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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... (Update)
Context of citations to this paper: More
...should refer to [16, 17, 19] for a general description of ECM, to [2, 23] for MPQS, and to [15, 13, 21] for NFS. A recent survey is [7]. The particular implementations of ECM by Brent and Montgomery are described in [6, 18] Table 3 shows the number of factors found by...
.... RSA keys are safe for the next 15 to 20 years, since both NFS relation collection and the NFS matrix step would be unfeasible (e.g. [4,21] and a NIST guideline draft [18] Our evaluation suggests that sieving can be achieved within one year at a cost of 10M (plus a one...
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3: Hardware to solve sparse systems of linear equations over GF (context) - Geiselmann, Steinwandt - 2003
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BibTeX entry: (Update)
R. P. Brent, Recent progress and prospects for integer factorisation algorithms, Computing and Combinatorics: Proc. Sixth Annual International Computing and Combinatorics Conference (Sydney, July 26-28, http://citeseer.ist.psu.edu/327036.html More
@article{ brent00recent,
author = "Richard P. Brent",
title = "Recent Progress and Prospects for Integer Factorisation Algorithms",
journal = "Lecture Notes in Computer Science",
volume = "1858",
pages = "3+",
year = "2000",
url = "citeseer.ist.psu.edu/327036.html" }
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