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Unformatted text preview: ity of 240. The x values won’t help Eve either; they were assigned randomly in step (1). In general, Eve has to expend approximately the square of the effort that Alice expends. This n to n2 advantage is small by cryptographic standards, but in some circumstances it may be enough. If Alice and Bob can try ten thousand keys per second, it will take them a minute each to perform their steps and another minute to communicate the puzzles from Bob to Alice on a 1.544 MB link. If Eve had comparable computing facilities, it would take her about a year to break the system. Other algorithms are even harder to break. 2.6 Digital Signatures
Handwritten signatures have long been used as proof of authorship of, or at least agreement with, the contents of a document. What is it about a signature that is so compelling ? 1. The signature is authentic. The signature convinces the document’s recipient that the signer deliberately signed the document. 2. The signature is unforgeable. The signature is proof that the signer, and no one else, deliberately signed the document. 3. The signature is not reusable. The signature is part of the document; an unscrupulous person cannot move the signature to a different document. 4. The signed document is unalterable. After the document is signed, it cannot be altered. 5. The signature cannot be repudiated. The signature and the document are physical things. The signer cannot later claim that he or she didn’t sign it. In reality, none of these statements about signatures is completely true. Signatures can be forged, signatures can be lifted from one piece of paper and moved to another, and documents can be altered after signing. However, we are willing to live with these problems because of the difficulty in cheating and the risk of detection. We would like to do this sort of thing on computers, but there are problems. First, computer files are trivial to copy. Even if a person’s signature were difficult to forge (a graphical image of a written signature,...
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- Fall '10