Advantages & Disadvantages

Enhanced security and convenience: private keys never require be transmitting or revealing to anyone. 

They can givce a method for digital signatures

 Public-key authentication prevents repudiation; every user has sole responsibility for protecting his or her private key. This property of public-key authentication is often known as non-repudiation. 

A disadvantage of using public-key cryptography for encryption is speed

 For encryption, the best solution is to join public- and secret-key systems.

The public-key system can be used to encrypt a secret key, which is used to encrypt the bulk of a file or message. Like a protocol is known as a digital envelope

 A successful attack on a certification authority will permit an adversary to impersonate whomever the adversary chooses to by using a public-key certificate from the compromised authority to bind a key of the adversary's choice to the name of another user. 

Public-key cryptography is not meant to change secret-key cryptography, but rather to supplement it, to make it more secure.