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Factoring Integers Using SIMD Sieves

  • Brandon Dixon
  • Arjen K. Lenstra
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 765)

Abstract

We describe our single-instruction multiple data (SIMD) implementation of the multiple polynomial quadratic sieve integer factoring algorithm. On a 16K MasPar massively parallel computer, our implementation can factor 100 digit integers in a few days. Its most notable success was the factorization of the 110-digit RSA-challenge number, which took about a month.

Keywords

Data Security Corporation Trial Division Small Subinterval Practical Remark Index Modulo 
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.
    Bernstein, D. J., Lenstra, A. K.: A general number field sieve implementation (to appear)Google Scholar
  2. 2.
    Caron, T. R., Silverman, R. D.: Parallel implementation of the quadratic sieve. J. Supercomputing 1 (1988) 273–290CrossRefGoogle Scholar
  3. 3.
    Davis, J. A., Holdridge, D. B.: Factorization using the quadratic sieve algorithm. Tech. Report SAND 83-1346, Sandia National Laboratories, Albuquerque, NM, 1983Google Scholar
  4. 4.
    Dixon, B., Lenstra, A.K.: Massively parallel elliptic curve factoring. Advances in Cryptology, Eurocrypt’92, Lecture Notes in Comput. Sci. 658 (1993) 183–193Google Scholar
  5. 5.
    Gjerken, A.: Faktorisering og parallel prosessering (in norwegian), Bergen, 1992Google Scholar
  6. 6.
    Lenstra, A. K.: Massively parallel computing and factoring. Proceedings Latin’92, Lecture Notes in Comput. Sci. 583 (1992) 344–355Google Scholar
  7. 7.
    Lenstra, A. K., Lenstra, H.W., Jr.: Algorithms in number theory. Chapter 12 in: van Leeuwen, J. (ed.): Handbook of theoretical computer science. Volume A, Algorithms and complexity. Elsevier, Amsterdam, 1990Google Scholar
  8. 8.
    Lenstra, A. K., Lenstra, H. W., Jr., Manasse, M. S., Pollard, J. M.: The factorization of the ninth Fermat number. Math. Comp. 61 (1993) (to appear)Google Scholar
  9. 9.
    Lenstra, A.K., Manasse, M.S.: Factoring by electronic mail. Advances in Cryptology, Eurocrypt’ 89, Lecture Notes in Comput. Sci. 434 (1990) 355–371Google Scholar
  10. 10.
    Lenstra, A. K., Manasse, M.S.: Factoring with two large primes. Math. Comp. (to appear)Google Scholar
  11. 11.
    MasPar MP-1 principles of operation. MasPar Computer Corporation, Sunnyvale, CA, 1989Google Scholar
  12. 12.
    Pomerance, C: Analysis and comparison of some integer factoring algorithms. 89–139 in: Lenstra, H. W., Jr., Tijdeman, R. (eds): Computational methods in number theory. Math. Centre Tracts 154/155, Mathematisch Centrum, Amsterdam, 1983Google Scholar
  13. 13.
    Pomerance, C, Smith, J. W., Tuler, R.: A pipeline architecture for factoring large integers with the quadratic sieve algorithm. SIAM J. Comput. 17 (1988) 387–403zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    te Riele, H., Lioen, W., Winter, D.: Factorization beyond the googol with mpqs on a single computer. CWI Quarterly 4 (1991) 69–72zbMATHMathSciNetGoogle Scholar
  15. 15.
    RSA Data Security Corporation Inc., sci.crypt, May 18, 1991; information available by sending electronic mail to challenge-rsa-list@rsa.comGoogle Scholar
  16. 16.
    Silverman, R. D.: The multiple polynomial quadratic sieve. Math. Comp. 84 (1987) 327–339Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Brandon Dixon
    • 1
  • Arjen K. Lenstra
    • 2
  1. 1.Department of Computer SciencePrinceton UniversityPrincetonUSA
  2. 2.Room MRE-2Q334BellcoreMorristownUSA

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