The magic words are squeamish ossifrage

Extended abstract
  • Derek Atkins
  • Michael Graff
  • Arjen K. Lenstra
  • Paul C. Leyland
Conference paper

DOI: 10.1007/BFb0000440

Part of the Lecture Notes in Computer Science book series (LNCS, volume 917)
Cite this paper as:
Atkins D., Graff M., Lenstra A.K., Leyland P.C. (1995) The magic words are squeamish ossifrage. In: Pieprzyk J., Safavi-Naini R. (eds) Advances in Cryptology — ASIACRYPT'94. ASIACRYPT 1994. Lecture Notes in Computer Science, vol 917. Springer, Berlin, Heidelberg

Abstract

We describe the computation which resulted in the title of this paper. Furthermore, we give an analysis of the data collected during this computation. From these data, we derive the important observation that in the final stages, the progress of the double large prime variation of the quadratic sieve integer factoring algorithm can more effectively be approximated by a quartic function of the time spent, than by the more familiar quadratic function. We also present, as an update to [15], some of our experiences with the management of a large computation distributed over the Internet. Based on this experience, we give some realistic estimates of the current readily available computational power of the Internet. We conclude that commonly-used 512-bit RSA moduli are vulnerable to any organization prepared to spend a few million dollars and to wait a few months.

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Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Derek Atkins
    • 1
  • Michael Graff
    • 2
  • Arjen K. Lenstra
    • 3
  • Paul C. Leyland
    • 4
  1. 1.CambridgeUSA
  2. 2.Iowa State UniversityAmesUSA
  3. 3.MRE-2Q334, BellcoreMorristownUSA
  4. 4.Oxford University Computing ServicesOxfordUK

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