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On the Combined Fermat/Lucas Probable Prime Test⋆

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Book cover Cryptography and Coding (Cryptography and Coding 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1746))

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Abstract

Based on the well-known Baillie/Wagstaff suggestion [2] we introduce a rapid pseudoprimality test with high confidence. The test is extremely fast and only requires evaluation of power polynomials and the Lucas V -sequence. This is in contrast to the original version, where usually the more cumbersome evaluation of the Lucas U-sequence is required as well. We analyze the underlying properties of the proposed test and give a characterization of the pseudoprimes. Software and hardware evaluation methods for both modular exponentiation and evaluation of recursion sequences are widely employed and very efficient. Therefore the test can be run at low cost for varieties of different bases/parameters. The number of those that pass the test are of great interest. We exhibit the exact number of these “liars”.

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Author information

Authors and Affiliations

  1. Dept. of Math., University of Klagenfurt, A, 9020, Klagenfurt, Austria

    Siguna Müller

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  1. Siguna Müller
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Editors and Affiliations

  1. Vodafone Limited, The Courtyard, 2-4 London Road Newbury, Berkshire, RG14 1JX, UK

    Michael Walker

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© 1999 Springer-Verlag Berlin Heidelberg

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Müller, S. (1999). On the Combined Fermat/Lucas Probable Prime Test⋆. In: Walker, M. (eds) Cryptography and Coding. Cryptography and Coding 1999. Lecture Notes in Computer Science, vol 1746. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46665-7_26

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  • DOI: https://doi.org/10.1007/3-540-46665-7_26

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66887-9

  • Online ISBN: 978-3-540-46665-9

  • eBook Packages: Springer Book Archive

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