Why public key cryptography?
The problem with conventional symmetric cryptography is that the two parties must have a method of exchanging a key. If the key is intercepted by an enemy party, a credit card thief for example, the whole transacting is compromised. If electronic commerce had to depend completely on symmetrical encryption, it would be impractical to secure anything, especially in a way that was transparent to the end user. Each electronic exchange of encrypted material would require a corresponding secure key exchange, meaning not through any method where the key could potentially be intercepted. The necessity of this key exchange which would eliminate any convenience gained from the use of an electronic information exchange in the first place. The solution to this problem is public key cryptography.