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In conventional signature, there is normally a one-to-many relationship between a signature and documents A person, for example, has a signature that is used to sign many checks, many documents, etc In digital signature, there is a one-to-one relationship between a signature and a message Each message has its own signature The signature of one message cannot be used in another message If Bob receives two messages, one after another, from Alice, he cannot use the signature of the first message to verify the second Each message needs a new signature
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Another difference between the two types of signatures is a quality called duplicity In conventional signature, a copy of the signed document can be distinguished from the original one on file In digital signature, there is no such distinction unless there is a factor of time (such as a timestamp) on the document For example, suppose Alice sends a document instructing Bob to pay Eve If Eve intercepts the document and the signature, she can resend it later to get money again from Bob
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In conventional signature a signature is like a private "key" belonging to the signer of the document The signer uses it to sign a document; no one else has this signature The copy of the signature is on file like a public key; anyone can use it to verify a document, to compare it to the original signature In digital signature, the signer uses her private key, applied to a signing algorithm, to sign the document The verifier, on the other hand, uses the public key of the signer, applied to the verifying algorithm, to verify the document Can we use a secret (symmetric) key to both sign and verify a signature The answer is no for several reasons First, a secret key is known only between two entities (Alice and Bob, for example) So if Alice needs to sign another document and send it to Ted, she needs to use another secret key Second, as we will see, creating a secret key for a session involves authentication, which normally uses digital signature We have a vicious cycle Third, Bob could use the secret key between himself and Alice, sign a document, send it to Ted, and pretend that it came from Alice
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A digital signature needs a public-key system
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Digital signature can be achieved in two ways: signing the document or signing a digest of the document
Signing the Document
Probably, the easier, but less efficient way is to sign the document itself Signing a document is encrypting it with the private key of the sender; verifying the document is decrypting it with the public key of the sender Figure 3111 shows how signing and verifying are done
Signing the message itself in digital signature
~ keys Alice
Signed document
Data flow
Plaintext
Plaintext
Encryption
Signing
Decryption
Verifying
We should make a distinction between private and public keys as used in digital signature and public and private keys as used for confidentiality In the latter, the private and public keys of the receiver are used in the process The sender uses the public key of the receiver to encrypt; the receiver uses his own private key to decrypt In digital signature, the private and public keys of the sender are used The sender uses her private key; the receiver uses the public key of the sender
In a cryptosystem, we use the private and public keys of the receiver; in digital signature, we use the private and public key of the sender
Signing the Digest
We mentioned that the public key is very inefficient in a cryptosystem if we are dealing with long messages In a digital signature system, our messages are normally long, but we have to use public keys The solution is not to sign the message itself; instead, we sign a digest of the message As we learned, a carefully selected message digest has a one-to-one relationship with the message The sender can sign the message digest, and the receiver can verify the message digest The effect is the same Figure 3112 shows signing a digest in a digital signature system A digest is made out of the message at Alice's site The digest then goes through the signing process using Alice's private key Alice then sends the message and the signature to Bob As we will see later in the chapter, there are variations in the process that are dependent on the system For example, there might be additional calculations before the digest is made or other secret keys might be used In some systems, the signature is a set of values
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