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how to make barcode in c#.net Composites in Software
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Making ISSN  10 In None Using Barcode drawer for Software Control to generate, create ISSN  13 image in Software applications. Scanning Data Matrix In C# Using Barcode reader for .NET Control to read, scan read, scan image in .NET applications. Randomness is a surprising ingredient in the design of fast algorithms for some problems The resulting algorithms are often very simple and output the correct answer with high probability This success probability depends on the random choices made by the algorithm, and holds for every input Instead of devoting a special chapter to this topic, in this book randomized algorithms are interspersed as they arise naturally Only a very elementary knowledge of probability theory is suf cient to follow these algorithms: the de nition of probability, expected value, the expected number of times we must ip a coin before getting heads, and the linearity of expectation Here are pointers to the major such algorithms in this book: one of the earliest and most dramatic examples of a randomized algorithm is the randomized primality test of Figure 18 Hashing is a general randomized data structure that supports inserts, deletes and lookup and is described later in this chapter, in Section 15 Randomized algorithms for sorting and median nding are described in 2 The randomized min cut algorithm is described in the box on page 139 Randomization plays an important role in heuristics as well; these are described in Section 93 And nally quantum mechanics is the source of true randomness, and the quantum algorithm for factoring (Section 107) works with high probability Generating EAN13 In Visual Basic .NET Using Barcode generation for .NET framework Control to generate, create UPC  13 image in .NET framework applications. Generating Code 128 Code Set A In None Using Barcode creator for Office Excel Control to generate, create Code 128A image in Microsoft Excel applications. 14 Cryptography
GS1 128 Generator In None Using Barcode generation for Online Control to generate, create EAN 128 image in Online applications. Making Barcode In None Using Barcode generator for Office Excel Control to generate, create bar code image in Microsoft Excel applications. Our next topic, the RivestShamirAdelman (RSA) cryptosystem, uses all the ideas we have introduced in this chapter! It derives very strong guarantees of security by ingeniously exploiting the wide gulf between the polynomialtime computability of certain numbertheoretic tasks (modular exponentiation, greatest common divisor, primality testing) and the intractability of others (factoring) The typical setting for cryptography can be described via a cast of three characters: Alice and Bob, who wish to communicate in private, and Eve, an eavesdropper who will go to great lengths to nd out what they are saying For concreteness, let s say Alice wants to send a speci c message x, written in binary (why not), to her friend Bob She encodes it as e(x), sends it over, and then Bob applies his decryption function d( ) to decode it: d(e(x)) = x Here e( ) and d( ) are appropriate transformations of the messages Bar Code Encoder In Visual C#.NET Using Barcode generator for VS .NET Control to generate, create bar code image in .NET applications. Bar Code Printer In None Using Barcode creation for Office Word Control to generate, create barcode image in Microsoft Word applications. Alice
Encoder
e(x) Decoder
x = d(e(x)) Alice and Bob are worried that the eavesdropper, Eve, will intercept e(x): for instance, she might be a sniffer on the network But ideally the encryption function e( ) is so chosen that without knowing d( ), Eve cannot do anything with the information she has picked up In other words, knowing e(x) tells her little or nothing about what x might be For centuries, cryptography was based on what we now call privatekey protocols In such a scheme, Alice and Bob meet beforehand and together choose a secret codebook, with which 36 they encrypt all future correspondence between them Eve s only hope, then, is to collect some encoded messages and use them to at least partially gure out the codebook Publickey schemes such as RSA are signi cantly more subtle and tricky: they allow Alice to send Bob a message without ever having met him before This almost sounds impossible, because in this scenario there is a symmetry between Bob and Eve: why should Bob have any advantage over Eve in terms of being able to understand Alice s message The central idea behind the RSA cryptosystem is that using the dramatic contrast between factoring and primality, Bob is able to implement a digital lock, to which only he has the key Now by making this digital lock public, he gives Alice a way to send him a secure message, which only he can open Moreover, this is exactly the scenario that comes up in Internet commerce, for example, when you wish to send your credit card number to some company over the Internet In the RSA protocol, Bob need only perform the simplest of calculations, such as multiplication, to implement his digital lock Similarly Alice and Bob need only perform simple calculations to lock and unlock the message respectively operations that any pocket computing device could handle By contrast, to unlock the message without the key, Eve must perform operations like factoring large numbers, which requires more computational power than would be afforded by the world s most powerful computers combined This compelling guarantee of security explains why the RSA cryptosystem is such a revolutionary development in cryptography

