Authentication is the process of verifying that a specific person sent a message. This can be accomplished with secret or public key encryption systems.
A secret key system can verify that one of the individuals who know the secret key sent the message, although it cannot necessarily identify which one of those individuals sent the message.
With an asymmetric key system and a digital signature, you know that only the people possessing the key used to create the signature could have sent the message. Since digital signatures are usually created with the senders private key, this tells you that that person was the sender of the message.
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