What are the advantages and disadvantages of public key cryptography?

Advantages and Disadvantages:

Improved security and convenience: private keys never require be transmitting or revealing to anyone.
They can give a method for digital signatures

Public-key authentication protects repudiation; all users have sole responsibility for protecting his or her private key. Such property of public-key authentication is frequently termed as non-repudiation.

A drawback of using public-key cryptography for encryption is speed. The best solution for encryption is to merge public and secret-key systems.

The public-key system can be utilized to encrypt a secret key that is used to encrypt the bulk of message or a file. Such a protocol is termed as a digital envelope. A successful attack upon a certification authority will permit an adversary to impersonate whomever the adversary decides to by using a public-key certificate through the compromised authority to bind a key of the adversary's pick to the name of other user. Public-key cryptography is not implies as replace secret-key cryptography, although rather to supplement this, to make this more secure.