Definition
A factor base is a set of values among which relations are constructed in certain algorithms for solving number theory–based problems.
Applications
The term factor base refers to the set of small prime numbers (and more generally, prime powers and irreducible polynomials) among which relations are constructed in various integer factoring algorithms (Sieving) as well as in certain algorithms for solving the discrete logarithm problem (Index Calculus).
The choice of factor base – and specifically the upper bound on the values in the factor base, called the smoothness bound – plays a crucial role in the time and hardware requirements for these algorithms. For further discussion, see smoothness.
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© 2011 Springer Science+Business Media, LLC
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Kaliski, B. (2011). Factor Base. In: van Tilborg, H.C.A., Jajodia, S. (eds) Encyclopedia of Cryptography and Security. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-5906-5_406
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DOI: https://doi.org/10.1007/978-1-4419-5906-5_406
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-5905-8
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