vb.net code 39 reader Figure 4-16 Pao-Chi s message has his public value first followed by the encrypted bulk data in Software

Create Code 39 Full ASCII in Software Figure 4-16 Pao-Chi s message has his public value first followed by the encrypted bulk data

Figure 4-16 Pao-Chi s message has his public value first followed by the encrypted bulk data
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The Diffie-Hellman algorithm does not encrypt data; instead, it generates a secret. Two parties can generate the same secret and then use it to build a session key for use in a symmetric algorithm. This procedure is called key agreement. Two parties are agreeing on a key to use. Another name found in the literature is key exchange. That description is not as accurate, but some people use it. It means that two parties perform an exchange, the result of which is a shared key. But if Pao-Chi and Gwen can generate the secret, why can t Satomi Satomi knows Gwen s public key and, if she s eavesdropping, Pao-Chi s temporary public key. If she puts those two keys together, what does she have Nothing useful. The secret appears only when combining a public and a private value (each from a different person). Satomi needs one of the private keys not both, just one. A DH public key consists of a generator, a modulus, and public value. The private key is the same modulus along with a private value. As with RSA, cryptographers exercise their creativity to give these numbers more melodious names: g, p, y, and x. The generator is g, the modulus is p, the public value is y, and the private value is x (see Figure 4-17). Here, p is a prime number; note that it s not the product of two or more prime numbers but rather is itself a prime. You generate a key pair by finding the prime p first, then a generator g that works well with your p, and then a random or pseudo-random x. If you combine those numbers using modular exponentiation (see Figure 4-18), you get y. y gx mod p
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We have said that there is a way to break all public-key algorithms. That includes DH. Satomi can break DH by deriving one of the private keys from its public partner. Because Satomi needs only one of the private keys, she ll probably go after Gwen s, which has been out there longer (remember, Pao-Chi generates his temporary private key only when he sends the message). Gwen s public key consists of y, g, and p. All Satomi has to do is find x. In the preceding equation, Satomi knows all the values except one. High school algebra describes this as one equation in one unknown. That s solvable, right Yes, it s solvable. It s known as the discrete log problem (finally, a more interesting name), and computer programs will solve it. But the longer the p, the more time the computer programs will take in fact, the same time as it would take to factor. As it happens, the factoring problem and the discrete log problem are related. It s commonly believed that if you solve one you solve them both. So in use, p should be 1,024 bits long.
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Figure 4-17 A 1,024-bit DH key pair. The number p is the modulus, g is the generator, y is the public value, and x is the private value
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Figure 4-18
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With RSA, you find two 512-bit primes and multiply them to get a 1,024-bit modulus. With DH, you find one 1,024-bit prime and use it as the modulus.
NOTE:
Discrete log doesn t refer to a felled tree that s good at keeping secrets (that would be a discreet log ). The word discrete means that we re working with the math of integers only no fractions or decimal points and the word log is short for logarithm. With RSA, you can t use a single prime as the modulus; you must multiply two primes. But with DH, you use a single prime as the modulus. Why is it that single-prime RSA can be broken but single-prime DH cannot The answer is that the two algorithms do different things. RSA encrypts data, whereas DH performs key agreement. With RSA, you use a value called d that is dependent on (n). With DH, you don t use d, and you don t mess around with (n). So Satomi will need a few million years to break Gwen s private key by going the discrete log route. What about brute force would that work The private key is really just x, a random or pseudo-random number that can be as long as Gwen wants it to be. If she wants it to be 160 bits, she can make it 160 bits. Then Satomi won t be able to mount a brute force attack on it. Gwen could make x even longer, but the longer it is, the longer it will
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