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Recent Progress and Prospects for Integer Factorisation Algorithms

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Computing and Combinatorics (COCOON 2000)

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Abstract

The integer factorisation and discrete logarithm problems are of practical importance because of the widespread use of public key cryptosystems whose security depends on the presumed difficulty of solving these problems. This paper considers primarily the integer factorisation problem. In recent years the limits of the best integer factorisation algorithms have been extended greatly, due in part to Moore’s law and in part to algorithmic improvements. It is now routine to factor 100-decimal digit numbers, and feasible to factor numbers of 155 decimal digits (512 bits). We outline several integer factorisation algorithms, consider their suitability for implementation on parallel machines, and give examples of their current capabilities. In particular, we consider the problem of parallel solution of the large, sparse linear systems which arise with the MPQS and NFS methods.

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Author information

Authors and Affiliations

  1. Oxford University Computing Laboratory, Wolfson Building, Parks Road, Oxford, OX1 3QD, UK

    Richard P. Brent

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  1. Richard P. Brent
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Editors and Affiliations

  1. Department of Computer Science and Engineering, University of Minnesota, MN 55455, Minneapolis, USA

    Ding-Zhu Du

  2. Department of Computer Science and Software Engineering, University of Newcastle, Callaghan, NSW 2308, Australia

    Peter Eades  & Vladimir Estivill-Castro  & 

  3. School of Computer Science and Engineering, University of Newcastle, NSW 2052, Sydney, Australia

    Xuemin Lin  & Arun Sharma  & 

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Brent, R.P. (2000). Recent Progress and Prospects for Integer Factorisation Algorithms. In: Du, DZ., Eades, P., Estivill-Castro, V., Lin, X., Sharma, A. (eds) Computing and Combinatorics. COCOON 2000. Lecture Notes in Computer Science, vol 1858. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44968-X_2

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  • DOI: https://doi.org/10.1007/3-540-44968-X_2

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