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continued Reading Code 3 Of 9 In None Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications. Encoding Code39 In None Using Barcode generation for Software Control to generate, create ANSI/AIM Code 39 image in Software applications. 4
ANSI/AIM Code 39 Decoder In None Using Barcode scanner for Software Control to read, scan read, scan image in Software applications. Creating ANSI/AIM Code 39 In C# Using Barcode creator for .NET framework Control to generate, create Code 3/9 image in VS .NET applications. bears his signature. Along with NSAM 160 is the Weisner Memorandum, which includes more details about permissive links. It can be inferred that the authors proposed equipping nuclear arms with cryptographic switches. Bombs could be activated only with the correct codes, with a form of publickey crypto guaranteeing correct codes (two principles referred to as authentication and nonrepudiation; see 5). What about the former Soviet Union or the People s Republic of China Did these nations have publickey algorithms before 1976 Or how about Hungary or Japan or any other government If they did, they re not saying. Code39 Generation In .NET Using Barcode generator for ASP.NET Control to generate, create Code39 image in ASP.NET applications. Encode USS Code 39 In .NET Using Barcode generation for Visual Studio .NET Control to generate, create Code 3 of 9 image in VS .NET applications. Figure 47 In symmetrickey crypto, generally the last thing done in encrypting is the first thing done (in reverse) in decrypting Painting Code 39 Extended In Visual Basic .NET Using Barcode creation for Visual Studio .NET Control to generate, create Code39 image in VS .NET applications. Code 128B Maker In None Using Barcode drawer for Software Control to generate, create ANSI/AIM Code 128 image in Software applications. Encrypt Last step 14 2F 38 86 Rotate right 7 0C 28 5E 71
Code 39 Creator In None Using Barcode generator for Software Control to generate, create Code39 image in Software applications. GS1128 Maker In None Using Barcode generator for Software Control to generate, create EAN 128 image in Software applications. Decrypt 0C 28 5E 71 Rotate left 7 14 2F 38 86 First step
EAN13 Supplement 5 Encoder In None Using Barcode generator for Software Control to generate, create EAN 13 image in Software applications. DataMatrix Creator In None Using Barcode printer for Software Control to generate, create ECC200 image in Software applications. and manipulates them using computer operations, publickey crypto operates on the data as numbers and plays with the numbers (see Figure 48). And the math is oneway: It s easy in one direction but not in the other direction. In fact, the foundation of any good publickey algorithm is a oneway function, the class of math problems on which publickey crypto is built. Actually, publickey oneway functions are more accurately described as oneway with a trap door. To the rest of the world the functions are oneway, but the private key operates as a trap door that allows the owner to recover the original data (see Figure 49). There are true oneway functions, and we talk about some of them in 5. ISBN  10 Printer In None Using Barcode creator for Software Control to generate, create International Standard Book Number image in Software applications. GTIN  128 Printer In Java Using Barcode maker for Android Control to generate, create GTIN  128 image in Android applications. The Key Distribution Problem and PublicKey Cryptography
Data Matrix Maker In .NET Framework Using Barcode generator for Visual Studio .NET Control to generate, create Data Matrix 2d barcode image in VS .NET applications. Barcode Generator In .NET Using Barcode creation for Visual Studio .NET Control to generate, create barcode image in VS .NET applications. Figure 48 Publickey crypto treats all data as numbers and performs mathematical operations on them
Creating EAN 128 In None Using Barcode generator for Word Control to generate, create UCC.EAN  128 image in Office Word applications. EAN 13 Scanner In VB.NET Using Barcode reader for .NET Control to read, scan read, scan image in Visual Studio .NET applications. Four bytes 0x14 0x2F 0x38 0x86 Four letters Goal
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A number 1,198,481,772 Algorithm
A number 1,963,012,242 Algorithm
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ASCII # In this book, we don t describe the full details of the math behind the various algorithms; you can find that in the RSA Labs FAQ on the accompanying CD. But in the following sections we talk about the three most widely used algorithms for solving the key distribution problem: RSA, DH, and ECDH (Elliptic Curve DiffieHellman). We tell you the names of the oneway functions and outline the problems. Figure 49 4
A oneway function with a trap door. Performing operations in one direction is easy, but reversing the steps is difficult unless you know the secret trap door The RSA Algorithm
The RSA algorithm encrypts data. If you feed your plaintext to the algorithm along with the public key, you get ciphertext as a result. With the digital envelope, the plaintext is the session key. It s certainly possible to use RSA to encrypt data other than a session key, but RSA is not as fast as the symmetric algorithms. For example, RC4 (probably the fastest symmetric algorithm in wide use today) will encrypt data at a rate 700 times faster than 1,024bit RSA (1,024 bits is the most commonly used RSA key size). RC5 (one of the fastest block ciphers) is about 500 times faster. NOTE: Incidentally, the R in RC4 and RC5 is the same R as in RSA. So the best way to use RSA is to create a digital envelope. For example, PaoChi can generate a random or pseudorandom 128bit RC4 key, use it to encrypt his email message to Gwen, and then use Gwen s RSA public key to encrypt the RC4 key. Encrypting the RC4 key (16 bytes) will take only a few milliseconds on most platforms. PaoChi s message to Gwen consists of two parts: the encrypted session key and the encrypted bulk data (see Figure 410). Gwen separates the two components, uses her RSA private key to decrypt the session key, and then uses that decrypted RC4 key to decrypt the bulk data. AM FL Y
The Key Distribution Problem and PublicKey Cryptography
Figure 410 In PaoChi s message, the encrypted session key comes first and the encrypted bulk data follows An RSA public key consists of two numbers: a modulus and a public exponent. The private key is made up of the same modulus and a private exponent (see Figure 411). The modulus, incidentally, is the product of two very large prime numbers. (A prime number, or prime, cannot be evenly divided; for example, 3, 5, 7, 13, and 17 are primes.) In the cryptographic literature, these numbers are usually given the romantic names n, e, and d, where n is the modulus, e is the public exponent, and d is the private exponent. Equally poetic are the names for the two primes that make up the modulus: p and q. When you generate an RSA key pair (or rather, when the program you re running generates an RSA key pair), you decide on a public exponent e, find two large primes p and q that work with the e you ve chosen, multiply p and q to get the modulus n, and finally compute your private Figure 411

