Speeding up prime number generation

  • Jorgen Brandt
  • Ivan Damgård
  • Peter Landrock
Conference paper

DOI: 10.1007/3-540-57332-1_37

Part of the Lecture Notes in Computer Science book series (LNCS, volume 739)
Cite this paper as:
Brandt J., Damgård I., Landrock P. (1993) Speeding up prime number generation. In: Imai H., Rivest R.L., Matsumoto T. (eds) Advances in Cryptology — ASIACRYPT '91. ASIACRYPT 1991. Lecture Notes in Computer Science, vol 739. Springer, Berlin, Heidelberg

Abstract

We present various ways of speeding up the standard methods for generating provable, resp. probable primes. For probable primes, the effect of using test division and 2 as a fixed base for the Rabin test is analysed, showing that a speedup of almost 50% can be achieved with the same confidence level, compared to the standard method. For Maurer's algorithm generating provable primes p, we show that a small extension of the algorithm will mean that only one prime factor of p−1 has to be generated, implying a gain in efficiency. Further savings can be obtained by combining with the Rabin test. Finally, we show how to combine the algorithms of Maurer and Gordon to make ”strong provable primes” that satisfy additional security constraints.

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Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • Jorgen Brandt
    • 1
  • Ivan Damgård
    • 1
  • Peter Landrock
    • 1
  1. 1.Mathematical InstituteAarhus UniversityAarhus CDenmark

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