12.
    Richard J. Lipton and Larry J. Stockmeyer. Evaluation of Polynomials with Super Preconditioning. Technical Report, IBM Thomas J. Watson Research Center, 1976.Google Scholar
  13. 13.
    Jean-Jacques Risler. Some Aspects of Complexity in Real Algebraic Geometry. Journal of Symbolic Computation, 5, 1988.Google Scholar
  14. 14.
    R.C. Read and W.T. Tutte. Chromatic Polynomials, in Selected Topics in Graph Theory, Academic Press, 1988.Google Scholar
  15. 15.
    Jean-Paul Van de Wiele. An Optimal Lower Bound on the Number of Total Operations to Compute 0–1 Polynomials Over the Field of Complex Numbers. In Proceedings of the 19th IEEE Symposium on Foundations of Computer Science, pages 159–165, 1978.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Richard J. Lipton
    • 1
  1. 1.Department of Computer SciencePrinceton UniversityPrinceton

Personalised recommendations