Advances in Cryptology — ASIACRYPT '91
Volume 739 of the series Lecture Notes in Computer Science pp 440449
Speeding up prime number generation
 Jorgen BrandtAffiliated withMathematical Institute, Aarhus University
 , Ivan DamgårdAffiliated withMathematical Institute, Aarhus University
 , Peter LandrockAffiliated withMathematical Institute, Aarhus University
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.
 Title
 Speeding up prime number generation
 Book Title
 Advances in Cryptology — ASIACRYPT '91
 Book Subtitle
 International Conference on the Theory and Application of Cryptology Fujiyosida, Japan, November 1991 Proceedings
 Pages
 pp 440449
 Copyright
 1993
 DOI
 10.1007/3540573321_37
 Print ISBN
 9783540573326
 Online ISBN
 9783540480662
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 739
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag
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 Editors
 Authors

 Jorgen Brandt ^{(1)}
 Ivan Damgård ^{(1)}
 Peter Landrock ^{(1)}
 Author Affiliations

 1. Mathematical Institute, Aarhus University, Ny Munkegade, DK 8000, Aarhus C, Denmark
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