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applied cryptography - protocols, algorithms, and source code in c

Here are some assumptions from 66 we believe that we

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Unformatted text preview: of distributed implementation. 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 © 1996-2000 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) Go! Keyword 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: Go! Previous Table of Contents Next ----------- The picture gets even worse. A new factoring algorithm has taken over from the quadratic sieve: the general number field sieve. In 1989 mathematicians would have told you that the general number field sieve would never be practical. In 1992 they would have told you that it was practical, but only faster than the quadratic sieve for numbers greater than 130 to 150 digits or so. Today it is known to be faster than the quadratic sieve for numbers well below 116 digits [472,635]. The general number field sieve can factor a 512-bit number over 10 times faster than the quadratic sieve. The algorithm would require less than a year to run on an 1800-node Intel Paragon. Table 7.4 gives the number of mips-years required to factor numbers of different sizes, given current implementations of the general number field sieve [1190]. Table 7.3 Factoring Using the Quadratic Sieve Year 1983 1985 1988 1989 1993 1994 # of decimal digits factored 71 80 90 100 120 129 How many times harder to factor a 512-bit number >20 million >2 million 250,000 30,000 500 100 And the general number field sieve is still getting faster. Mathematicians keep coming up with new tricks, new optimizations, new techniques. There’s no reason to think...
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