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Algorithms for Generating, Testing and Proving Primes: A Survey

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Cryptography and Computational Number Theory

Part of the book series: Progress in Computer Science and Applied Logic ((PCS,volume 20))

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Abstract

We survey methods of testing and proving primality and their implementation for generation of cryptographic primes. While discussing a wider variety of primality tests of theoretical or practical relevance, the focus is on criteria for practical use.

We give a new model for sources producing prime numbers with biased distributions and use it for measuring the security of biases against unknown attacks (adapted solutions to the discrete logarithm or integer factoring problems) which could make use of knowledge of the bias. Some results can be proved based solely upon the bias distribution, without prior knowledge of the attacks. Thus an important class of sources with polynomially bounded bias are secure in the sense that algorithms which can use the bias with a performance gain, can be turned into improvements to state of the art attacks in presence of uniform distributed sources.

The paper concludes with an overview of some outstanding schemes for generation of cryptographic primes. These are compared according to their performance and confidence of decision.

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Author information

Authors and Affiliations

  1. Institut für Wissenschaftliches Rechnen ETH, 8090, Zürich, Switzerland

    Preda Mihăilescu

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  1. Preda Mihăilescu
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Editor information

Editors and Affiliations

  1. Department of Computer Science, National University of Singapore, 2 Science Drive 2, 117543, Singapore

    Kwok-Yan Lam

  2. Department of Computing, Macquarie University, NSW, 2109, Australia

    Igor Shparlinski

  3. Department of Computer Science, University of Wollongong, NSW, 2522, Australia

    Huaxiong Wang

  4. Department of Mathematics, National University of Singapore, 2 Science Drive 2, 117543, Singapore

    Chaoping Xing

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Mihăilescu, P. (2001). Algorithms for Generating, Testing and Proving Primes: A Survey. In: Lam, KY., Shparlinski, I., Wang, H., Xing, C. (eds) Cryptography and Computational Number Theory. Progress in Computer Science and Applied Logic, vol 20. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8295-8_10

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  • DOI: https://doi.org/10.1007/978-3-0348-8295-8_10

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9507-1

  • Online ISBN: 978-3-0348-8295-8

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