Unformatted text preview: of this algorithm is called the double large prime variation of the multiple polynomial quadratic sieve. Elliptic curve method (ECM) [957,1112,1113]. This method has been used to find 43digit factors, but nothing larger. Pollard’s Monte Carlo algorithm [1254,248]. (This algorithm also appears in volume 2, page 370 of Knuth [863].) Continued fraction algorithm. See [1123,1252,863]. This algorithm isn’t even in the running. Trial division. This is the oldest factoring algorithm and consists of testing every prime number less than or equal to the square root of the candidate number. Previous Table of Contents Next Products  Contact Us  About Us  Privacy  Ad Info  Home Use of this site is subject to certain Terms & Conditions, Copyright © 19962000 EarthWeb Inc. All rights reserved. Reproduction whole or in part in any form or medium without express written permission of EarthWeb is prohibited. Read EarthWeb's privacy statement. To access the contents, click the chapter and section titles. Applied Cryptography, Second Edition: Protocols, Algorthms, and Source Code in C (cloth)
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Brief Full Advanced Search Search Tips (Publisher: John Wiley & Sons, Inc.) Author(s): Bruce Schneier ISBN: 0471128457 Publication Date: 01/01/96 Search this book:
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 See [251] for a good introduction to these different factoring algorithms, except for the NFS. The best discussion of the NFS is [953]. Other, older references are [505, 1602, 1258]. Information on parallel factoring can be found in [250]. If n is the number being factored, the fastest QS variants have a heuristic asymptotic run time of: e(1+ 0(1))(ln (n))(1/2)(ln (ln (n)))(1/2) The NFS is much faster, with a heuristic asymptotic time estimate of: e(1.923+ 0(1))(ln (n))(1/3)(ln (ln (n)))(2/3) In 1970, the big news was the factoring of a 41digit hard number [1123]. (A “hard” number is one that does not have any small factors and is not of a special form that allows it to be factored more easily.) Ten years later, factoring hard numbers twice tha...
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