Download CRC Press - Handbook of Applied Cryptography by A. Menezes, P. VanOorschot, S. Vanstone PDF

By A. Menezes, P. VanOorschot, S. Vanstone

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53 Remark (key sizes: symmetric key vs. , factoring) more efficient than exhaustive search. , by a factor of 10 or more. It is, of course, arguable that some public-key schemes which are based on hard mathematical problems have a long history since these problems have been studied for many years. Although this may be true, one must be wary that the mathematics was not studied with this application in mind. c 1997 by CRC Press, Inc. — See accompanying notice at front of chapter. 9 Hash functions One of the fundamental primitives in modern cryptography is the cryptographic hash function, often informally called a one-way hash function.

58 Definition A protocol failure or mechanism failure occurs when a mechanism fails to meet the goals for which it was intended, in a manner whereby an adversary gains advantage not by breaking an underlying primitive such as an encryption algorithm directly, but by manipulating the protocol or mechanism itself. 59 Example (mechanism failure) Alice and Bob are communicating using a stream cipher. Messages which they encrypt are known to have a special form: the first twenty bits carry information which represents a monetary amount.

In this case has forged a signature of . This is an example of what is called existential forgery. ) If contains only a negligible fraction of messages from , then the probability of some entity forging a signature of in this manner is negligibly small. 52 Remark (digital signatures vs. confidentiality) Although digital signature schemes based on reversible public-key encryption are attractive, they require an encryption method as a primitive. There are situations where a digital signature mechanism is required but encryption is forbidden.

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