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Most cryptographic signatures are in fact the hash of the message encrypted with the signer's private asymmetric key. By decrypting the key using the matching public key, the verifier can obtain the original hash, and hence, match that to a locally calculated value of the message's hash.
Suppose that Bob wants to send Alice a private message3, but Bob doesn’t trust the channel used to transmit the message. If it falls in the wrong hands, Bob wants to avoid that the message meant for Alice’s eyes only, can be read by anyone else.I believe this answers your new question well. Regards, Joe
Bob could use an algorithm to encrypt his message, and then Alice would need to use an algorithm to decrypt it. If the same key can be used for encryption as well as decryption (or if the key for decryption can be derived from the key used for encryption), Bob and Alice are using a symmetric key algorithm. The problem with such an algorithm is that Bob and Alice need to exchange that algorithm in a safe way first. Anybody with access to the key can decrypt your message.
To avoid this, Bob and Alice can choose an asymmetric key algorithm. In this case two different keys are used: one key to encrypt, the other one to decrypt the message. One key cannot be derived from the other. Now if Bob wants to send Alice a private message, Alice can send her public key to Bob. Anybody can use this key to encrypt messages meant for Alice. When Bob sends Alice such an encrypted message, Alice will use her private key to decrypt it. Suppose that Chuck intercepts the message, he won’t be able to read it as long as he doesn’t have access to Alice’s private key.
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