Unformatted text preview: fie points out [492,494] that this risk is mitigated by two factors: 1. The operations on which public key cryptography currently depends—multiplying, exponentiating, and factoring—are all fundamental arithmetic phenomena. They have been the subject of intense mathematical scrutiny for centuries and the increased attention that has resulted from their use in public key cryptosystems has on balance enhanced rather than diminished our confidence. 2. Our ability to carry out large arithmetic computations has grown steadily and now permits us to implement our systems with numbers sufficient in size to be vulnerable only to a dramatic breakthrough in factoring, logarithms, or root extraction. As we have seen, not all publickey algorithms based on these problems are secure. The strength of any publickey algorithm depends on more than the computational complexity of the problem upon which it is based; a hard problem does not necessarily imply a strong algorithm. Adi Shamir listed three reasons why this is so [1415]: 1. Complexity theory usually deals with single isolated instances of a problem. A cryptanalyst often has a large collection of statistically related problems to solve—several ciphertexts encrypted with the same key. 2. The computational complexity of a problem is typically measured by its worstcase or averagecase behavior. To be useful as a cipher, the problem must be hard to solve in almost all cases. 3. An arbitrarily difficult problem cannot necessarily be transformed into a cryptosystem, and it must be possible to insert trapdoor information into the problem so that a shortcut solution is possible with this information and only with this information. 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...
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 Fall '10
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 Cryptography, Bruce Schneier, Applied Cryptography, EarthWeb, Search Search Tips

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