# Why do digital signatures use a hash algorithm instead of a checksum?

Based on my knowledge, all digital signature algorithms use a hash function to sign a message, and then encrypt the hash result. So why do these algorithms not use a checksum instead of a hash algorithm? By the end, both are going to encrypted, correct? A checksum is faster than a hash algorithm.

• The underlying hash-function must not have any collisions. Otherwise, two documents $M$ and $M'$ with $H(M)=H(M')$ would have the same signature. Apr 1 '18 at 17:11
• "Based on my knowledge all digital signature algorithms use a hash function to sign a message, and then encrypt the hash result."; actually, only RSA and Rabin-Williams can really be described that way (and even in those cases, it's not precisely accurate). Other signature algorithms work differently; generating a hard to duplicate/easy to verify relation between the signature, message and public key Apr 1 '18 at 20:07