What is the Difference between a Hash and MAC (Message Authentication code)?
By their definitions they seem to serve the same function.
Can someone explain what the difference is?
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The main difference is conceptual: while hashes are used to guarantee the integrity of data, a MAC guarantees integrity AND authentication.
This means that a hashcode is blindly generated from the message without any kind of external input: what you obtain is something that can be used to check if the message got any alteration during its travel.
A MAC instead uses a private key as the seed to the hash function it uses when generating the code: this should assure the receiver that, not only the message hasn’t been modified, but also who sent it is what we were expecting: otherwise an attacker couldn’t know the private key used to generate the code.
According to wikipedia you have that:
Of course, although their similarities, they are implemented in a different way: usually a MAC generation algorithm is based upon a hash code generation algorithm with the extension that cares about using a private key.