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Number Theory

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Encyclopedia of Cryptography and Security

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Notes

  1. 1.

    The difference between a primality test and a primality proving algorithm is that a proof is never wrong, while a test has a small chance of error.

  2. 2.

    Proper implementation is a subject in its own right. It is not trivial to do everything right, and the slightest mistake could entirely defeat the security.

  3. 3.

    The quadratic sieve evolved from Schroeppel's linear sieve, and Kraitchik had independently invented a similar algorithm many years earlier. See integer factoring and the quadratic sieve for details on each person's contribution.

  4. 4.

    If the number is a product of two primes that are equal in size, then it is asymptotically the same as the quadratic sieve in run time. Otherwise, it is better.

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Authors
  1. Scott Contini
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Editors and Affiliations

  1. Eindhoven University of Technology, Eindhoven, The Netherlands

    Henk C. A. van Tilborg

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Contini, S. (2005). Number Theory. In: van Tilborg, H.C.A. (eds) Encyclopedia of Cryptography and Security. Springer, Boston, MA . https://doi.org/10.1007/0-387-23483-7_282

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