What is the minimum number of keys necessary when utilizing public key cryptography?

How few keys are required for minimally secure implementation of public-key cryptography?

How many keys are needed to use cryptography with a shared secret key?

Public key cryptography has a number of strengths and weaknesses relative to symmetric key cryptography Please make two lists: strengths and weaknesses. In the first list (strengths) put all the things that public key does better than symmetric key (generally speaking). Include things that are not possible at all with symmetric key cryptography. In the second list (weaknesses) give some areas or respects in which public key algorithms are less advantageous than symmetric key methods.