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vb.net code 39 reader The Key Distribution Problem and PublicKey Cryptography in Software
The Key Distribution Problem and PublicKey Cryptography Code39 Decoder In None Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications. Print Code39 In None Using Barcode encoder for Software Control to generate, create USS Code 39 image in Software applications. Figure 413 In a popular 1,024bit RSA key, the modulus is 1,024 bits, built by multiplying two 512bit primes Read Code39 In None Using Barcode recognizer for Software Control to read, scan read, scan image in Software applications. Code39 Encoder In Visual C#.NET Using Barcode generation for VS .NET Control to generate, create Code 3/9 image in .NET applications. You may wonder why the modulus has to be the product of two primes. Why can t the modulus itself be a prime number The reason is that for a prime number p, (p) is (p 1). Because your modulus is public, if the modulus were p, a prime number, any attacker would be able to find (p); it s simple subtraction. Armed with (p), an attacker can easily find d. Incidentally, Satomi has a couple of brute force opportunities. First, she could try to find d by trying every value it could possibly be. Fortunately, d is a number as big as the modulus. For a 1,024bit RSA private key, d is 1,024 bits long (maybe a bit or two smaller). No, brute force on d is not an option. A second possibility is to find p or q. Satomi could get a number b (call it b for brute force candidate) and then compute n b (n divided by b). If that doesn t work (b does not divide n evenly; there is a remainder), she tries another b. She keeps trying until she finds a b that works (one that divides n evenly). That b will be one of the factors of n. And the answer to n b is the other factor. Satomi would then have p and q. But the factors of n are half the size of the modulus (see Technical Note: MultiPrime RSA ). For a 1,024bit RSA key, p and q are 512 bits each. So Satomi would be trying a brute force attack on a 512bit number, and Code 39 Extended Creator In VS .NET Using Barcode encoder for ASP.NET Control to generate, create Code 39 image in ASP.NET applications. Code39 Generator In .NET Using Barcode drawer for .NET Control to generate, create Code 39 Full ASCII image in Visual Studio .NET applications. 4
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UCC128 Printer In None Using Barcode drawer for Software Control to generate, create EAN128 image in Software applications. Encode EAN13 Supplement 5 In None Using Barcode creator for Software Control to generate, create EAN13 image in Software applications. Faster performance is always a goal of programmers, so anything that would speed up the RSA algorithm would be welcome. The first speed improvement came in 1982 from Belgian researchers JeanJacques Quisquater and C. Couvreur. They showed that it s possible to make private key operations (opening a digital envelope) faster if you keep the p and q around, by using what is known as the Chinese Remainder Theorem (CRT). This theorem dates to the fourth century and originated in, as the name implies, China. It s a result of research into how to count columns and columns of soldiers more quickly. Remember that an RSA private key is made up of the two numbers n and d, where n is built by multiplying two primes, p and q. When you have your d, you throw away p and q. According to the theorem, if you don t throw away your p and q, and if, while generating your key pair, you make a few other calculations and save a few more values, the private key operations you perform can run almost three times faster. The fundamental reason is that p and q are smaller than n (there s more to it than that, but at its foundation, that is the reason). Because p and q must be kept private, this technique will not help public key operations. But, as you ll see in the section Performance, RSA public key operations are already rather fast. Recently, people have been looking into using three or more primes to make up n. Here s why. When you multiply two numbers, if you add the sizes of those two numbers you get the size of the result. For example, if you multiply a 512bit number by a 512bit number, you get a 1,024bit number because 512 512 1,024 (it could end up being 1,023 bits, but let s not quibble). Actually, you could multiply a 612bit number by a 412bit number to get a 1,024bit result, but for security reasons, it s better to have the numbers the same size or very close. Virtually all programs that generate RSA key pairs find two 512bit primes and multiply them to make n. If you want a 1,024bit number as a result of multiplying three smaller numbers, how big should they be One possibility is 341, 341, and 342 bits. If p and q are each 512 bits, and if private key operations are faster because they are smaller than n (which is Code 3 Of 9 Creation In None Using Barcode generation for Software Control to generate, create USS Code 39 image in Software applications. Paint Bar Code In None Using Barcode drawer for Software Control to generate, create bar code image in Software applications. Make OneCode In None Using Barcode encoder for Software Control to generate, create OneCode image in Software applications. Encode Bar Code In ObjectiveC Using Barcode printer for iPhone Control to generate, create bar code image in iPhone applications. Create Bar Code In Java Using Barcode generation for BIRT Control to generate, create bar code image in Eclipse BIRT applications. GTIN  13 Generation In .NET Framework Using Barcode creator for Reporting Service Control to generate, create EAN13 image in Reporting Service applications. Print USS Code 128 In .NET Using Barcode creator for ASP.NET Control to generate, create Code 128C image in ASP.NET applications. EAN13 Encoder In None Using Barcode encoder for Word Control to generate, create GTIN  13 image in Office Word applications. UPCA Supplement 2 Creator In ObjectiveC Using Barcode creation for iPad Control to generate, create GTIN  12 image in iPad applications. Code128 Drawer In ObjectiveC Using Barcode maker for iPad Control to generate, create Code 128 image in iPad applications. 
