Associated to a secure connexion between the Host A and the host B$,$ define mathematically the two concepts specified below in terms of the following variables

pukA: public key of the host A

prkA: private key of the host A

pukB: public key of the host B

prkB: private key of the host B

pukCA: public key of the certification authority CA

prkCA: private key of the certification authority CA

m: message m

H$($m$)$: sha$1$ digest of the message m

$1.-$ Digital signature of the message m sent by the host A to the host B$.$

ds$($m$,$ A$)=$

$2.-$ Digital certificate of the host A requested by the host B to the Certification Authority CA$.$

dc$($A$)=$