Public key encryption

[Zuuljin]

Before you give me crap, I'v already been to wikipedia and looked this stuff up, but I still dont understand how it works.

I understand the basics in that I encrypt a message with a public key, and my reciever decrypts it with his private key. My question is, how does his private key know how to decipher my message if neither of us has exchanged the decrypting key?

Say theres 3 people, Bob, Tom, and Steve. Bob encrypts a message with his public key, sends it to Tom, who decryptes it. Steve tries to intercept it, but cant because its encrypted. Now Bob sends Steve an encrypted message, and Steve decrypts it with his private key. Since Bob sent messages to both people, using the same public key, and both recievers got the message, why cant the non-recipient intercept a message and decrypt it with the exact same private key that they just used to decipher the message when it was sent to them? I dont get it.

[Vorph]

It's not the same public key. You use Tom's public key to send messages to Tom, Steve's public key to send to Steve, etc. and you give each of them your public key so that they can reply. That's why you see people on usenet and other places where encryption is used often put their public key in their signature.

[Zuuljin]

Ahhh ok so I had it backwards. I'm not encrypting with my public key, I'm encrypting with their public key, which matches their private key.

Thanks all knowing Vorph. =)

[Slide]

The public key is exactly that, public - you distribute it far and wide and keep your private key secret (and password protected). There's some setup involved, but there are also some companies that have a business in providing a directory of public keys to ease some of it.