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Encyclopedia of Cryptography and Security pp 867–873Cite as

Number Field Sieve for the DLP

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Synonyms

Number field sieve

Related Concepts

Discrete Logarithm Problem; Function Field Sieve; Generic Attacks Against DLP; Index Calculus; Integer Factoring; Number Field Sieve for Factoring; Sieving in Function Fields

Definition

The number field sieve for the discrete logarithm problem, or nfs-dlp, is a family of algorithms for computing the discrete logarithms problem in the multiplicative group of finite fields \({\mathbb{F}}_{q}^{{_\ast}}\) which make use of the representation of \({\mathbb{F}}_{q}\) as residue fields in number fields. These are the fastest known methods for finite fields of large characteristic, in the general case where the fields do not have extra properties.

Most nfs-dlp algorithms are heuristic algorithms. More precisely, their complexity analysis requires a heuristic assumption about the probability of simultaneous smoothness of related numbers. In particular, all the fast \({L}_{q}(1/3)\) algorithms are heuristic (Refer the entry L-Notation) and the only...

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Author information

Authors and Affiliations

  1. Laboratoire Prism, Universit de Versailles Saint-Quentin-en-Yvelines, 45 avenue des Etats-Unis, 78035, Versailles Cedex, France

    Antoine Joux (Professor)

  2. Institut de recherche mathématique de Rennes, Université de Rennes 1, Campus de Beaulieu, F-35042, Rennes Cedex, France

    Reynald Lercier (Professor)

Authors
  1. Antoine Joux
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  2. Reynald Lercier
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Editor information

Editors and Affiliations

  1. Department of Mathematics and Computing Science, Eindhoven University of Technology, 5600 MB, Eindhoven, The Netherlands

    Henk C. A. van Tilborg

  2. Center for Secure Information Systems, George Mason University, Fairfax, VA, 22030-4422, USA

    Sushil Jajodia

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Joux, A., Lercier, R. (2011). Number Field Sieve for the DLP. 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_834

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