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Integer Factoring

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Encyclopedia of Cryptography and Security

Related Concepts

Factorization Circuits; Number Field Sieve for Factoring; Quadratic Sieve

Definition

Integer factoring is the following problem: given a positive composite integer n, find positive integers v and w, both greater than 1, such that \(n = v \cdot w\).

Background

Integer factoring is widely assumed to be a hard problem. Obviously, it is not hard for all composites, but composites for which it is believed to be difficult can easily be generated. This belief underlies the security of RSA public-key encryption and the RSA digital signature scheme . To the present day, no proof of the difficulty of factoring has been published. This is quite unlike the discrete logarithm problem , where the difficulty is provable for a generic group [19,  27].

However, this result does not have much practical relevance. In particular it does not say anything about the hardness of computing discrete logarithms in multiplicative groups of finite fields, a problem that is widely regarded as being...

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Author information

Authors and Affiliations

  1. Laboratory for cryptologic algorithms - LACAL, School of Computer and Communication Sciences, École Polytechnique Fédérale de Lausanne, Switzerland

    Arjen K. Lenstra (Prof.)

Authors
  1. Arjen K. Lenstra
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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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Lenstra, A.K. (2011). Integer Factoring. 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_455

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