Skip to main content

Achieving superlinear speedups for the multiple polynomial quadratic sieve factoring algorithm on a distributed memory multiprocessor

  • Algorithmic Studies For Hypercube-Type Systems
  • Conference paper
  • First Online:
CONPAR 90 — VAPP IV (VAPP 1990, CONPAR 1990)

Abstract

We first study the parallelization of the MPQS factoring algorithm for a distributed memory multiprocessor. We then propose a solution ensuring no communications during the sieve phase through a new distribution strategy of the polynomials. We derive an implementation on the FPS T40 hypercube. We compare various distribution strategy and show how we can achieve superlinear speedups.

This work has been partially supported by the Coordinated Research Program C3 of the French CNRS and DRET

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. T. R. CARON, D. SILVERMAN, "Parallel Implementation of the Quadratic Sieve", The Journal of Supercomputing, 1, 1988, pp. 273–290.

    Google Scholar 

  2. M. COSNARD, B. TOURANCHEAU, G. VILLARD, "Gaussian Elimination on Message Passing Architectures", Proceedings of ICS 1987, Athens, 1987, Springer Verlag.

    Google Scholar 

  3. J. DAVIS, D. HOLDRIDGE, "Factorization of Large Integers on a Massively Parallel Computer", Eurocrypt '88 Abstracts, IACR, 1988, pp. 235–243.

    Google Scholar 

  4. J. DAVIS, D. HOLDRIDGE, G. J. SIMMONS, "Status Report on Factoring", Proceedings of EuroCrypto 84, LCNS.

    Google Scholar 

  5. J. GERVER, "Factoring Large Numbers with a Quadratic Sieve", Math. Comp., Vol. 41, 1983, pp. 287–294.

    Google Scholar 

  6. M. KRAITCHIK, "Théorie des nombres. Tome II", Gauthier-Villars, Paris, 1926.

    Google Scholar 

  7. A. K. LENSTRA, M. S. MANASSE, "Factoring by electronic mail", Proceedings Eurocrypt '89, 1989.

    Google Scholar 

  8. D. PARKINSON, M. WUNDERLICH, "A Compact Algorithm for Gaussian Elimination over GF(2) Implemented on Highly Parallel Computers", Parallel Computing, 1984, pp. 65–73.

    Google Scholar 

  9. C. POMERANCE, "Analyis and Comparison of some Integer Factoring Algorithms", in "Comput. Methods in Num. Th." (H.W. Lenstra, J. and R. Tijdeman, eds), Math. Cent. Tr., no 154, Part I, Amsterdam, 1982, pp. 65–73.

    Google Scholar 

  10. C. POMERANCE, "The Quadratic Sieve Factoring Algorithm", Advances in Cryptology (T. Beth, N. Cot and I. Ingemarrson, eds), LNCS, 209, Springer Verlag, 1985, pp. 169–182.

    Google Scholar 

  11. C. POMERANCE, J. W. SMITH, R. TULER, "A Pipeline Architecture for Factoring Large Integers with the Quadratic Sieve Factoring Algorithm", SIAM J. Comput., Vol. 17, no 2, April 1988, pp. 387–403.

    Google Scholar 

  12. H. J. J. TE RIELE, W. M. LIOEN, D. T. WINTER, "Factoring with the Quadratic Sieve on Large Vector Computers", Report NM-R8805, Centrum voor Wiskunde en Informatica, Amsterdam, 1988.

    Google Scholar 

  13. J. L. ROCH, "Calcul Formel et Parallélisme. L'Architecture du Système PaC et son Arithmétique Rationnelle", Thesis, Grenoble, december 1989.

    Google Scholar 

  14. R. D. SILVERMAN, "The Multiple Polynomial Quadratic Sieve", Math. of Comp., Vol. 48, no 177, January 1987, pp. 329–339.

    Google Scholar 

  15. D. H. WIEDEMAN, "Solving sparse linear equations over finite fields", IEEE Trans. Inform. Theory, IT-32, 1986, pp. 54–62.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Helmar Burkhart

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Cosnard, M., Philippe, JL. (1990). Achieving superlinear speedups for the multiple polynomial quadratic sieve factoring algorithm on a distributed memory multiprocessor. In: Burkhart, H. (eds) CONPAR 90 — VAPP IV. VAPP CONPAR 1990 1990. Lecture Notes in Computer Science, vol 457. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-53065-7_161

Download citation

  • DOI: https://doi.org/10.1007/3-540-53065-7_161

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53065-7

  • Online ISBN: 978-3-540-46597-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics