Chapter

Advances in Cryptology — ASIACRYPT '91

Volume 739 of the series Lecture Notes in Computer Science pp 440-449

Date:

Speeding up prime number generation

  • Jorgen BrandtAffiliated withMathematical Institute, Aarhus University
  • , Ivan DamgårdAffiliated withMathematical Institute, Aarhus University
  • , Peter LandrockAffiliated withMathematical Institute, Aarhus University

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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.