Hybrid signatures

Just like public-key crypto, signing large messages is slow.

We can also hybridize signatures to make them faster:

Alice sends the (unsigned) message, and also a signature on a hash of the message.
The hash is much smaller than the message, and so faster to sign and verify.

Remember that authenticity and secrecy are separate; if you want both, you need to do both.
Generally, sign the message, then encrypt the message plus signature together.