Definition
Hash-and-Sign
Hash-and-sign is the approach of computing a digital signature on the hash of a message rather than on the message itself.
Rationale
Efficiency
A single hash computation (fast) and a single signing operation are required, even for arbitrarily large messages.
Dependence on Every Bit
The signature depends on every bit of the original message because the hash function provides diffusion. Changing a single bit of the message changes the hash unpredictably.
Collision Resistance
Collision resistance ensures that it is infeasible to find another message for which the signature is valid.