Unformatted text preview: approximately one in ln n. So the total number of primes less than n is n /(ln n). There are only 1077 atoms in the universe. If every atom in the universe needed a billion new primes every microsecond from the beginning of time until now, you would only need 10109 primes; there would still be approximately 10151 512-bit primes left. 2. What if two people accidentally pick the same prime number? It won’t happen. With over 10151 prime numbers to choose from, the odds of that happening are significantly less than the odds of your computer spontaneously combusting at the exact moment you win the lottery. 3. If someone creates a database of all primes, won’t he be able to use that database to break public-key algorithms? Yes, but he can’t do it. If you could store one gigabyte of information on a drive weighing one gram, then a list of just the 512-bit primes would weigh so much that it would exceed the Chandrasekhar limit and collapse into a black hole...so you couldn’t retrieve the data anyway. But if factoring numbers is so hard, how can generating prime numbers be easy? The trick is that the yes/no question, “Is n prime?” is a much easier question to answer than the more complicated question, “What are the factors of n? ” 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)
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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