vb.net data matrix reader The Uniqueness of a Digital Signature in Software

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The Uniqueness of a Digital Signature
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Suppose Pao-Chi sells four printing presses to Satomi and must now communicate the sale to the home office. He sends a message to Daniel in the shipping office:
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Daniel, I sold 4 presses to Satomi. Ship immediately.
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The Digital Signature
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Pao-Chi can send this e-mail using a digital envelope (see 4), and only Daniel can read it. But how can Daniel know that this message really came from Pao-Chi and not someone posing as him For all Daniel knows, Satomi sent that message, maybe she s trying to get four printing presses shipped to her for free. In the paper world, you can look at the signature on a document. Generally, everyone has a unique way of writing his or her name, a way that is supposed to be hard to forge. If Pao-Chi and Daniel have corresponded by paper in the past, Daniel can probably spot the difference between Pao-Chi s signature and a fake, but with e-mail, there s no such signature. Pao-Chi could encrypt the plaintext (his e-mail) using his RSA private key, producing ciphertext. Daniel could then use Pao-Chi s public key on the ciphertext. If the result of that decryption were gibberish, Daniel would know it was not encrypted using Pao-Chi s private key and would figure Pao-Chi did not send it (see Figure 5-2). Sure, it s possible that the message came from Pao-Chi and that he actually encrypted it using some key other than his private key. But why would he do that What would he accomplish No he s trying to prove to Daniel that he did indeed send the e-mail and that the contents have not been altered along the way. Daniel can safely conclude that Pao-Chi did not send that message.
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Figure 5-2 If Pao-Chi s public key produces gibberish, it means the ciphertext was not encrypted with his private key
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If, on the other hand, using Pao-Chi s public key produces a reasonable message, it must be that his private key was used to encrypt the plaintext. Is it possible that someone other than Pao-Chi produced a chunk of data that looks like ciphertext and, when decrypted with Pao-Chi s public key, produces a reasonable message (see Figure 5-3) As far as we know, no one has yet been able to do that. So we say there is only one way to produce
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Figure 5-3
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(A) Pao-Chi s digital signature is encrypted using his private key and verified by decrypting with his public key. (B) If the plaintext is encrypted using a different key, can the resulting ciphertext be decrypted with Pao-Chi s public key (C) Is it possible to perform some operation on the plaintext, possibly using Pao-Chi s public key as a guide, and produce correct ciphertext
The Digital Signature
the ciphertext: Start with the plaintext, and encrypt it with the private key. Because the message was encrypted using Pao-Chi s private key and because we re assuming that Pao-Chi is the only person with access to his private key, it must have come from him. Because it must have come from him, we can call the ciphertext a digital signature. A signature is a way of vouching for the contents of a message of saying, Yes, I m the one who wrote it. In addition, a digital signature lets you check that the data has not been altered. Digital signatures depend on two fundamental assumptions: first, that the private key is safe and only the owner of the key has access to it, and second, that the only way to produce a digital signature is to use the private key. The first assumption has no technical answer except that keys must be protected (for details, see 3). But the second assumption can be examined from a mathematical point of view. Is it possible to show that a signature is unique Figure 5-3a shows the path that data takes to become a digital signature and to be verified. Is it possible to send data on another path that ends up at the same place An attacker might want to start with the plaintext, encrypt it with a key other than the true private key, and still produce the correct ciphertext (Figure 5-3b). Or maybe the attacker would try to perform some other operation on the plaintext (not regular RSA encryption), possibly using the public key as a guide, and still produce the correct ciphertext (Figure 5-3c). If that were possible, a digital signature would not be unique. If it were not unique, it would not be possible to claim that the owner of the private key is vouching for the plaintext. The best that cryptographers can say is that no one knows of any such successful attack. The literature contains phrases such as computationally infeasible, it is believed to be true, and for some classes of signatures, it is possible to prove certain security properties. But no one has completely proven signature uniqueness for any signature scheme. Researchers have spent countless hours trying to come up with alternative paths to break uniqueness, and no one has yet come close.
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