Suppose a host A communicates with another host B$.$ Host A has its public$/$private key pair $()$; B has its own public$/$private key pair $().$ A certificate authority $($CA$)$ has its public$/$private key pair $().$ A message digest hash function is denoted as $,$ message for transmission is denoted as $.$

If host A sends the message m to host B and wants to ensure authentication and integrity of the message, what is the notation to represent the message$$s $$Digital Signature$?$ What key must host B have in order to verify this digital signature?

What is the notation to represent the $$Digital Certificate$$ for host A$,$ certified by the certificate authority CA$?$ In order for host B to verify this digital certificate, what key must host B have in order to do the verification?