As we know, hash algorithms can be used for authenticity of a message. In my understanding, since the message lengths are too large, we convert it into a hash value using hash algorithms and these hash values will be sent along with the message for authenticity. This is my understanding on why we use hashing algorithms.
But in SHA3-512, if input is 128 bits long then we are getting a hash value of 512 bits.
My question then is that if the message length is small then why are we increasing it's size to 512 bits?