In the context of cryptography, authentication means "ensuring that the message you got comes from who you think it did".
Authentication is one of the hardest parts of cryptography, because the only truly secure way to do it is by driving to the other party yourself to establish a pre-shared key so you can do message authentication code. Or to share your public key with them if you are satisfied with the safety of post-quantum cryptography.
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A Man-in-the-Middle (MitM) attack is a type of cyberattack where an attacker intercepts communication between two parties without their knowledge. The attacker secretly relays and possibly alters the communication between the two parties, who believe they are directly communicating with each other. This type of attack allows the hacker to eavesdrop on the conversation, collect sensitive information, or manipulate the data being transmitted.