Assuming that by security you mean confidentiality
To provide Message Integrity and authentication, we can sign the message with sender private key and send message+sign.
However for Nonrepudiation , one has to take help of trusted 3rd party as an assurance that sender cannot deny that the message was sent by him.
Also one can encrypt the message to using the reciever public key to provide confidentiality
following diagram show how we can use encryption with digital signature to provide security , authenticity and data integrity
Regarding Nonrepudiation via trusted center
To provide all these ,sender can perform following steps:
1. Sender compute the message digest using the Hash function ===> for message integrity
2. Sender then encrypt this message digest using its private key===> for message authentication
3. Sender to provide additional security can encrypt the message using the receiver public key ==> confidentiality
4. sender send this encrypted message +digital signature
At Receiver
1. Receiver decrypt the message using its private key
2. compute the message digest or hash B
3. decrypt the digital signature using public key of the sender to get the precomputed hash A
4. match precomputed hash A and computed hash B
5 . if match , data is received correctly